We have recently proposed and developed a multiobjective approach to training classification systems. In this approach, the objectives, i.e., the sensitivity and specificity, of a classifier are simultaneously optimized, resulting in a series of solutions that are equivalent in the absence of any a priori knowledge regarding the relative merits of the two objectives. These solutions form a receiver operating characteristic (ROC) curve that is, theoretically, the best possible ROC curve that can be obtained using the given classifier and given training dataset. We have applied this technique to the optimization of classifiers for the computerized detection of mass lesions in digitized mammograms. Comparisons will be made between the results obtained using the multiobjective approach and results obtained using more conventional approaches. We employed a database of 60 consecutive, non-palpable mass lesion cases. Features relating to the geometry, intensity, and gradients of the images were calculated for each visible lesion and for many false detections. Using a conventionally trained linear classifier we were able to achieve an A_z of 0.84 while the multiobjective approach to training a linear classifier yielded an A_z of 0.87 in the task of distinguishing between true lesions and false detections. Using a multiobjective approach to train a rule-based classifier with 5 thresholding rules resulted in an A_z of 0.88 in the task of distinguishing between true lesions and false detections.

A constraint satisfaction neural network (CSNN) has been developed for breast cancer diagnosis from mammographic and clinical findings. CSNN is a circuit network aiming to maximize the activation of its nodes given the constraints existing among them. The constraints are built into the network weights. An autoassociative backpropagation (auto-BP) learning scheme is initially used to determine the CSNN weights. During the training phase, the auto-BP learns to map any given pattern to itself. During the testing phase, the CSNN is applied to new cases. The CSNN weights remain fixed (as determined by auto-BP) but the activation levels of the nodes are modified iteratively to optimize a goodness function. The medical findings act as the external inputs to the corresponding nodes. For every test case, CSNN tries to reconstruct the diagnosis nodes given the network constraints and the external inputs to the network. The activation levels achieved by the target nodes are used as decision variables for further analysis. Our CSNN was successfully applied on 500 patients with biopsy confirmed diagnosis. The CSNN was also used as an associative memory simulating dynamic scenarios for prototype analysis in our database.

We propose a method for detection of masses in mammographic images that employs pyramidal or hierarchical decomposition and Gaussian filtering operations as pre-processing steps. A procedure is then developed to segment the mass portions by establishing gradual intensity links from the central portions of masses into the surrounding areas in the image. The proposed mass detection algorithm was tested with 39 cases (28 benign and 11 malignant) selected from the Mammographic Image Analysis Society database. The technique achieved a success rate of 91% in detecting the malignant tumors and 68% in detecting the benign masses in the test set. The segmented mass portions were evaluated in terms of their benign versus malignant discriminant capabilities by computing two gradient- based features and texture features based on gray-level co- occurrence matrices (GCMs). The features were computed using a ribbon of pixels across the mass boundaries. The GCM-based texture features in combination with the gradient-based features resulted in the best benign versus malignant classification of the mass regions segmented by the proposed algorithm, with an area of 0.84 under the receiver operating characteristics curve.

Mammography is recognized as an important means to reduce breast cancer mortality. However, its accuracy is limited, both in sensitivity (some cancers are missed) and specificity (many non-cancer cases are referred for invasive procedures). It has been shown that computer classification of expert radiologist's findings can improve the specificity of mammography. Our project is aimed at automatically extracting measurements by computer analysis of digital mammograms, so as to provide automatic inputs for a benign/malignant classifier. We tested classification of radiological findings and found an area under the ROC curve of 0.95, comparable to what has been reported in the literature. Image measurements were taken from manual segmentations of lesions as well as from two different automatic segmentations. We found that segmentation using a fuzzy clustering method with some post-processing gives results comparable to results on manual outlines with a positive predictive value of 73%. The fuzzy clustering strategy has the potential to provide fully automatic classifications comparable to those based on expert radiological findings. This approach may dramatically reduce the false alarm rate currently seen in screening mammography.

The General Regression Neural Network (GRNN) is well known to be an extremely effective prediction model in a wide variety of problems. It has been recently established that in many prediction problems, the results obtained by intelligently combining the outputs of several different prediction models are generally superior to the results obtained by using any one of the models. An overseer model that combines predictions from other independently trained prediction models is often called an oracle. This paper describes how the GRNN is modified to serve as a powerful oracle for combining decisions from four different breast cancer benign/malignant prediction models using mammogram data. Specifically, the GRNN oracle combines decisions from an evolutionary programming derived neural network, a probabilistic neural network, a fully- interconnected three-layer, feed-forward, error backpropagation network, and a linear discriminant analysis model. In all experiments conducted, the oracle consistently provided superior benign/malignant classification discrimination as measured by the receiver operator characteristic curve Az index values.

We are developing a computerized approach to characterize pulmonary nodules through quantitative analysis between sequential 3-D thoracic images. In this approach the registration procedure of sequential 3-D pulmonary images consisted of two transformation steps: the rigid transformation step between two sequential 3-D thoracic CT images and the affine transformation step between two sequential region-of-interest (ROI) images including the pulmonary nodule. In both transformation step, the normalized mutual information was used as a voxel-based similarity measure. After the registration procedure, the 3-D pulmonary nodule image was segmented from the ROI image by a deformable surface method. The curvatures of each voxel in the nodule were computed directly from the gray-level 3-D image. Through curvatures a local description of the lesion was obtained by using shape index, curvedness, and CT value. Based on this local description of the nodule, the evolution of geometrical parameters was tracked through the time interval. Additionally, to characterize globally the evolution of the local description, the shape and the curvedness spectra were introduced. The interval changes of the lesion were traced in the feature spaces. The application results of our method to the sequence of 3-D thoracic images demonstrated that the interval changes of pulmonary nodules could be made visible.

We have developed a novel method called local contralateral subtraction for reduction of false positives reported by a computer-aided diagnosis (CAD) scheme for detection of lung nodules in chest radiographs. Our method is based on the removal of normal structures in the regions of interest (ROIs), based on symmetry between the left and right lungs. In our method, two ROIs were extracted, one from the position where a candidate of a nodule is located, and the other from the anatomically corresponding location in the opposite lung, which contains similar normal structures. We employed a wavelet-based multiresolution image registration method to match the two ROIs, and subtraction was performed. A signal- to-noise ratio (SNR) between a central region and the adjacent background region was calculated for quantification of the remaining structures in the subtracted ROI. The SNR was then used for distinction between nodules and false positives. In an analysis of 550 ROIs consisting of 51 nodules and 499 false positives reported as detected nodules by our current CAD scheme, we were able to eliminate 44% of false positives with loss of only one nodule with this new method. This result indicates that our new method is effective in reducing false positives due to normal anatomic structures, and thus can improve the performance of our CAD scheme for detection of pulmonary nodules in chest radiographs.

We are developing an automated method to analyze the three- dimensional nature of structures within CT scans and identify those structures that represent lung nodules. The set of segmented lung regions from all sections of a CT scan forms a segmented lung volume within which multiple gray-level thresholds are applied. Contiguous three-dimensional structures are identified within each thresholded lung volume, and structures that satisfy a volume criterion constitute an initial set of nodule candidates. A feature vector is then computed for each nodule candidate. A rule-based scheme is applied to the initial candidate set to reduce the number of nodule candidates that correspond to normal anatomy. Feature vectors for the remaining candidates are merged through an automated classifier to further distinguish between candidates that correspond to nodules and candidates that correspond to normal structures. This automated method demonstrates promising performance in its ability to detect lung nodules in CT images. Such a technique may assist radiologists evaluate, for example, images from low-dose, screening thoracic CT examinations.

The development of computer assisted diagnosis systems for image-patterns is still in the early stages compared to the powerful image and object recognition capabilities of the human eye and visual cortex. Rules have to be defined and features have to be found manually in digital images to come to an automatic classification. The extraction of discriminating features is especially in medical applications a very time consuming process. The quality of the defined features influences directly the classification success. Artificial neural networks are in principle able to solve complex recognition and classification tasks, but their computational expenses restrict their use to small images. A new improved image object classification scheme consists of neural networks as feature extractors and common statistical discrimination algorithms. Applied to the recognition of different types of tumor nuclei images this system is able to find differences which are barely discernible by human eyes.

After Cataract surgery where a plastic implant lens is implanted into the eye to replace the natural lens, many patients suffer from cell growth across a membrane situated at the back of the lens which degrades their vision. The cell growth is known as Posterior Capsule Opacification (or PCO). It is important to be able to quantify PCO so that the effect of different implant lens types and surgical techniques may be evaluated. Initial results obtained using a neural network to detect PCO from implant lenses are compared to an established but less automated method of detection, which segments the images using texture segmentation in conjunction with co- occurrence matrices. Tests show that the established method performs well in clinical validation and repeatability trials. The requirement to use a neural network to analyze the implant lens images evolved from the analysis of over 1000 images using the established co-occurrence matrix segmentation method. The work shows that a method based on neural networks is a promising tool to automate the procedure of calculating PCO.

We evaluated the practical application of a Computer-Aided Diagnosis (CAD) system for viewing spiral computed tomography (CT) of the chest low-dose screening examinations which includes an automatic detection of pulmonary nodules. A UNIX- based CAD system was developed including a detection algorithm for pulmonary nodules and a user interface providing an original axial image, the same image with nodules highlighted, a thin-slab MIP, and a cine mode. As yet, 26 CT examinations with 1625 images were reviewed in a clinical setting and reported by an experienced radiologist using both the CAD system and hardcopies. The CT studies exhibited 19 nodules found on the hardcopies in consensus reporting of 2 experienced radiologists. Viewing with the CAD system was more time consuming than using hardcopies (4.16 vs. 2.92 min) due to analyzing MIP and cine mode. The algorithm detected 49% (18/37) pulmonary nodules larger than 5 mm and 30% (21/70) of all nodules. It produced an average of 6.3 false positive findings per CT study. Most of the missed nodules were adjacent to the pleura. However, the program detected 6 nodules missed by the radiologists. Automatic nodule detection increases the radiologists's awareness of pulmonary lesions. Simultaneous display of axial image and thin-slab MIP makes the radiologist more confident in diagnosis of smaller pulmonary nodules. The CAD system improves the detection of pulmonary nodules at spiral CT. Lack of sensitivity and specificity is still an issue to be addressed but does not prevent practical use.

As a strategic move toward improving the utility of computer- aided diagnosis (CAD) in breast cancer detection, this work aims to develop a computer-based decision support system, through a visual mapping of featured database, to explain the entire decision making process jointly by the computer-encoded knowledge and the user-interaction. The main purpose of the work is twofold: enhance the clinical utility of CAD and provide a mechanism for optimal system design. We adopt a mathematical feature extraction procedure to construct the featured database from the suspicious mass sites localized by the enhanced segmentation. The optimal mapping of the data points is then obtained by learning a hierarchical normal mixtures and associated decision boundaries. A visual explanation of the decision making is further invented through a multivariate data mining and knowledge discovery scheme. In particular, using multiple finite normal mixture models and hierarchical visualization spaces, new strategy is that the top-level model and projection should explain the entire data set, best revealing the presence of clusters and relationships, while lower-level models and projections should display internal structure within individual clusters, such as the presence of subclusters, which might not be apparent in the higher-level models and projections. We demonstrate the principle of the approach on several multimodal numerical data sets, and we then apply the method to the visual explanation in CAD for breast cancer detection from digital mammograms.

We previously developed a computerized method to classify mammographic masses as benign or malignant. In this method, mammographic features that are similar to the ones used by radiologists are automatically extracted to characterize a mass lesion. These features are then merged by an artificial neural network (ANN), which yields an estimated likelihood of malignancy for each mass. The performance of the method was evaluated on an independent database consisting of 110 cases (60 benign and 50 malignant cases). The method achieved an A_z of 0.91 from round-robin analysis in the task of differentiating between benign and malignant masses using the computer-extracted features only. As the most important clinical risk factor for breast cancer, age achieved a performance level (A_z equals 0.79) similar to that (A_z equals 0.77 and 0.80) of the computer-extracted spiculation features, which are the most important indicators for malignancy of a mass, in differentiating between the malignant and benign cases. In this study, age is included as an additional input feature to the ANN. The performance of the scheme (A_z equals 0.93) is improved when age is included. However, the improvement is not found to be statistically significant. Our results indicated that age may be a strong feature in predicting malignancy of a mass. For this database, however, the inclusion of age may not have a strong impact on the determination of the likelihood for a mammographic mass lesion when the major mammographic characteristics (e.g., spiculation) of a mass are accurately extracted and analyzed along with other features using an artificial neural network.

An evolutionary programming (EP) technique was investigated to reduce the complexity of artificial neural network (ANN) models that predict the outcome of mammography-induced breast biopsy. By combining input variables consisting of mammography lesion descriptors and patient history data, the ANN predicted whether the lesion was benign or malignant, which may aide in reducing the number of unnecessary benign biopsies and thus the cost of mammography screening of breast cancer. The EP has the ability to optimize the ANN both structurally and parametrically. An EP was partially optimized using a data set of 882 biopsy-proven cases from Duke University Medical Center. Although many different architectures were evolved, the best were often perceptrons with no hidden nodes. A rank ordering of the inputs was performed using twenty independent EP runs. This confirmed the predictive value of the mass margin and patient age variables, and revealed the unexpected usefulness of the history of previous breast cancer. Further work is required to improve the performance of the EP over all cases in general and calcification cases in particular.

Design of a generalized technique for medical image segmentation is a challenging task. Currently a number of approaches are being investigated for 2-D and 3-D medical image segmentation for diagnostic and research applications. The methodology used in this work is aimed at obtaining a generalized solution of non-convex optimization problems by including a structural constraint of mass or density and the concept of additivity properties of entropy to a recently developed statistical approach to clustering and classification. The original computationally intensive procedure is made more efficient both in processing time and accuracy by employing a new similarity parameter for generating the initial clusters that are updated by minimizing an energy function relating the image entropy and expected distortion. The application of the computationally intensive yet generalized solution to nonconvex optimization to a limited set of medical images has resulted in excellent segmentation when compared to other clustering based segmentation approaches. The addition of the parametric approach to determine the initial number of clusters allows significant reduction in processing time and better design of automated segmentation procedure. This research work generalizes a deterministic annealing i.e. a specific statistical approach to solve nonconvex optimization problems by developing a more efficient technique applicable to nonconvex optimization problems (getting trapped in local minima). However, the DA approach is extremely computationally intensive for applications such as image segmentation. The new integrated approach developed in this work allows this optimization technique to be used for medical image segmentation.

The National Library of Medicine has archived a collection of 17,000 digitized x-rays of the cervical and lumbar spines. Extensive health information has been collected on the subjects of these x-rays, but no information has been derived from the image contents themselves. We are researching algorithms to segment anatomy in these images and to derive from the segmented data measurements useful for indexing this image set for characteristics important to researchers in rheumatology, bone morphometry, and related areas. Active Shape Modeling is currently being investigated for use in location and boundary definition for the vertebrae in these images.

Thresholding is a popular image segmentation method that converts a gray level image into a binary image. The selection of optimum thresholds has remained a challenge over decades. Besides being a segmentation tool on its own, often it is also a step in many advanced image segmentation techniques in spaces other than the image space. Most of the thresholding methods reported to date are based on histogram analysis using information-theoretic approaches. These methods have not harnessed the information buried in image morphology. Here, we introduce a novel thresholding method that accounts for both intensity-based class uncertainty -- a histogram-based property -- and region homogeneity -- an image morphology- based property. The idea here is to select the optimum threshold at which pixels with high class uncertainty accumulate mostly around object boundaries. To achieve this, a new threshold energy criterion is formulated using class- uncertainty and region homogeneity such that, at any image location, a high energy is created when both class uncertainty and region homogeneity are high or both are low. Finally, the method selects that threshold which corresponds to the minimum overall energy. Qualitative experiments based on both phantoms and clinical images show significant improvements using the proposed method over a recently-published maximum segmented image information (MSII) method. Quantitative analysis on phantoms generated under a range of conditions of blurring, noise, and background variation confirm the superiority of the new method.

Many medical imaging modalities produce spatial or temporal stacks of image data. Segmentation of such image stacks has many applications ranging from quantitative measurements to surgical and radiation treatment planning. The key idea presented in this paper is that of propagating information serially from one slice to the next within an interactive framework. Since information on adjacent slices is very similar, segmentation on one slice can be propagated with slight modification to adjacent slices. The segmentation algorithms that we have developed within this framework are all based on energy minimization principles with an additional constraint that the segmentation on a given image slice is similar to the segmentation predicted from the previous image slice. An optical flow approach is used to predict segmentation from one slice to the next. Three types of algorithms have been developed within the above paradigm for different applications --(1) A Mumford and Shah energy- minimizing algorithm combining edge and region information in a region-growing framework, (2) an active contour model-based tracking method, and (3) an algorithm based on pixel classification and Markov random fields. We recognize the fact that interactivity is very important in medical image segmentation. Therefore, our segmentation tools are available in a Java-based graphical user interface (GUI), allowing users to initialize various segmentation algorithms or to edit the results of automatic segmentation, if desired.

The purpose of this work was to develop an automated method for segmenting pediatric kidneys in contrast-enhanced helical CT images and measuring the volume of the renal parenchyma. An automated system was developed to segment the abdomen, spine, aorta and kidneys. The expected size, shape, topology an X-ray attenuation of anatomical structures are stored as features in an anatomical model. These features guide 3-D threshold-based segmentation and then matching of extracted image regions to anatomical structures in the model. Following segmentation, the kidney volumes are calculated by summing included voxels. To validate the system, the kidney volumes of 4 swine were calculated using our approach and compared to the 'true' volumes measured after harvesting the kidneys. Automated volume calculations were also performed retrospectively in a cohort of 10 children. The mean difference between the calculated and measured values in the swine kidneys was 1.38 (S.D. plus or minus 0.44) cc. For the pediatric cases, calculated volumes ranged from 41.7 - 252.1 cc/kidney, and the mean ratio of right to left kidney volume was 0.96 (S.D. plus or minus 0.07). These results demonstrate the accuracy of the volumetric technique that may in the future provide an objective assessment of renal damage.

Image segmentation techniques using fuzzy connectedness principles have shown their effectiveness in segmenting a variety of objects in several large applications in recent years. However, one problem with these algorithms has been their excessive computational requirements. In an attempt to substantially speed them up, in the present paper, we study systematically a host of 18 algorithms under two categories -- label correcting and label setting. Extensive testing of these algorithms on a variety of 3D medical images taken from large ongoing applications demonstrates that a 20 - 360 fold improvement over current speeds is achievable with a combination of algorithms and fast modern PCs. The reliable recognition (assisted by human operators) and the accurate, efficient, and sophisticated delineation (automatically performed by the computer) can be effectively incorporated into a single interactive process. If images having intensities with tissue specific meaning (such as CT or standardized MR images) are utilized, all parameters for the segmentation method can be fixed once for all, all intermediate data can be computed before the user interaction is needed, and the user can be provided with more information at the time of interaction.

Active Appearance Models (AAM), which have been recently introduced by Cootes et al., describe the shape of objects and gray level appearance from a set of example images. An AAM is created from user-placed contours defining the shape of objects of interest in each training image. The information about shape changes observed in the training set is used to model the shape variation. Principle component analysis (PCA) is utilized to model gray level variation observed in the training set. The resulting model describes objects as a linear combination of eigen vectors both in shape and gray levels applied to the mean image. The main purpose of this work is to investigate the clinical potential of AAMs for segmentation of cardiovascular MR images acquired in routine clinical practice. An AAM was constructed using 102 end- diastolic short-axis cardiac MR images at the papillary muscle level from normals and patients with varying pathologies. The resulting AAM is a compact representation consisting of a mean image and a limited number of coefficients of eigen vectors, representing 97% of shape and gray level variation observed in the training set. The segmentation performance is tested in 60 end-diastolic short-axis cardiac MR images from different patients.

The 3-D regions obtained as a result of a volume image segmentation often need to be geometrically modeled and rendered. In this paper, use of rational Gaussian (RaG) surfaces in modeling and rendering 3-D regions is described. A new parametrization technique is introduced that morphs a sphere in a coarse-to-fine fashion to a 3-D region. Knowing parameters of points on the sphere, parameters of voxels on the region are determined. Having the parameters of the voxels, a RaG surface is then fitted to the voxels to obtain a smooth representation for the region. Examples of the proposed representation on various 3-D regions are presented.

To facilitate hepatic surgical planning, we have developed a new system for the automatic 3D delineation of anatomical and pathological hepatic structures from a spiral CT scan. This system also extracts functional information useful for surgery planning, such as portal vein labeling and anatomical segment delineation following the conventional Couinaud definition. From a 2 mm thick enhanced spiral CT scan, a first stage automatically delineates the skin, bones, lungs and kidneys, by combining the use of thresholding, mathematical morphological methods and distance maps. Next, a reference 3D model is immerged in the image and automatically deformed to the liver contour. Then an automatic Gaussians fitting on the imaging histogram allows to threshold the intensities of parenchyma, vessels and lesions. The next stage improves this first classification by an original topological and geometrical analysis, providing an automatic and precise delineation of lesions and veins. Finally, a topological and geometrical analysis based on medical knowledge provides the hepatic functional information invisible in medical imaging: portal vein labeling and hepatic anatomical segments. Clinical validation performed on more than 30 patients shows that this method allows a delineation of anatomical structures, often more sensitive and more specific than manual delineation by a radiologist.

Identification of anatomical structure boundaries in radiographs is a necessary step for detecting abnormalities. The aim of this study is to develop a knowledge-based approach to automatically segment the interested structure boundaries in X-ray images. Our method contains four main steps. First, the original gray-level radiograph is segmented into a binary image. Second, the region of interest (ROI) is detected by matching the features extracted from the binary image with a pre-defined anatomical model, and the location of ROI will serve as the landmark for the following search. Third, an anatomical model will be hierarchically applied to the original image. Correlation values and anatomical constraints will be applied to choose the closer match edge candidates. According to the shape of the global model, the best match edge candidates will be selected and connected to generate the boundaries of the interested structure. Finally, active contour model is used to refine the boundaries. The results show the effectiveness and the efficiency of this proposed method.

Medical images provide experienced physicians with meaningful visual stimuli but their features are frequently hard to decipher. The development of a computational model to mimic physicians' expertise is a demanding task, especially if a significant and sophisticated preprocessing of images is required. Learning from well-expertised images may be a more convenient approach, inasmuch a large and representative bunch of samples is available. A four-stage approach has been designed, which combines image sub-sampling with unsupervised image coding, supervised classification and image reconstruction in order to directly extract medical expertise from raw images. The system has been applied (1) to the detection of some features related to the diagnosis of black tumors of skin (a classification issue) and (2) to the detection of virus-infected and healthy areas in retina angiography in order to locate precisely the border between them and characterize the evolution of infection. For reasonably balanced training sets, we are able to obtained about 90% correct classification of features (black tumors). Boundaries generated by our system mimic reproducibility of hand-outlines drawn by experts (segmentation of virus-infected area).

We propose a segmentation method different from active contours, which can cope with incomplete edges. The algorithm has been developed to segment heart cavities, but may be extended to more complex object shapes. Due to the almost convex geometry of heart cavities we are using a polar coordinate system with its origin near the cavity's center. The image is scanned from the origin for potential edge points. In order to assess the likelihood of an edge point to belong to the myocardial wall, region based information, such as visibility and local wall thickness, is included. The local information (edge points) progressively is expanded by first grouping the edge points to line segments and then selecting a subgroup of segments to obtain the final closed contour. This is done by means of minimizing a cost function. The plausibility of the result is checked and, if needed, the contour is corrected and/or refined by searching for additional potential edge points. For multidimensional images the algorithm is applied slice-by-slice without the need of further user interaction. The new segmentation method has been applied to clinical ultrasound images, the result being that the myocardial wall correctly was detected in the vast majority of cases.

In this paper an image-based method founded on mathematical morphology is presented in order to facilitate the segmentation of cerebral structures on 3D magnetic resonance images (MRIs). The segmentation is described as an immersion simulation, applied to the modified gradient image, modeled by a generated 3D region adjacency graph (RAG). The segmentation relies on two main processes: homotopy modification and contour decision. The first one is achieved by a marker extraction stage where homogeneous 3D regions are identified in order to attribute an influence zone only to relevant minima of the image. This stage uses contrasted regions from morphological reconstruction and labeled flat regions constrained by the RAG. The goal of the decision stage is to precisely locate the contours of regions detected by the marker extraction. This decision is performed by a 3D extension of the watershed transform. Upon completion of the segmentation, the outcome of the preceding process is presented to the user for manual selection of the structures of interest (SOI). Results of this approach are described and illustrated with examples of segmented 3D MRIs of the human head.

Derived from a model based segmentation algorithm for hand radiographs proposed in our former work we now present a method to determine skeletal maturity by an automated analysis of regions of interest (ROI). These ROIs including the epiphyseal and carpal bones, which are most important for skeletal maturity determination, can be extracted out of the radiograph by knowledge based algorithms.

The purpose of individual 3D region-of-interest atlas extraction is to automatically define anatomically meaningful regions in 3D MRI images for quantification of functional parameters (PET, SPECT: rMRGlu, rCBF). The first step of atlas extraction is to automatically classify brain tissue types into gray matter (GM), white matter (WM), cerebrospinal fluid (CSF), scalp/bone (SB) and background (BG). A feed-forward neural network with back-propagation training algorithm is used and compared to other numerical classifiers. It can be trained by a sample from the individual patient data set in question. Classification is done by a 'winner takes all' decision. Automatic extraction of a user-specified number of training points is done in a cross-sectional slice. Background separation is done by simple region growing. The most homogeneous voxels define the region for WM training point extraction (TPE). Non-white-matter and nonbackground regions are analyzed for GM and CSF training points. For SB TPE, the distance from the BG region is one feature. For each class, spatially uniformly distributed training points are extracted by a random generator from these regions. Simulated and real 3D MRI images are analyzed and error rates for TPE and classification calculated. The resulting class images can be analyzed for extraction of anatomical ROIs.

After neural network-based classification of tissue types, the second step of atlas extraction is knowledge-based class image analysis to get anatomically meaningful objects. Basic algorithms are region growing, mathematical morphology operations, and template matching. A special algorithm was designed for each object. The class label of each voxel and the knowledge about the relative position of anatomical objects to each other and to the sagittal midplane of the brain can be utilized for object extraction. User interaction is only necessary to define starting, mid- and end planes for most object extractions and to determine the number of iterations for erosion and dilation operations. Extraction can be done for the following anatomical brain regions: cerebrum; cerebral hemispheres; cerebellum; brain stem; white matter (e.g., centrum semiovale); gray matter [cortex, frontal, parietal, occipital, temporal lobes, cingulum, insula, basal ganglia (nuclei caudati, putamen, thalami)]. For atlas- based quantification of functional data, anatomical objects can be convoluted with the point spread function of functional data to take into account the different resolutions of morphological and functional modalities. This method allows individual atlas extraction from MRI image data of a patient without the need of warping individual data to an anatomical or statistical MRI brain atlas.

To allow a more objective interpretation of 3D carotid bifurcation images, we have implemented and evaluated on patient data, automated volume registration of 3D magnetic resonance angiography (MRA), 3D power Doppler (PD) ultrasound, and 3D B-mode ultrasound. Our algorithm maximizes the mutual information between the thresholded intensities of the MRA and PD images. The B-mode images, acquired simultaneously in the same orientation as PD, are registered to the MRA using the transformation obtained from the MRA-PD registration. To test the algorithm we misaligned clinical ultrasound images and simulated mismatches between the datasets due to different appearances of diseased vessels by removing 3D sections of voxels from each of the paired scans. All registrations were assessed visually using integrated 3D volume, surface, and 2D slice display. 97% of images misaligned within a range of 40 degrees and 40 pixels were correctly registered. The deviation from the mean registration parameters due to the simulated defects was 1.6 +/- 2.5 degrees, 1.5 +/- 1.6 pixels in X, Y and 0.7 +/- 0.7 pixels in Z direction. The algorithm can be used to register carotid images with misalignment range of 40 pixels in X, Y directions, 10 pixels in Z direction and 40 degree rotations, even in the case of different image appearances due to vessel stenoses.

In this paper we propose a novel method to register at least two vide images to a 3D surface model. The potential applications of such a registration method could be in image guided surgery, high precision radiotherapy, robotics or computer vision. Registration is performed by optimizing a similarity measure with respect to the pose parameters. The similarity measure is based on 'photo-consistency' and computes for each surface point, how consistent the corresponding video image information in each view is with a lighting model. We took four video views of a volunteer's face, and used an independent method to reconstruct a surface that was intrinsically registered to the four views. In addition, we extracted a skin surface from the volunteer's MR scan. The surfaces were misregistered from a gold standard pose and our algorithm was used to register both types of surfaces to the video images. For the reconstructed surface, the mean 3D error was 1.53 mm. For the MR surface, the standard deviation of the pose parameters after registration ranged from 0.12 to 0.70 mm and degrees. The performance of the algorithm is accurate, precise and robust.

This paper presents the first comparison between theoretical estimates and clinically observed values for registration accuracy in point-based rigid-body registration. Rigid-body registration is appropriate for applications in which relatively rigid parts of the body are involved. In some such applications rigid-body registration is accomplished by aligning two sets of discrete points. In neurosurgical guidance, for example, the points are found by localizing the centroids of fiducial markers. We have previously provided two fundamental theoretical results on the relationship between localization error and registration error in rigid-body, point-based registration and have justified these results by showing them to be close to those given by numerical simulations. Rigid-body, point-based registration is accomplished by finding a rigid-body transformation that aligns pairs of homologous 'fiducial' points. The imprecision in locating a fiducial point is known as the 'fiducial localization error' (FLE). Fiducial points may be centroids of attached markers, which tend to have small, equal FLEs, or salient points in segmented anatomic features, whose FLEs tend to be larger and more varied. Alignment is achieved by minimizing the 'fiducial registration error' (FRE), which is the root mean square distance between homologous fiducials after registration. Closed form solutions for the rigid transformation that minimizes FRE have been known since 1966. A more critical and direct measure of registration error is the 'target registration error' (TRE), which is the distance between homologous points other than the centroids of fiducials. This error measure has been investigated by numerical simulation for many years, and we presented at this meeting in 1998 the first derivation of theoretical estimates of TRE. In that paper we showed that these estimates agree well with our simulations and those of others. We made the simplifying assumption in both the derivations and the simulations that the FLE is isotropic, i.e. that it has the same distribution in each coordinate direction. In the present work, we extend the validation beyond simulated data sets to clinically acquired head images from a set of 86 patients. We use the actual localizations of skull-implanted, visible fiducial markers in the images to compare the observed TRE values with those estimated by theory. This approach provides a clinically relevant estimate of the usefulness of the theoretical predictions. We also make a comparison between the observed TRE values and those given by numerical simulation: this allows us to determine whether the assumptions we use for the derivation of our results are good ones in practice. Although the distributions of observed and theoretical values appear different, ROC analysis shows that the theoretical values are good predictors of the observed ones. This gives some validity to the assumptions we make governing the point- based registration process (e.g., that the FLE is isotropic, and that it is independent and identically distributed at each fiducial point), and shows that our theory has practical use in a clinical setting.

In this paper, we present an automated multi-modality registration algorithm based on hierarchical feature extraction. The approach, which has not been used previously, can be divided into two distinct stages: feature extraction (edge detection, surface extraction), and geometric matching. Two kinds of corresponding features -- edge and surface -- are extracted hierarchically from various image modalities. The registration then is performed using least-squares matching of the automatically extracted features. Both the robustness and accuracy of feature extraction and geometric matching steps are evaluated using simulated and patient images. The preliminary results show the error is on the average of one voxel. We have shown the proposed 3D registration algorithm provides a simple and fast method for automatic registering of MR-to-CT and MR-to-PET image modalities. Our results are comparable to other techniques and require no user interaction.

We present an operator-independent software technique for segmentation, realignment and analysis of brain perfusion images, with both voxel-wise and regional quantitation methods. Inter-subject registration with normalized mutual information was tested with simulated defects. Brain perfusion images (HMPAO-SPECT) from 56 subjects (21 AD; 35 controls) were retrospectively analyzed. Templates were created from the 3-D registration of the controls. Automatic segmentation was developed to remove extraneous activity that disrupts registration. Two new registration methods, robust least squares (RLS) and normalized mutual information (NMI) were implemented and compared with sum of absolute differences (CD). The automatic segmentation method caused a registration displacement of 0.4 +/- 0.3 pixels compared with manual segmentation. NMI registration proved to be less adversely effected by simulated defects than RLS or CD. The error in quantitating the patient-template parietal ratio due to mis- registration was 2.0% and 0.5% for 70% and 85% hypoperfusion defects, respectively. The registration processing time was 1.6 min (233 MHz Pentium). The most accurate discriminant utilized a logistic equation parameterized by mean counts of the parietal and temporal regions of the map, (91 +/- 8% Se, 97 +/- 5% Sp). BRASS is a fast, objective software package for single-step analysis of brain SPECT, suitable to aid diagnosis of AD.

This paper presents work towards a system for intra-operative registration of 3D CT data to 2D X-ray radiographs. The registration procedure involves iterative comparison of Digitally Reconstructed Radiographs (DRRs) with X-ray images acquired during surgery. A new data structure called a Transgraph permits rapid generation of DRRS, and greatly speeds up the registration process. The underlying data structures are described, and the registration algorithm is evaluated for application to an existing image guided radiosurgery system.

This work introduces an enhancement to currently existing methods of intra-operative vertebral registration by allowing the portion of the spinal column surface that correctly matches a set of physical vertebral points to be automatically selected from several possible choices. Automatic selection is made possible by the shape variations that exist among lumbar vertebrae. In our experiments, we register vertebral points representing physical space to spinal column surfaces extracted from computed tomography images. The vertebral points are taken from the posterior elements of a single vertebra to represent the region of surgical interest. The surface is extracted using an improved version of the fully automatic marching cubes algorithm, which results in a triangulated surface that contains multiple vertebrae. We find the correct portion of the surface by registering the set of physical points to multiple surface areas, including all vertebral surfaces that potentially match the physical point set. We then compute the standard deviation of the surface error for the set of points registered to each vertebral surface that is a possible match, and the registration that corresponds to the lowest standard deviation designates the correct match. We have performed our current experiments on two plastic spine phantoms and one patient.

Body motion and heart upward creep are among the most frequent sources of artifacts in the single-photon emission computed tomography (SPECT) of nuclear medicine. This paper provides a new method for automatic correction of such motions. Under the formulation of a variable length correlation, abrupt body motions, gradual body motions, and heart upward creep are corrected in sequential passes. An affine transformation is used to compensate for changes in heart appearance caused by varying view angles in image acquisition. Additionally, a method is proposed for automatic exclusion of non-cardiac organs. The effectiveness of the method has been demonstrated with experimental results.

We investigated the use of MI to register images of the pelvis and thorax regions which is a complex problem compared to the head since changes occur in soft tissue while the bony anatomy stays stable. We focused on the bony anatomy eliminating the soft tissue data by applying the MI for bone intensities. Instead of linear binning the whole spectrum of CT intensities, we bin the intensities chosen by the user as corresponding to the bone. We truncated the data spatially by choosing a region, because some bony anatomy might move from scan to scan relative to the stable parts i.e. ribs in the lung region might move with breathing or legs in the pelvis. We compare the effects of using our intensity-dependent- regional MI to the original MI for 9 pairs of CT-CT pelvis, 3 pairs of CT-CT lung and 5 pairs of CT-PET patient studies. With the original algorithm, the root-mean-square registration error can be as high 2 cm for CT-CT. The registration error with the intensity-dependent-regional algorithm, however, was on the average 2 mm for CT-CT pelvic and 4 mm for CT-CT lung studies. Using just the bone intensities and a specific region, we have a smaller sample size, which decreased our calculation time up to 8 times to less than 15 seconds. For CT-PET studies the average registration error is reduced from 3.2 cm to 0.5 cm.

We present an algorithm for registering, segmenting and quantifying multiple scanned electrophoresis images. (2D gel) Electrophoresis is a technique for separating proteins or other macromolecules in organic material according to net charge and molecular mass and results in scanned grayscale images with dark spots against a light background marking the presence of such macromolecules. The algorithm begins by registering each of the images using a non-rigid registration algorithm. The registered images are then jointly segmented using a Markov random field approach to obtain a single segmentation. By using multiple images, the effect of noise is greatly reduced. We demonstrate the algorithm on several sets of real data.

Non-rigid registration of multi-modality images is an important tool for assessing temporal and structural changesbetween images. For rigid registration, voxel similarity measures like mutual information have been shown to alignimages from different modalities accurately and robustly. For non-rigid registration, mutual information can besensitive to local variations of intensity which in MR images may be caused by RF inhomogeneity. The reasonfor the sensitivity of mutual information towards intensity variations stems from the fact that mutual informationignores any spatial information. In this paper we propose an extension of the mutual information framework whichincorporates spatial information about higher-order image structure into the registration process and has the potentialto improve the accuracy and robustness of non-rigid registration in the presence of intensity variations. We haveapplied the non-rigid registration algorithm to a number of simulated MR brain images of a digital phantom whichhave been degraded by a simulated intensity shading and a known deformation. In addition, we have applied thealgorithm for the non-rigid registration of eight pre- and post-operative brain MR images which were acquired withan interventional MR scanner and therefore have substantial intensity shading due to RF field inhomogeneities. Inall cases the second-order estimate of mutual information leads to robust and accurate registration.

In previous work we have introduced an approach to improving the registration of EPI fMRI data with anatomical MRI by accounting for differences in magnetic field induced geometric distortion in the two types of MRI acquisition. In particular we began to explore the use of imaging physics based constraints in a non-rigid multi-modality registration algorithm. In this paper we present phantom based experimental work examining the behavior of different non-rigid registration constraints compared to a field map acquisition of the MRI distortion. This acquisition provides a pixel by pixel 'ground truth' estimate of the displacement field within the EPI data. In our registration based approach we employ a B-spline based estimate of the relative geometric distortion with a multi-grid optimization scheme. We maximize the normalized mutual information between the two types of MRI scans to estimate the B-Spline parameters. Using the field map estimates as a gold standard, registration estimates using no additional geometric constraints are compared to those using the spin echo based signal conservation. We also examine the use of logarithmic EPI values in the criteria to provide additional sensitivity in areas of low signal. Results indicate that registration of EPI to conventional MRI incorporating a spin echo distortion model can provide comparable estimates of geometric distortion to those from field mapping data without the need for significant additional acquisitions during each fMRI sequence.

This paper presents a fast hierarchical method to perform dense deformable inter-subject matching of 3D MR Images of the brain. To recover the complex morphological variations in neuroanatomy, a hierarchy of 3D deformations fields is estimated, by minimizing a global energy function over a sequence of nested subspaces. The nested subspaces, generated from a single scaling function, consist of deformation fields constrained at different scales. The highly non linear energy function, describing the interactions between the target and the source images, is minimized using a coarse-to-fine continuation strategy over this hierarchy. The resulting deformable matching method shows low sensitivity to local minima and is able to track large non-linear deformations, with moderate computational load. The performances of the approach are assessed both on simulated 3D transformations and on a real data base of 3D brain MR Images from different individuals. The method has shown efficient in putting into correspondence the principle anatomical structures of the brain. An application to atlas-based MRI segmentation, by transporting a labeled segmentation map on patient data, is also presented.

In this pair, we describe experiments designed to validate some techniques used for spatial normalization of diffusion tensor (DT) images. In particular, we have previously described the problems involved in applying transformations to these images and proposed several techniques for addressing this problem. DTs contain orientational information, which must be handled appropriately when a DT image is transformed. In this paper, we review the previously proposed techniques for estimating the appropriate reorientation of each DT that should accompany a given transformation of the image. We describe the design of some synthetic data sets and some experiments, which use this data to test the effectiveness of the techniques under affine transformations of DT images. Results confirm that one particular technique, which takes into account the more complex reorientational effects of shearing and stretching transformations, is the most effective.

Soft-tissue deformation can be a problem if a pre-operative modality is used to help guide a surgical or an interventional procedure. We present a method which can warp a pre-operative CT image to represent the intra-operative scene shown by an interventional fluoroscopy image. The method is a novel combination of a 2D-3D image registration algorithm and a deformation algorithm which allows rigid bodies to be incorporated into a non-linear deformation based on a radial basis function. The 2D-3D registration algorithm is used to obtain information on relative vertebral movements between pre-operative and intra-operative images. The deformation algorithm uses this information to warp the pre-operative image to represent the intra-operative scene more accurately. Images from an aortic stenting procedure were used. The observed deformation was 5 degree flexion and 5 mm lengthening of the lumbar spine. The vertebral positions in the warped CT volume represent the intra-operative scene more accurately than in the pre-operative CT volume. Although we had no gold- standard with which to assess the registration accuracy of soft-tissue structures, the position of soft-tissue structures within the warped CT volume appeared visually realistic.

The advanced single-slice rebinning algorithm (ASSR) is a highly accurate and efficient approximative algorithm for cone-beam spiral CT that (1) yields high image quality even at large cone angles, (2) makes use of available 2D backprojection algorithms/hardware and (3) allows for sequential data processing. It uses virtual R-planes (reconstruction planes) that are tilted to optimally fit 180 degree spiral segments. Along these R-planes data of a virtual 2D parallel scanner are synthesized via rebinning from the measured spiral cone-beam data. Reconstruction with 2D filtered backprojection yields the object cross-section in world coordinates [x, y, z(x, y)] which is resampled to carthesian coordinates (x, y, z) by z-filtering. Geometrical misalignments as well as any arbitrary detector geometry can be easily incorporated in the ASSR algorithm. ASSR, unlike other approximate algorithms, does not show severe cone-beam artifacts when going to larger cone angles. Even for scanners with a high number of detector rows, e.g. 64 rows, a high and isotropic z-resolution is achieved. In-plane resolution is determined by the 2D reconstruction filters which can be chosen as in 2D CT. Even in the case of only M equals 4 or M equals 8 simultaneously measured slices, ASSR may outperform standard z-interpolation algorithms such as 180 degree MFI. Due to its high efficiency and high image quality ASSR has the potential to be used for medical cone-beam CT.

A recently published local region-of-interest (ROI) technique makes it possible to image a ROI in a long object in cone beam spiral scans without blurring from the overlaying materials; the local ROIs refer to the portions of the object bounded by the parallel projections of the spiral scan path on the (phi) planes in the Radon space. First, the Radon derivative data for the local ROIs are computed from the cone beam data; second, the local ROIs are reconstructed; and finally the ROI is reconstructed from the local ROIs. For any cone beam image detected near the top and the bottom of the spiral path, the integration line segments are limited in different manners depending on whether the local ROI projects onto the corresponding (phi) plane on the uppermost/lowermost complete stage of the projected spiral or not. In this first part in a series of two papers reformulating the local ROI method into a filtered backprojection (FBP)-based algorithm, the theoretical derivation of the FBP-based local ROI method is presented, and the demanding numerical implementation together with the simulation results are reported in the second paper. We have developed a simple procedure to group line segments for the filtering operation according to the manner they are limited. Furthermore, it is found that the filtering operation on the cone beam images is equivalent to a number of 1D Hilbert transforms followed by 1D differentiation in the projected scan path direction.

In the long object problem it is intended to reconstruct exactly a region-of-interest (ROI) of an object from spiral cone beam data which covers the ROI and its nearest vicinity only. In the first paper in a series of two the theory of the local ROI method is derived using the filtered-backprojection approach. In the present second paper the demanding numerical implementation is described. The straightforward 4-step algorithm is applied. It mainly consists of explicit calculations of the derivatives of partial plane integrals of the object from line segments in the projection images. In the local ROI method grouping of line segments to particular (phi) -planes in 3-D Radon space is important. A rigorous grouping causes artifacts which can be avoided by a fuzzy correspondence of line segments to (phi) -planes. In the ROI the same image quality is achieved for a partial scan as for a full scan. However, the method suffers from high computational requirements. The filtering step can be speeded up by replacing the 4-step algorithm by convolution with spatially variant 1-D Hilbert transforms. An in-depth analysis of the empirical PSF of detector pixels filtered by the 4-step algorithm confirmed the theoretical results. Modifications for practical implementation are outlined which are subject to further investigations.

Cone beam reconstruction has been the focus of many studies. One of the most widely referenced and used algorithms for circular trajectory is the Feldkamp algorithm. The advantage of the algorithm is its simplicity of implementation, efficiency in computation, and close resemblance to the well- known filtered backprojection algorithm for fan beam and parallel beam reconstruction. The algorithm is effective in terms of combating some of the cone beam artifacts. However, when objects with high density and non-uniform distribution are placed off the center plane (the fan beam plane), severe shading artifact will result. In the paper, we propose a two- pass cone beam reconstruction scheme. The algorithm is based on the observation that the high-density object reconstructed with the Feldkamp algorithm is accurate to a first order. The shading and streaking artifacts near the high-density objects are caused mainly by the incomplete sample of the circular trajectory. As a result, we can use the reconstructed ages with Feldkamp algorithm as the basis for error estimation. By segmenting these objects, we could recreate the cone beam artifacts by synthesizing the projection and reconstruction processing. The final images are produced by removing error images from the first-pass images.

A multitude of approximate cone-beam algorithms have been proposed suited for reconstruction of small cone angle CT data. The goal of this study is to identify a practical and efficient approximate cone-beam method, and to investigate its performance at medium cone angles associated to area detectors. Three different approximate algorithms for spiral cone-beam CT will be compared: the (pi) -method, the Multirow- Fourier-Reconstruction and the Advanced Single-Slice Rebinning method. These algorithms are different in the way how the two- dimensional detector images are filtered. In each view x-ray samples are identified which describe an approximation to a virtual reconstruction plane. The image quality of the respective reconstruction will be assessed with respect to image artifacts, the slice sensitivity profile, and the in- plane modulation transfer function. It turns out that the performance of approximate reconstruction improves as the virtual reconstruction plane better fits the spiral focus path. The Advanced Single-Slice Rebinning method using tilted reconstruction planes is a practical algorithm, providing image quality comparable to that of a single-row scanning system even with a 46 row detector at a table feed of 64 mm per rotation of the gantry.

A nonlinear inversion scheme formulated on small subzones of the total region of interest (ROI) is developed. The algorithm reconstructs the distribution of a linear elastic stiffness term and a Maxwellian damping parameter over the entire ROI through a least squares optimization. The subzones are generated in a hierarchical manner based on progressive error minimization and processed in an automated, sweeping fashion until certain performance criterion are met. Simulation results show that the algorithm works well to minimize global error and is capable of simultaneously reconstructing both property parameter distributions even in the presence of random noise, although initial experience suggests that the elastic property image is superior to its attenuation coefficient counterpart.

The Bayes Inference Engine (BIE) has been used to perform a 4D reconstruction of a first-pass radiotracer bolus distribution inside a CardioWest Total Artificial Heart, imaged with the University of Arizona's FastSPECT system. The BIE estimates parameter values that define the 3D model of the radiotracer distribution at each of 41 times spanning about two seconds. The 3D models have two components: a closed surface, composed of bi-quadratic Bezier triangular surface patches, that defines the interface between the part of the blood pool that contains radiotracer and the part that contains no radiotracer, and smooth voxel-to-voxel variations in intensity within the closed surface. Ideally, the surface estimates the ventricular wall location where the bolus is infused throughout the part of the blood pool contained by the right ventricle. The voxel-to-voxel variations are needed to model an inhomogeneously-mixed bolus. Maximum a posterior (MAP) estimates of the Bezier control points and voxel values are obtained for each time frame. We show new reconstructions using the Bezier surface models, and discuss estimates of ventricular volume as a function of time, ejection fraction, and wall motion. The computation time for our reconstruction process, which directly estimates complex 3D model parameters from the raw data, is performed in a time that is competitive with more traditional voxel-based methods (ML-EM, e.g.).

In optical tomography (OT) one attempts to reconstruct cross- sectional images of various body parts given data from near- infrared transmission measurements. The cross-sectional images display the spatial distribution of optical properties, such as the absorption coefficient (mu) _a, the reduced scattering coefficient (mu) _s^', or a combination thereof. One of the major problems of the novel imaging technology is that many different spatial distributions of optical properties inside the medium can lead to the same detector readings on the surface of the medium. Therefore, the reconstruction problem in optical tomography is ill posed. The choice of an appropriate method to overcome this problem is of crucial importance for any successful optical tomographic image reconstruction algorithm. In this work we approach the problem within a gradient-based image iterative reconstruction (GIIR) scheme. The image reconstruction is considered as a minimization of an appropriately defined objective function. The objective function can be separated into a least-square- error term, which compares predicted and actual detector readings, and additional penalty terms that may contain a priori information about the system. We present the underlying concepts in our approach to overcome ill-posedness in optical tomography and show how different penalty terms affects the performance of the image reconstruction.

We present an algorithm which is able to reconstruct dynamic emission computed tomography (ECT) image series directly from inconsistent projection data that have been obtained using a rotating camera. By finding a reduced dimension time-activity curve (TAC) basis with which all physiologically feasible TAC's in an image may be accurately approximated, we are able to recast this large non-linear problem as one of constrained linear least squares (CLLSQ) and to reduce parameter vector dimension by a factor of 20. Implicit is the assumption that each pixel may be modeled using a single compartment model, as is typical in ^99mTc teboroxime wash-in wash-out studies; and that the blood input function is known. A disadvantage of the change of basis is that TAC non-negativity is no longer ensured. As a consequence, non-negativity constraints must appear in the CLLSQ formulation. A warm-start multiresolution approach is proposed, whereby the problem is initially solved at a resolution below that finally desired. At the next iteration, the number of reconstructed pixels is increased and the solution of the lower resolution problem is then used to warm-start the estimation of the higher resolution kinetic parameters. We demonstrate the algorithm by applying it to dynamic myocardial slice phantom projection data at resolutions of 16 X 16 and 32 X 32 pixels. We find that the warm-start method employed leads to computational savings of between 2 and 4 times when compared to cold start execution times. A 20% RMS error in the reconstructed TAC's is achieved for a total number of detected sinogram counts of 1 X 10⁵ for the 16 X 16 problem and at 1 X 10⁶ counts for the 32 X 32 grid. These errors are 1.5 - 2 times greater than those obtained in conventional (consistent projection) SPECT imaging at similar count levels.

Truncated Projection Computer Tomography (TPCT) is similar to conventional Computer Tomography (CT) in that it acquires projection information. The difference is that it weights and/or truncates the projections along their integration paths. The problem is succinctly stated as an integral equation termed the incomplete Radon transform. TPCT image reconstruction is equivalent to inversion of the incomplete Radon transform. We presented an inversion formula for this transform at SPIE Medical Imaging 1999. The solution involves the application of an integral transform that is equivalent to a combination of a square-root geometrical distortion and a Fourier transform. Subsequent to the 1999 presentation, we recast part of the inversion derivation in terms of Lagrange multipliers. Doing so led us to the realization that the incomplete Radon transform is a member of a much larger class of integral equations that lend themselves to the TPCT inversion techniques. In the present work we touch briefly on several topics. We will exhibit the larger class of integral equations in the form of Hilbert-space scalar products. They define generalized spatial filtering operations anchored simultaneously in direct space and any one of a multitude of transform spaces. In the examples relating to the TPCT reconstruction algorithm's stability, we perform computer simulations using off-axis Gaussian distributions as objects.

The Temple University Medical School has a sequence of over 400 serial sections of adult normal ventricular human heart tissue, cut at 25 micrometer thickness. We used a Zeiss Ultraphot with a 4x planapo objective and a Pixera digital camera to make a series of 45 sequential montages to use in the 3D reconstruction of a fascicle (muscle bundle). We wrote custom software to merge 4 smaller image fields from each section into one composite image. We used SurfDriver software, developed by Scott Lozanoff of the University of Hawaii and David Moody of the University of Alberta, for registration, object boundary identification, and 3D surface reconstruction. We used an Epson Stylus Color 900 printer to get photo-quality prints. We describe the challenge and our solution to the following problems: image acquisition and digitization, image merge, alignment and registration, boundary identification, 3D surface reconstruction, 3D visualization and orientation, snapshot, and photo-quality prints.

In continuous X-ray fluoroscopy images are sometimes blurred uniformly due to motion of the operating table. Additionally, low-dose fluoroscopy images are degraded by relatively strong quantum noise, which is not affected by the blur. We quantify the degradation due to motion blur by assessing the blur's effect on the Detective Quantum Efficiency (DQE), which captures the signal- and noise transfer properties of an imaging system. The estimation of the motion blur parameters, viz. direction and extent, is carried out one after the other. The central idea for direction detection is to apply an inertia-like matrix to the global spectrum of the degraded image, which assesses the anisotropy caused by the blur. Once the blur direction is obtained by this tensor approach, its extent is identified from an estimated power spectrum or bispectrum slice along this direction. The decision for either method is based on the eigenvalues of the inertia matrix. The blur parameters are used as input for a nonlinear Maximum-a- posteriori restoration technique based on a Generalized Gauss- Markov Random field for which several efficient optimization strategies are presented. This approach includes a thresholdless edge model. The DQE is generalized as a quality measure to assess the signal- and noise transfer properties of the restoration method.

We present a new method of enhancing cerebral vessels in subtraction angiography that defines shape attributes in terms of pixel features. Vessel knowledge comprises information on the imaging process, e.g., distribution of contrast media, noise characteristics, and morphological information on the vessels. The latter is computed as a fuzzy measure because pixels have not yet been classified into vessel and background pixels. We model our image as result of a process of projecting discrete contrast media voxels on the image plane. The projection is assumed to be distorted by noise. The shape feature is derived from the Karhunen-Loeve transformation (KLT) that is computed at each pixel from the covariance of the contrast distribution in a given neighborhood. Vessel likelihood is computed from local elongatedness. The latter is derived from the variances along the two principal axes and from the first central moment of the contrast distribution. The directional information from the KLT is used for anisotropic diffusion for noise reduction. Results of the enhancement step on angiographic data showed a significant improvement of the contrast while not blurring the image. Closely neighboring vessels could be differentiated if they were one pixel apart and if the SNR were better than 2:1.

Treatment planning in brachytherapy depends heavily on the accurate localization of markers in a catheter implant. We are developing an interactive system to combine the image information of biplane X-ray images to reconstruct the 3D marker positions. Current systems ask the user to identify all corresponding markers in both images manually. Especially in cases where multiple, eventually crossing catheters are present this is very time consuming and difficult as markers that are visible in one image may be hidden in the other image. To improve the procedure of marker detection we apply image-processing techniques. We investigate two approaches. One is based on 3D snakes. This is a model-based technique that is not sensitive to noise or ambiguities in the image. After the user has given a number of corresponding points per catheter, the system automatically detects the complete catheter and determines all 3D-marker positions. The second approach uses edge detection in a small region of interest (ROI). In both cases, knowledge about the catheter is used to guide the marker detection algorithm. The user has to examine the result visually. In case of erroneous marker detection the user can move, add or delete single maker points. To be able to judge the accuracy of the reconstruction it is necessary to locate possible error sources. For an accurate reconstruction of the catheter positions it is important to know the exact geometry of the imaging system. With a mathematical model the influence of uncertainties in parameters on the reconstruction result is studied.

This paper presents a sub-voxel analysis method for multi- parameter volumetric images such as MRI to provide partial volume estimation. The proposed method finds a continuous function for a neighboring structure of each voxel. The estimation function and neighboring structure are chosen from the quadratic/cubic polynomials and a set of 2D/3D symmetric neighborhood architectures, respectively. Then, a new form of the eigenimage method, based on Gram-Schmidt orthogonalization, is derived for each choice of estimation function and neighboring structure. Finally, the above estimators are applied to a simulation model consisting of materials similar to CSF, WM, and GM of the human brain in T1- , T2-, and PD-weighted MRI. In the presence of noise, the examined continuous estimators show a smaller standard deviation (up to 40%) than the standard eigenimage method. Also the chosen estimators have analytical solution for their Gram-Schmidt filters, so their execution times are comparable with that of the standard eigenimage method. In addition, the proposed approach can determine the 3D distribution of each material and extract the connecting surfaces of the materials within each voxel.

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.

One of the important clinical features to differentiate benign melanocytic nevi from malignant melanomas is the irregularity of the lesion border. A careful examination of a lesion border reveals two types of irregularity: texture irregularity and structure irregularity. Texture irregularities are the small variations along the border, while structure irregularities are the global indentations and protrusions, which may suggest excess of cell growth or regression of a melanoma. Therefore, measuring border irregularity by structural indentations and protrusions may detect the malignancy of the lesion. The common shape descriptors such as compactness index and fractal dimension are more sensitive to texture irregularities than structure irregularities. They do not provide an accurate estimation for the structure irregularity. Therefore, we have designed a new measurement for border irregularity. The proposed method first locates all indentations and protrusions along the lesion border. Then a new area-based index, called irregularity index, is computed for each indentation and protrusion. The overall border irregularity is estimated by the sum of all individual indices. In addition, the new method offers an extra feature: localization of the significant indentations and protrusions. As the result, the new measure is sensitive to structure irregularities and may be useful for diagnosing melanomas.

Variation in the diameter of vessels is a key information for treatment of stenosis. This information is usually obtained from standard 2-D projective acquisitions. We propose an automatic method for the quantification of vessels cross- sections in 3D vascular reconstructions from x-ray images. First, a closed continuous surface is extracted. This surface represents the vessels contours selected with a given centerline. Then, the area of the cross-sections along the central axis is obtained by intersection of the contour and the plane of each cross-section. A model of the vessels allows to correct the first estimation. Tests on phantom images give a precision of the vessels radius below 0.5 voxel. Results are also presented on real vessels containing stenosis.

Registration of anatomical images is useful for many applications including image segmentation, characterization of normal and abnormal shape, and creating deformable anatomical shape atlases. The usefulness of the information derived from image registration depends on the degree of anatomically meaningful correspondence between the images. We assume that an ideal image registration algorithm can determine an unique correspondence mapping between any two image volumes imaged from a homogeneous population of anatomies; and that these transformations have the properties of invertibility and transitivity. Unfortunately, current image registration algorithms are far from ideal. In this paper we test the invertibility and transitivity of transformations computed from a 'traditional' and a consistent linear-elastic registration algorithm. Invertibility of the transformations was evaluated by comparing the composition of transformations from image A-to-B and B-to-A to the identity mapping. Transitivity of the transformations was evaluated by measuring the difference between the identity mapping and the composition the transformations from image A-to-B, B-to-C, and C-to-A. Transformations were generated by matching computer generated phantoms, CT data of infant heads, and MRI data of adult brains. The consistent algorithm out performed the 'traditional' algorithm by 8 to 16 times for the invertibility test and 2 to 5 times for the transitivity test.

We describe a method for creating semi-isometric flat maps of sections of the human cortical surface. These maps can be used for a wide range of applications including visualization of the distribution of functional activation over the unfolded brain surface and generating parametric models for the cortical surface that are appropriate for performing geometrical transformations and surface based inter-subject registration. In particular, their application in creating multi-resolution representations of arbitrarily shaped complex surfaces is presented in this paper. Using the property that every simultaneous conformal and equiareal mapping is isometric, we have formulated the calculation of an isometric mapping between surfaces as a constrained optimization problem. We have designed an energy function whose minima occur when the surface points are positioned in an unfolded configuration. Constraint functions imposing the requirements of preservation of angles and areas guarantee that the surface will deform to produce conformal and equiareal mappings. The constraints are imposed using penalty functions in an unconstrained conjugate gradient algorithm. The surface unfolds gradually, deforming to a near-flat form that corresponds to a minimum of the weighted sum of the energy and penalty function terms.

An essential part of the IRMA-project (Image Retrieval in Medical Applications) is the categorization of digitized images into predefined classes using a combination of different independent features. To obtain an automated and content-based categorization, the following features are extracted from the image data: Fourier coefficients of normalized projections are computed to supply a scale- and translation-invariant description. Furthermore, histogram information and Co-occurrence matrices are calculated to supply information about the gray value distribution and textural information. But the key part of the feature extraction is the shape information of the objects represented by an Active Shape Model. The Active Shape Model supports various form variations given by a representative training set; we use one particular Active Shape Model for each image class. These different Active Shape Models are matched on preprocessed image data with a simulated annealing optimization. The different extracted features were chosen with regard to the different characteristics of the image content. They give a comprehensive description of image content using only few different features. Using this combination of different features for categorization results in a robust classification of image data, which is a basic step towards medical archives that allow retrieval results for queries of diagnostic relevance.

This paper presents a factor analytic approach to morphometry in which strong intercorrelations among a high-dimensional set of shape-related variables are sought. The correlated variables potentially correspond to substructures of anatomy and thus have a natural interpretation. The analysis is based on information about the pointwise size differences between the anatomy depicted in a template image and the anatomy in a subject image, obtained by registering the template to the subject and then calculating the Jacobian determinant of the registration transformation over the image volume. The method is demonstrated in a preliminary study of shape differences between the corpora callosa of schizophrenic patients and normal controls. We show that the regions where these differences occur can be determined by unsupervised analysis, indicating the method's potential for exploratory studies.

One of the most important tasks for virtual endoscopy is path planning for viewing the lumen of hollow organs. For geometry complex objects, for example the lungs, it remains an unsolved problem. While alternative visualization modes have been proposed, for example, cutting and flattening the hollow wall, a skeleton of the lumen is still necessary as a reference for the cutting. A general-purpose skeletonization algorithm often generates redundant skeletons because of the local shape variation. In this study, a multistage skeletonization method for tree-like volumes, such as airway system, blood vessels, and colon, was presented. By appropriately defining the distance between voxels, the distance to the root from each voxel in the volume can be effectively determined with means of region growing techniques. The end points of all branches and the shortest path from each end point to the root can be extracted based on this distance map. A post-processing algorithm is applied to the shortest paths to remove redundant ones and to centralize the remained ones. The skeleton generated is one-voxel wide, along which every branch of the 'tree' can be viewed. For effectively processing volume of large size, a modified multiresolution analysis was also developed to scale down the binary segmented volume. Tests on airway, vessel, and colon dataset were promising.

Image acquisition techniques often suffer from low signal-to- noise ratio (SNR) and/or contrast-to-noise ratio (CNR). Although many acquisition techniques are available to minimize these, post acquisition filtering is a major off-line image processing technique commonly used to improve the SNR and CNR. A major drawback of filtering is that it often diffuses/blurs important structures along with noise. In this paper, we introduce two novel scale-based filtering methods that use local structure size or 'object scale' information to arrest smoothing around fine structures and across even low-gradient boundaries. The first of these methods uses a weighted average over a scale-dependent neighborhood while the other employs scale-dependent diffusion conductance to perform filtering. Both methods adaptively modify the degree of filtering at any image location depending on local object scale. Qualitative experiments based on both phantoms and patient MR images show significant improvements using the scale-based methods over the extant anisotropic diffusive filtering method in preserving fine details and sharpness of object boundaries. Quantitative analysis on phantoms generated under a range of conditions of blurring, noise, and background variation confirm the superiority of the new scale-based approaches.

We present a semi-automated method for constraining the topology of inner cerebral cortex volumes generated from T1- weighted magnetic resonance images (MRI). An initial tissue classification is generated based on a measurement model that accounts for partial volume effects and the presence of image inhomogeneities due to field non-uniformities. This classification is used to generate an interior cerebral white matter brain volume. This volume is processed by our algorithm to ensure that the topology of the cortical surface, that of a two-dimensional sheet, is represented in tessellations of the volume. We extend our previous work on topological constraints, which introduced an automated correction procedure that creates graph representations of volumetric objects in order to identify topological defects in their segmentation. We improve this method by performing an iterative correction process that limits the severity of changes made to the initial segmentation. The previous method also requires the duplication of slices of data wherever a change is required, which significantly increases the size of the volume. In the new method we identify a set of corrections that can be made without slice duplication. The key benefits to the improvements in our method are improved localization and correction of topological defects resulting in increased accuracy of the resulting cortical surface representation and a decrease in the size of the resulting volume.

A fully automated 3D version of the so-called white matter method for correcting intensity non-uniformity in MR T1- weighted neuro images is presented. The algorithm is an extension of the original work published previously. The major part of the extension was the development of a fully automated method for the generation of the reference points. In the design of this method, a number of measures were introduced to minimize the effects of possible inclusion of non-white matter voxels in the selection process. The correction process has been made iterative. A drawback of this approach is an increased cost in computational time. The algorithm has been tested on T1-weighted MR images acquired from a longitudinal study involving elderly subjects and people with probable Alzheimer's disease. More quantitative measures were used for the evaluation of the algorithm's performance. Highly satisfactory correction results have been obtained for images with extensive intensity non-uniformity either present in raw data or added artificially. With intensity correction, improved accuracy in the measurement of the rate of brain atrophy in Alzheimer's patients as well as in elderly people due to normal aging has been achieved.

The design of a database containing head Computed Tomography (CT) studies is presented, along with a justification for the database's composition. The database will be used to validate software algorithms that screen normal head CT studies from studies that contain pathology. The database is designed to have the following major properties: (1) a size sufficient for statistical viability, (2) inclusion of both normal (no pathology) and abnormal scans, (3) inclusion of scans due to equipment malfunction, technologist error, and uncooperative patients, (4) inclusion of data sets from multiple scanner manufacturers, (5) inclusion of data sets from different gender and age groups, and (6) three independent diagnosis of each data set. Designed correctly, the database will provide a partial basis for FDA (United States Food and Drug Administration) approval of image processing algorithms for clinical use. Our goal for the database is the proof of viability of screening head CT's for normal anatomy using computer algorithms. To put this work into context, a classification scheme for 'computer aided diagnosis' systems is proposed.

Recent developments in digital detectors have led to investigating the importance of grids in mammography. We propose to examine the use Bayesian Image Estimation (BIE) as a software means of removing scatter post acquisition and to compare this technique to a grid. BIE is an iterative, non- linear statistical estimation technique that reduces scatter content while improving CNR. Images of the ACR breast phantom were acquired both with and without a grid on a calibrated digital mammography system. A BIE algorithm was developed and was used to process the images acquired without the grid. Scatter fractions (SF) were compared for the image acquired with the grid, the image acquired without the grid, and the image acquired without the grid and processed by BIE. Images acquired without the anti-scatter grid had an initial SF of 0.46. Application of the Bayesian image estimation technique reduced this to 0.03. In comparison, the use of the grid reduced the SF to 0.19. The use of Bayesian image estimation in digital mammography is beneficial in reducing scatter fractions. This technique is very useful as it can reduce scatter content effectively without introducing any adverse effects such as aliasing caused by gridlines.

This paper presents development and application of an optimal linear filter for delineation of activated areas of the brain from functional MRI (fMRI) time series data. The steps of the work accomplished are as follows. (1) Delineation of activated areas is formulated as an optimal linear filtering problem. In this formulation, a linear filter (image combination method) is looked for, which maximizes the signal-to-noise ratio (SNR) of the activated areas subject to the constraint of removing inactivated areas from the image. (2) An analytical solution for the problem is found. (3) Image pixel vectors and expected time series pattern (signature) for inactivated pixels are used to calculate the weighting vectors numerically. (4) The segmented image by the proposed method is compared to those generated by the conventional methods (correlation, t- statistic, and z-statistic). Visual qualities of the images as well as their SNR's are compared. The optimal linear filter outperforms the conventional methods of fMRI analysis based on improved SNR and contrast-to-noise ratio (CNR) of the images generated by the proposed method compared to those generated by the other methods. In addition, this method does not require a priori knowledge of the fMRI response to the paradigm for its application. The method is linear and most of the work is done analytically, thereby numerical implementation and execution of the method are faster than the conventional methods.

Recognizing that conspicuous multiple sclerosis (MS) lesions have high intensities in both dual-echo T2 and PD-weighted MR brain images, we show that it is possible to automatically determine a thresholding mechanism to locate conspicuous lesion pixels and also to identify pixels that suffer from reduced intensity due to partial volume effects. To do so, we first transform a T2-PD feature space via a log(T2)- log(T2+PD) remapping. In the feature space, we note that each MR slice, and in fact the whole brain, is approximately transformed into a line structure. Pixels high in both T2 and PD, corresponding to candidate conspicuous lesion pixels, also fall near this line. Therefore we first preprocess images to achieve RF-correction, isolation of the brain, and rescaling of image pixels into the range 0 - 255. Then, following remapping to log space, we find the main linear structure in feature space using a robust estimator that discounts outliers. We first extract the larger conspicuous lesions which do not show partial volume effects by performing a second robust regression for 1D distances along the line. The robust estimator concomitantly produces a threshold for outliers, which we identify with conspicuous lesion pixels in the high region. Finally, we perform a third regression on the conspicuous lesion pixels alone, producing a 2D conspicuous lesion line and confidence interval band. This band can be projected back into the adjacent, non-conspicuous, region to identify tissue pixels which have been subjected to the partial volume effect.

Melanoma diagnosis greatly relies on the observation of some characteristic features on skin tumors. Similarly, a computer- based diagnostic system has been designed to detect these features. However, specificity and sensitivity of features often rely on their location within the tumor. Locating the border of lesions is therefore of utmost importance. Segmentation of tumors is not easy because of high variability of coloration from one tumor to another and because of numerous 'artifacts' such as hairs, or skin lines. An adaptive and supervised approach was consequently chosen to segment lesions. Dermatologists were asked to hand-outline borders of lesions and, after an automatic selection of a point inside the tumor, radial intensity profiles were generated. The location of border was associated with each of them. A neural network was taught to predict border from these labeled profiles. Our approach has been found efficient and robust in such a way that human correction of automatic segmentation are most of the time insignificant. Features such as asymmetry of texture and inhomogeneity of colors can subsequently be observed and their clinical significance evaluated.

An image segmentation algorithm based on back-propagation neural network with robust supervised training, is presented. Using this algorithm it is possible to do brain MRI segmentation with good resolution between white and gray matter and recognition of some structures. Initial weight parameter evaluation takes fair amount of computational time resulting in a fast slice segmentation once the network has been trained. The training step consists of choosing a set of optimal weights for interchanging network nodes such that when the values of gray level patterns are presented to the network, it classifies them for different tissue types.

An automatic method for the delineation of posterior ribs in frontal chest radiographs is presented. We develop a statistical shape model for the complete rib cage. Contrary to previous work, we fit the global rib cage directly to a radiograph, instead of detecting rib border candidates locally and applying rules to infer the rib cage from these candidates. Each posterior rib is modeled by two parallel parabolas. The full rib cage, from rib 2 up and including rib 10, therefore contains 72 parameters. This number is reduced with principal component analysis: It is demonstrated that 10 parameters explain over 98% of the variability in a training set of 35 chest radiographs. The rib cage is fitted with Powell's direction set method for optimizing the model parameters, with a fit measure that gives high output when rib borders are located on edge pixels in the image. The method is robust and fairly accurate: On the 35 test images with a resolution of 512 by 512 pixels, rib borders are located with an accuracy of 3 pixels on average.

This paper describes the application of a statistical-based deformable model algorithm to the segmentation of kidneys in x-ray computed tomography (CT) images of laboratory mice. This segmentation algorithm has been developed as the crucial first step in a process to automatically screen mice for genetically-induced polycystic kidney disease (PKD). The algorithm is based on active shape models (ASMs) initially developed by Cootes, et al. Once the segmentation is complete, texture measurements are applied within kidney boundaries to detect the presence of PKD. The challenges associated with the segmentation of mouse kidneys (non-rigid organs) are presented, and the motivation for using ASMs in this application is discussed. Also, improvements were made to published ASM methods that may be generally helpful in other segmentation applications. In 15 of the 18 cases tested, the mouse kidneys and spine were detected with only minor errors in boundary position. In the remaining three cases, small parts of the kidneys were missed and/or some extra abdominal tissue was inadvertently included by the boundary. In all 18 cases, however, the kidneys were successfully detected at a level where PKD could be automatically screened for using mean-of-local-variance (MOLV) texture measurements.

The aim of this study is to evaluate the use of a local affine transformation for computer-aided interval change analysis in mammography. A multistage regional registration technique was developed for identifying masses on temporal pairs of mammograms. In the first stage, the breast images from the current and prior mammograms were globally aligned. An initial fan-shape search region was defined on the prior mammogram. In the second stage, the location of the fan-shape region was refined by warping, based on an affine transformation and simplex optimization. A new refined search region was defined on the prior mammogram. In the third stage a search for the best match between the lesion template from the current mammogram and a structure on the prior mammogram was carried out within the search region. This technique was evaluated on 124 temporal pairs of mammograms containing biopsy-proven masses. Eighty-six percent of the estimated lesion locations resulted in an area overlap of at least 50% with the true lesion locations. The average distance between the estimated and the true centroid of the lesions on the prior mammogram was 4.4 +/- 5.9 mm. The registration accuracy was improved in comparison with our previous study that used a data set of 74 temporal pairs of mammograms. This improvement gain is mainly from the local affine transformation.

This paper presents an automated method for segmenting CT images of the fractured foot. Segmentation boundary is determined by fuzzy inference with two types of knowledge acquired from orthopedic surgeons. Knowledge of joint is used to determine the boundary of adjacent normal bones. It gives higher degree to the articular cartilage according to local structure (parallelity) and intensity distribution around a joint part. Knowledge of fragment is used to find a contact place of fragments. It evaluates Euclidian distance map (EDM) of the contact place and gives higher degree to the narrow part. Each of the knowledge is represented by fuzzy if-then rules, which can provide degrees for segmentation boundary. By evaluating the degrees in region growing process, a whole foot bone is decomposed into each of anatomically meaningful bones and fragments. An experiment was done on CT images of the subjects who have depressed fractures on their calcanei. The method could effectively give higher degrees on the essential boundary, suppressing generation of useless boundary caused by the internal cavities in the bone. Each of the normal bones and fragments were correctly segmented.

We are developing computerized feature extraction and classification methods to analyze malignant and benign pulmonary nodules in three-dimensional (3-D) thoracic images. This paper focuses on an approach for characterizing the internal texture which is one of important clues for differentiating between malignant and benign nodules. In this approach, each voxel was described in terms of shape index derived from curvatures on the voxel. The voxels inside the nodule were aggregated via shape histogram to quantify how much shape category was present in the nodule. Topological features were introduced to characterize the morphology of the cluster constructed from a set of voxels with the same shape category. The properties such as curvedness and CT density were also built into the representation. We evaluated the effectiveness of the topological and histogram features extracted from 3-D pulmonary nodules for classification of malignant and benign internal structures. We also compared the performance of the computerized classification with the experienced physicians. The classification performance based on the combined feature space reached the performance of the experienced physicians. Our results demonstrate the feasibility of using topological and histogram features for analyzing internal texture to assist physicians in making diagnostic decisions.

The aim of this work was to determine a methodology to selection of the best features subset and artificial neural network (ANN) topology to classify masses lesions. The backpropagation training algorithm was used to adjust the weights of ANN. A total of 118 regions of interest images were chosen (68 benign and 50 malignant lesions). In a first step, images were submitted to a combined process of thresholding, mathematical morphology, and region growing techniques. After, fourteen texture features (Haralick descriptors) and fourteen shape features (circularity, compactness, Gupta descriptors, Shen descriptors, Hu descriptors, Fourier descriptor and Wee descriptors) were extracted. The Jeffries-Matusita method was used to select the best features. Three shape features sets and three texture features sets were selected. The Receiver Operating Characteristic (ROC) analyses were conducted to evaluated the classifier performance. The best result for shape feature set was accurate classification rate of 98.21%, specificity of 98.37%, sensitivity of 98.00% and the area under ROC curve of 0.99, for a ANN with 5 hidden units. The best result for texture feature set was accurate classification rate of 97.08%, specificity of 98.53%, sensitivity of 95.11% and the area under ROC curve of 0.98, for an ANN with 4 hidden units.

In this paper, we propose an efficient semi-automatic algorithm to segment a 3-D object by using a given segmentation result in a single slice. In the proposed algorithm, the segmentation is performed slice-by-slice using z correlation as well as xy correlation based on the assumption that the region to be segmented is homogeneous and has discernable boundaries. We first estimate a parametric motion model of the organ from the previous slice to the current slice, and find an estimated boundary of the organ by projecting the previous result. Then, we extract 3 kinds of seeds in the current slice by using the projected boundaries and the pixel luminance values. All extracted seeds are grown to produce the precise boundary of the organ. And wrong boundary portions due to region growing at low gradient areas are corrected by the post-processing based on a Fourier descriptor. Finally, to catch up on newly appearing areas, a two-way tracking method is applied. The proposed algorithm provides satisfactory results in segmenting kidneys from an X- ray CT body image set of 82 slices.

This paper presents a fuzzy rule-based region growing method for segmenting two-dimensional (2-D) and three-dimensional (3- D) magnetic resonance (MR) images. The method is an extension of the conventional region growing method. The proposed method evaluates the growing criteria by using fuzzy inference techniques. The use of the fuzzy if-then rules is appropriate for describing the knowledge of the legions on the MR images. To evaluate the performance of the proposed method, it was applied to artificially generated images. In comparison with the conventional method, the proposed method shows high robustness for noisy images. The method then applied for segmenting the dynamic MR images of the liver. The dynamic MR imaging has been used for diagnosis of hepatocellular carcinoma (HCC), portal hypertension, and so on. Segmenting the liver, portal vein (PV), and inferior vena cava (IVC) can give useful description for the diagnosis, and is a basis work of a pres-surgery planning system and a virtual endoscope. To apply the proposed method, fuzzy if-then rules are derived from the time-density curve of ROIs. In the experimental results, the 2-D reconstructed and 3-D rendered images of the segmented liver, PV, and IVC are shown. The evaluation by a physician shows that the generated images are comparable to the hepatic anatomy, and they would be useful to understanding, diagnosis, and pre-surgery planning.

A novel approach is presented for fully automated boundary extraction and rectification of bony tissue from planar CT data. The approach extracts and rectifies feature boundary in a hierarchical fashion. It consists of a fuzzy multilevel thresholding operation, followed by a small void cleanup procedure. Then a binary morphological boundary detector is applied to extract the boundary. However, defective boundaries and undesirable artifacts may still be present. Thus two innovative anatomical knowledge based algorithms are used to remove the undesired structures and refine the erroneous boundary. Results of applying the approach on lumbar CT images are presented, with a discussion of the potential for clinical application of the approach.

In this paper, we propose a method to automate the segmentation of airway tree structures in lung from a stack of gray-scale computed tomography (CT) images. A three- dimensional seeded region growing is performed on images without any preprocessing operation to obtain the segmented bronchus area. We first apply genetic algorithm (GA) to retrieve the seed point and it is based on the geometric features (shape, location and size) of the airway tree. By the feature of the size of the lung and airway tree, an optimal threshold value is obtained. The final extracted bronchus area with the optimal threshold value is reconstructed and visualized by 3D texture mapping method.

In this paper a method for three-dimensional (3-D) semi- automatic segmentation of volumes of medical images is described. The method is semi-automatic in the sense that, in the initial phase, the user assistance is required for manual segmentation of a certain number of slices (cross-sections) of the volume. In the second phase, the algorithm for automatic segmentation is started. The segmentation algorithm is based on the active contour approach. A semi 3-D active contour algorithm is used in the sense that additional inter-slice forces are introduced in order to constrain the obtained solution. The energy function which is minimized is modified to exploit information provided by the manual segmentation of some of the slices performed by the user. The experiments have been performed using computed tomography (CT) scans of the abdominal region of the human body. In particular, CT images of abdominal aortic aneurysms have been segmented to determine the location of aorta. The experiments have shown the feasibility of the approach.

A technique for segmentation of articular cartilage from 3D MRI scans of the knee has been developed. It overcomes the limitations of the conventionally used region growing techniques, which are prone to inter- and intra-observer variability, and which can require much manual intervention. We describe a hybrid segmentation method combining expert knowledge with directionally oriented Canny filters, cost functions and cubic splines. After manual initialization, the technique utilized 3 cost functions which aided automated detection of cartilage and its boundaries. Using the sign of the edge strength, and the local direction of the boundary, this technique is more reliable than conventional 'snakes,' and the user had little control over smoothness of boundaries. This means that the automatically detected boundary can conform to the true shape of the real boundary, also allowing reliable detection of subtle local lesions on the normally smooth cartilage surface. Manual corrections, with possible re-optimization were sometimes needed. When compared to the conventionally used region growing techniques, this newly described technique measured local cartilage volume with 3 times better reproducibility, and involved two thirds less human interaction. Combined with the use of 3D image registration, the new technique should also permit unbiased segmentation of followup scans by automated initialization from a baseline segmentation of an earlier scan of the same patient.

Heart image analysis is a challenging and important process used for a range of purposes such as image based measurement, visualization, etc. The most important step in medical image analysis is segmentation. In this work we present an algorithm for CT heart image segmentation. The segmentation is based on two basic pieces of information, pixels brightness and motion. The motion information is gathered as the optical flow information. Such information is later used for definition of an energy function for image labeling. This energy function represents a Markov random field (MRF) posterior distribution function. The MAP estimation of the segmented image has been determined using the simulated annealing (SA) algorithm.

In this study, a computerized method for detection of pulmonary embolism in spiral CT angiography was developed. The method is based on segmentation of pulmonary vessels to limit the search space for thrombi. Several three-dimensional image features such as local contrast, second derivatives, and distance to the vessel wall were employed for detection of thrombi and for elimination of false positives. Volume rendering was applied for display of detection results. Preliminary results based on several clinical data show the potential of our method.

We present further improvements to the methods of interpretation of the Posterior Capsular Opacification (PCO) images. These retro-illumination images of the back surface of the implanted lens are used to monitor the state of patient's vision after cataract operation. A common post-surgical complication is opacification of the posterior eye capsule caused by the growth of epithelial cells across the back surface of the capsule. Interpretation of the PCO images is based on their segmentation into transparent image areas and opaque areas, which are affected by the growth of epithelial cells and can be characterized by the increase in the image local variance. This assumption is valid in majority of cases. However, for different materials used for the implanted lenses it sometimes happens that the epithelial cells grow in a way characterized by low variance. In such a case segmentation gives a relatively big error. We describe an application of an anisotropic diffusion equation in a non-linear pre-processing of PCO images. The algorithm preserves the high-variance areas of PCO images and performs a low-pass filtering of small low- variance features. The algorithm maintains a mean value of the variance and guarantees existence of a stable solution and improves segmentation of the PCO images.

Fractal dimension (fd) of lesion borders has been proposed as a feature to discriminate between malignant and benign masses on MR breast images. The fd value is computed using a sample space of fractal models, an approach that reduces sensitivity to signal noise and image variability. The user specifies a rectangular region of interest (ROI) around the mass and the algorithm generates a segmentation zone from the ROI. Fractal models are constructed on multiple threshold intensity contours within the segmentation zone. Preliminary results show that the combination of statistical fd feature and expert-observer interpretations improves separation of benign from malignant breast masses when compared to expert-observer interpretations alone. The statistical fd feature has been incorporated into a prototype computer-aided-diagnosis (CAD) system that outputs the following to assist the diagnostician in determining clinical action: (1) A likelihood-of-cancer measure computed from fd and reader interpretations, (2) A binary categorical value indicating whether a test case is fd- highly suspicious or fd-inconclusive, (3) The ROI with portions of the mass border with the most cancer-like fractal characteristics highlighted.

We have developed a computer algorithm to detect breast masses on digitized mammograms. In this study, we analyze the performance of the trained algorithm with independent, clinical mammograms to assess its potential as an aid to the radiologist in mammographic interpretation. A digitized mammogram is processed with an adaptive enhancement filter followed by region growing to detect significant breast structures. Morphological and texture features are then extracted from each of the detected structures and used to identify potential breast masses. In the current study, we evaluated the performance of the algorithm with independent sets of 92 prior mammograms (films acquired 1 to 4 years prior to biopsy) and 260 preoperative mammograms from 123 patients. The computer algorithm had a 'by-film' mass detection sensitivity of 51% with 2.3 FPs/image when applied to the prior mammograms including the detection of 57% of the malignant masses. When applied to the set of preoperative mammograms, the algorithm identified 73% of the masses with 2.2 FPs/image and had a malignant mass detection sensitivity of 83%. The 'by-case' sensitivity was 67% (74% for malignant masses) and 85% (92% for malignant masses) for the prior and preoperative mammograms, respectively. This study indicates that the computer algorithm may be useful as a second reader in the clinical interpretation of mammograms because it has the ability to detect masses in both preoperative and prior mammograms.

Liver cancer is one of the leading cancerous diseases that can disappoint a physician before reaching the final diagnosis. Thus far, all cancer diagnoses should and usually do have tissue diagnose. A physician gets a little piece of tissue from the abnormal area and a pathologist determines if it is cancer or not. Therefore, the biopsy is the definitive test for liver cancer. In this paper, we present an unsupervised approach using Hopfield Neural Network (HNN) to segment color images of liver tissues prepared by standard staining method. The segmentation problem is formulated as the minimization of an energy function synonymous to that of HNN for optimization. We modify the HNN to reach a status close to the global minimum in a prespecified time of convergence. Furthermore, the nuclei and their corresponding cytoplasm regions are automatically extracted based on the features of color image histogram. The nuclei and cytoplasm regions are then used to formulate the diagnostic rules. In the analysis, we show a tables of the ratio of (nuclei/cytoplasm) image areas inside different subwindow sizes of the image. Each liver color image is represented in the RGB, HSV and HLS color spaces to investigate the effect of color system choice on the results. The automation of the extraction process in the liver pathological image can be easily implemented in the clinic in order to provide more accurate quantitative information that can help for a better liver cancer diagnosis.

We present development, application, and performance evaluation of three different texture feature extraction methods for classification of benign and malignant microcalcifications in mammograms. The steps of the work accomplished are as follows. (1) A total of 103 regions containing microcalcifications were selected from a mammographic database. (2) For each region, texture features were extracted using three approaches: co-occurrence based method of Haralick; wavelet transformations; and multi-wavelet transformations. (3) For each set of texture features, most discriminating features and their optimal weights were found using a real-valued genetic algorithm (GA) and a training set. For each set of features and weights, a KNN classifier and a malignancy criterion were used to generate the corresponding ROC curve. The malignancy of a given sample was defined as the number of malignant neighbors among its K nearest neighbors. The GA found a population with the largest area under the ROC curve. (4) The best results obtained using each set of features were compared. The best set of features generated areas under the ROC curve ranging from 0.82 to 0.91. The multi-wavelet method outperformed the other two methods, and the wavelet features were superior to the Haralick features. Among the multi-wavelet methods, redundant initialization generated superior results compared to non-redundant initialization. For the best method, a true positive fraction larger than 0.85 and a false positive fraction smaller than 0.1 were obtained.

We formulate a model for probability distributions on image spaces. We show that any distribution of images can be factored exactly into conditional distributions of feature vectors at one resolution (pyramid level) conditioned on the image information at lower resolutions. We would like to factor this over positions in the pyramid levels to make it tractable, but such factoring may miss long-range dependencies. To fix this, we introduce hidden class labels at each pixel in the pyramid. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters can be found with maximum likelihood estimation using the EM algorithm. We have obtained encouraging preliminary results on the problems of detecting masses in mammograms.

In this paper, we propose a method of recognition of lung nodules using 3D nodule and blood vessel models considering uncertainty of recognition. Region of interest (ROI) areas are extracted by our quoit filter which is a kind of Mathematical Morphology filter. We represent nodules as sphere models, blood vessels as cylinder models and the branches of the blood vessels as the connections of the cylinder models, respectively. All of the possible models for nodules and blood vessels are generated which can occur in the ROI areas. The probabilities of the hypotheses of the ROI areas coming from the sphere models are calculated and the probabilities for the cylinder models are also calculated. The most possible sphere models and cylinder models which maximize the probabilities are searched considering uncertainty of recognition. If the maximum probability for the nodule model is higher, the shadow candidate is determined to be abnormal. By applying this new method to actual CT images (37 patient images), good results have been acquired.

This paper describes a prototype computer aided diagnosis system to assist in the interpretation of mammograms. The distinctive feature of our work is the combination of image processing and decision support. We wish, in our system, to relate the data in a digital image to a decision contained in a clinical guideline describing a patient's management. Our system is designed to present a user with sets of arguments for each of the possible interpretations of a feature detected on the image and for each of the possible management options that might be followed in handling the patient's care. We have carried out an extensive knowledge elicitation exercise, involving the analysis of 'think out loud' protocols obtained from expert radiologists interpreting mammograms form a carefully selected test set. The results of this analysis reveal which terms capture the most salient characteristics of calcifications. These terms will be used to construct the arguments used in the decision support provided by CADMIUM II. The final element of CADMIUM II is a library of image processing algorithms. A set of different approaches to the detection and characterization of calcifications has been implemented. The image processing is used to provide a quantitative estimate of the evidence that an image contains in support of an argument.

Multiple Sclerosis (MS) is an acquired disease of the central nervous system. Subjective cognitive and ambulatory test scores on a scale called EDSS are currently utilized to assess the disease severity. Various MRI protocols are being investigated to study the disease based on how it manifests itself in the images. In an attempt to eventually replace EDSS by an objective measure to assess the natural course of the disease and its response to therapy, we have developed image segmentation methods based on fuzzy connectedness to quantify various objects in multiprotocol MRI. These include the macroscopic objects such as lesions, the gray matter (GM), white matter (WM), cerebrospinal fluid (CSF), and brain parenchyma as well as the microscopic aspects of the diseased WM. Over 1000 studies have been processed to date. By far the strongest correlations with the clinical measures were demonstrated by the Magnetization Transfer Ratio (MTR) histogram parameters obtained for the various segmented tissue regions emphasizing the importance of considering the microscopic/diffused nature of the disease in the individual tissue regions. Brain parenchymal volume also demonstrated a strong correlation with the clinical measures indicating that brain atrophy is an important indicator of the disease. Fuzzy connectedness is a viable segmentation method for studying MS.

In this paper, we present a computer-aided diagnosis (CAD) system for lung cancer to detect nodule candidates at an early stage from the present and the early helical CT screening of the thorax. We developed an algorithm that can compare automatically the slice images of present and early CT scans for the assistance of comparative reading in retrospect. The algorithm consists of the ROI detection and shape analysis based on comparison of each slice image in the present and the early CT scans. The slice images of present and early CT scans are both displayed in parallel and analyzed quantitatively in order to detect the changes in size and intensity affection. We validated the efficiency of this algorithm by application to image data for mass screening of 50 subjects (total: 150 CT scans). The algorithm could compare the slice images correctly in most combinations with respect to physician's point of view. We validated the efficiency of the algorithm which automatically detect lung nodule candidates using CAD system. The system was applied to the helical CT images of 450 subjects. Currently, we are carrying out the clinical field test program using the CAD system. The results of our CAD system have indicated good performance when compared with physician's diagnosis. The experimental results of the algorithm indicate that our CAD system is useful to increase the efficiency of the mass screening process. CT screening of thorax will be performed by using the CAD system as a counterpart to the double reading technique actually used in herical CT screening program, not by using the film display.

Chest radiographs represent a difficult class of images concerning automatic analysis with image processing methods. In our former work we presented a model based method to detect the rib borders and implemented a compensation algorithm of the rib structures. Recently we developed an improved method for rib border detection and algorithms to find the objects like chest border, vertebral spine, heart and intravascular catheter within a model driven approach. The determined borders of these objects allow further analysis and image enhancement for diagnose assistance.

Any segmentation approach assumes certain knowledge concerning data modalities, relevant organs and their imaging characteristics. These assumptions are necessary for developing criteria by which to separate the organ in question from the surrounding tissue. Typical assumptions are that the organs have homogeneous gray-value characteristics (region growing, region merging, etc.), specific gray-value patterns (classification methods), continuous edges (edge-based approaches), smooth and strong edges (snake approaches), or any combination of these. In most cases, such assumptions are invalid, at least locally. Consequently, these approaches prove to be time consuming either in their parameterization or execution. Further, the low result quality makes post- processing necessary. Our aim was to develop a segmentation approach for large 3D data sets (e.g., CT and MRI) that requires a short interaction time and that can easily be adapted to different organs and data materials. This has been achieved by exploiting available knowledge about data material and organ topology using anatomical models that have been constructed from previously segmented data sets. In the first step, the user manually specifies the general context of the data material and specifies anatomical landmarks. Then this information is used to automatically select a corresponding reference model, which is geometrically adjusted to the current data set. In the third step, a model-based snake approach is applied to determine the correct segmentation of the organ in question. Analogously, this approach can be used for model-based interpolation and registration.

Segmentation of brain hemispheres is necessary to study left- right differences in structure and function. For extraction of a 3D individual region-of-interest atlas of the human brain, detection of the midplane is the sine qua non as it provides the reference plane for determining other anatomical objects. Extraction of the sagittal midplane is done in two main steps. First, a 2D filter is used to give a first approximation of the midplane position. To model symmetry properties of the midplane neighborhood, the different filter columns contain class-dependent weights for cerebrospinal fluid, gray and white matter. The filter can be rotated in a range of angles. In a user-defined range of planes, the global maximum of the filter response is searched for and the resulting position is utilized to restrict the search in the remaining planes. In a second step, midplane extraction is refined by searching for the optimal path of the midplane within the filter mask at optimum position. Symmetry properties are modeled analogous to the first step with class-dependent weights of the filter columns. The extraction of the midplane gives accurate and reliable results in simulated data sets and patient studies even if asymmetric artifacts are simulated.

To model the true shape of MRI brain images, automatically classified T1-weighted 3D MRI images (gray matter, white matter, cerebrospinal fluid, scalp/bone and background) are utilized for simulation of grayscale data and imaging artifacts. For each class, Gaussian distribution of grayscale values is assumed, and mean and variance are computed from grayscale images. A random generator fills up the class images with Gauss-distributed grayscale values. Since grayscale values of neighboring voxels are not correlated, a Gaussian low-pass filtering is done, preserving class region borders. To simulate anatomical variability, a Gaussian distribution in space with user-defined mean and variance can be added at any user-defined position. Several imaging artifacts can be added: (1) to simulate partial volume effects, every voxel is averaged with neighboring voxels if they have a different class label; (2) a linear or quadratic bias field can be added with user-defined strength and orientation; (3) additional background noise can be added; and (4) artifacts left over after spoiling can be simulated by adding a band with increasing/decreasing grayscale values. With this method, realistic-looking simulated MRI images can be produced to test classification and segmentation algorithms regarding accuracy and robustness even in the presence of artifacts.

One of the basic algorithm for the determination of the watershed transformation is the Meyer 2 algorithm. Unfortunately, the algorithm can lead to isolated regions and like other watershed approaches it also results in some inaccuracies due to the general approach of the WST. We developed a new strategy for the Meyer 2 algorithm resulting in the solution for these problems. For this the algorithm is applied on a more precise derivative with subpoint accuracy computing the derivatives for each direction separately. The labeled local derivatives are then used to label the image points. Immediately closed contours at subpoint locations are obtained and each point is assigned to a label or region respectively.

This paper reports the development of a non-rigid registration technique to bring into alignment a sequence of a patient's single-view mammograms acquired at different times. This technique is applied in a patient site model supported change detection algorithm with a clinical goal of lesion detection and tracking. The algorithm flow contains four steps: preprocessing, image alignment, change detection, and site model updating. The preprocessing step includes segmentation, using standard finite normal mixture and Markov random field models, morphological processing, monotony operators, and Gaussian filtering. The site model in this research is composed of object boundaries, previous change, potential control points, and raw/segmented images. In the alignment step, the current mammogram is aligned to the site model using a two step process consisting of principle axis of the skin line followed by thin-plate spline using matched points from the potential control point pool. With the assumption of minimal global change, subtraction and thresholding will be used to create the change map that highlights significant changes. Finally, the change information will be used to update the site model. This two-step registration process facilitates change detection by aligning corresponding regions of mammograms so local change analysis can be performed in a coherent manner. The result of the change detection algorithm will be a local change and a patient specific site model showing past and present conditions.

Spiral CT images were obtained of 21 SPN patients before and after the injection of an intravenous contrast agent. On pre- and post-injection images, nodules were isolated using a semi- automated contouring procedure; the resulting contours, as well as their internal pixels, were combined to form regions of interest (ROIs). These ROIs were then used to measure each nodule's CT attenuation, texture, volume and shape. Peak enhancement was calculated as the maximum difference between average gray levels in central areas of post-contrast and pre- contrast images for each nodule. Stepwise feature selection chose the best subset of discriminating measurements. A linear classifier was then trained and tested using chosen features. Using a commonly applied feature, peak enhancement, by itself, all malignant cases were classified correctly, but 6/12 benign cases were misclassified. Using peak contrast enhancement, a three-dimensional shape measure and two texture measures, 20/21 cases (95.2%) were classified correctly by resubstitution, and 17/21 (81.0%) by jackknifing. The combination of contrast enhancement, three dimensional shape features and texture features holds promise for accurate classification of solitary pulmonary nodules imaged on CT.

Ultrasound B-scan images often exhibit intensity inhomogeneities caused by non-uniform beam attenuation within the body. These cause major problems for image analysis, both by manual and computer-aided techniques, particularly the computation of quantitative measurements. We present a statistical model that exploits knowledge of tissue properties and intensity inhomogeneities in ultrasound for simultaneous contrast enhancement and image segmentation. The underlying model was originally proposed for correction of the B₁ bias field distortion and segmentation of magnetic resonance (MR) images. A physics-based model of intensity inhomogeneities in ultrasound images shows that the bias field correction method is well suited to ultrasound B-scan images. The tissue class labeling and the intensity correction field are estimated using the maximum a posteriori (MAP) principle, in an iterative, multi-resolution manner. The algorithm has been applied to breast and cardiac ultrasound images. The results demonstrate that it can successfully remove intensity inhomogeneities caused by varying attenuation as well as uninteresting intensity changes of background tissues. With the removal of intensity inhomogeneities, significant improvement is achieved in tissue contrast and segmentation result.

The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain MR images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogram-based model, the FM has an intrinsic limitation -- no spatial information is taken into account. This causes the FM model to work only on well-defined images with low noise level. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a Markov random field whose state sequence cannot be observed directly but which can be observed through observations. Mathematically, it can be shown that the FM model is a degenerate version of the HMRF model. The advantage of the HMRF model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites. To fit the HMRF model, an expectation-maximization (EM) algorithm is used. We show that by incorporating both the HMRF model and the EM algorithm into an HMRF-EM framework, an accurate and robust segmentation can be achieved, which is demonstrated by comparison experiments with the FM model-based segmentation.

An algorithm is developed for fast, accurate identification of lung fields in chest radiographs for use in various computer- aided diagnosis (CAD) schemes. The method we presented simplifies the current approach of edge detection from derivatives by using only the first derivative of the profiles of each image, and combining it with pattern classification and image feature analysis in determining both the region of interest (ROI) and the actual lung boundaries. Moreover, instead of using the traditional curve fitting to delineate the detected lung field, we applied an iterative contour smoothing algorithm to each of the four detected boundary segments (lateral, medial, top and diaphragm edges) to form a closed smooth boundary for each lung. These improvements result in dramatic reduction of the running time and more accurate boundary detection, especially the diaphragm edges. The proposed algorithm has been tested with 40 posterior- anterior (PA) chest images. The detected left and right lung fields have an averaged accuracy of over 95%.

The analysis of functional MR images of the brain such as FMRI and neuro perfusion is significantly limited by movement of the head during image acquisition. Already small motions introduce artifacts in voxel-based statistical analysis and restrict the assessment of functional information. The retrospective compensation of head motion is usually addressed by image registration techniques which spatially align the images of the time-series. In this paper we investigate the relevance of intermediate interpolation during the registration process, similarity measure and optimization scheme by means of statistical consistency of the registration results. Experiments show that cubic and quartic interpolation remarkably improve the consistency when compared to linear methods. The use of larger interpolation kernels, however, does not result in further improvements. Measures based on the mean squared error are successfully applied to FMRI time- series which provide constant tissue-to-image transfer. However, they are not suitable for neuro perfusion imaging since the change of image intensity during the inflow of the contrast agent affords measures typically applied in multi- modality registration. Our results indicate that a recently proposed measure based on local correlation is preferable to mutual information in the case of neuro perfusion.

It is often the case that information about a process can be obtained using a variety of methods. Each method is employed because of specific advantages over the competing alternatives. An example in medical neuro-imaging is the choice between fMRI and MEG modes where fMRI can provide high spatial resolution in comparison to the superior temporal resolution of MEG. The combination of data from varying modes provides the opportunity to infer results that may not be possible by means of any one mode alone. We discuss a Bayesian and learning theoretic framework for enhanced feature extraction that is particularly suited to multi-modal investigations of massive data sets from multiple experiments. In the following Bayesian approach, acquired knowledge (information) regarding various aspects of the process are all directly incorporated into the formulation. This information can come from a variety of sources. In our case, it represents statistical information obtained from other modes of data collection. The information is used to train a learning machine to estimate a probability distribution, which is used in turn by a second machine as a prior, in order to produce a more refined estimation of the distribution of events. The computational demand of the algorithm is handled by proposing a distributed parallel implementation on a cluster of workstations that can be scaled to address real-time needs if required. We provide a simulation of these methods on a set of synthetically generated MEG and EEG data. We show how spatial and temporal resolutions improve by using prior distributions. The method on fMRI signals permits one to construct the probability distribution of the non-linear hemodynamics of the human brain (real data). These computational results are in agreement with biologically based measurements of other labs, as reported to us by researchers from UK. We also provide preliminary analysis involving multi-electrode cortical recording that accompanies behavioral data in pain experiments on freely moving mice subjected to moderate heat delivered by an electric bulb. Summary of new or breakthrough ideas: (1) A new method to estimate probability distribution for measurement of nonlinear hemodynamics of brain from a multi- modal neuronal data. This is the first time that such an idea is tried, to our knowledge. (2) Breakthrough in improvement of time resolution of fMRI signals using (1) above.

Image guidance of cryotherapy is usually performed using ultrasound or x-ray CT. Despite the ability of CT to display the full 3D structure of the iceball, including frozen and unfrozen regions, the quality of the images is compromised by the presence of high density streak artifacts. To suppress these artifacts we applied Temporal Digital Subtraction (TDS). This TDS method has the added advantage of improving the gray scale contrast between frozen and unfrozen tissue in the CT images. Two sets of CT images were taken of a phantom material, cryoprobes and a urethral warmer (UW) before and during the cryoprobe freeze cycle. The high density artifacts persisted in both image sets. TDS was performed on these two image sets using the corresponding mask image of unfrozen material and the same geometrical configuration of the cryoprobes and the UW. The resultant difference image had a significantly reduced content of the artifacts. This TDS can be used in x-ray CT assisted cryotherapy to significantly suppress or eliminate high density x-ray CT streak artifacts by digitally processing x-ray CT images. Applying TDS in cryotherapy will facilitate estimation of the amount and location of all frozen and unfrozen regions, potentially making cryotherapy safer and less operator dependent.

Medical imaging modalities often provide image material in more than two dimensions. However, the analysis of voxel data sets or image sequences is usually performed using only two- dimensional methods. Furthermore, four-dimensional medical image material (sequences of stacks of images) is available already for clinical diagnoses. Contrarily, four-dimensional image processing methods are almost unknown. We present an active contour model based on balloon models that allows a coherent segmentation of image material of any desired dimension. Our model is based on linear finite elements and combines a shape representation with an iterative segmentation algorithm. Additionally, we present a novel definition for the computation of external influences to deform the model. The appearance of relevant edges in the image is defined by image potentials and a filter kernel function. The filter kernel is applied with respect to the location and orientation of finite elements. The model moves under the influence of internal and external forces and avoids collisions of finite elements in this movement. Exemplarily, we present segmentation results in 2D (radiographs), 3D (video sequence of the mouth), and 4D (synthetic image material) and compare our results with propagation methods. The new formalism for external influences allows the model to act on graylevel as well as color images without pre-filtering.

We describe a 'learning-from-examples'-method to automatically adjust parameters for a balloon model. Our goal is to segment arbitrarily shaped objects in medical images with as little human interaction as possible. For our model, we identified six significant parameters that are adjusted with respect to certain applications. These parameters are computed from one manual segmentation drawn by a physician. (1) The maximal edge length is derived from a polygon-approximation of the manual segmentation. (2) The size of the image subset that exerts external influences on edges is set according to the scale of gradients normal to the contour. (3) The offset of the assignment from graylevels to image potentials is adjusted such that the propulsive pressure overcomes image potentials in homogeneous parts of the image. (4) The gain of this assignment is tuned to stop the contour at the border of objects of interest. (5) The strength of deformation force is computed to balance the contour at edges with ambiguous image information. (6) These parameters are computed for both, positive and negative pressure. The variation that gives the best segmentation result is chosen. The analytically derived adjustments are optimized with a genetic algorithm that evolutionarily reduces the number of misdetected pixels. The method is used on a series of histochemically stained cells. Similar segmentation quality is obtained applying both, manual and automatic parameter setting. We further use the method on laryngoscopic color image sequences, where, even for experts, the manual adjustment of parameters is not applicable.

With the advent of corneal confocal microscopy, investigators can determine keratocyte density in the corneal stroma in vivo. We and others have written automated algorithms to measure keratocyte density from human corneal confocal images. Such algorithms are only accurate if they exclude images of stromal nerve bundles (elongated objects) that would otherwise be counted as keratocytes. In this study we devised an algorithm to identify stromal nerve bundles and exclude them from measurements of keratocyte density. Nerve bundles were detected based on their size and aspect ratio, and were then subtracted from images by using a combination of morphology operations and direction calculations. The validity of nerve removal on measurements of keratocyte density was assessed. Keratocyte density was measured from confocal images of three normal human corneas in vivo by using our algorithm with nerve removal. After the same eyes underwent enucleation, density was measured manually from histologic sections. Keratocyte density was also measured from confocal images of 57 normal corneas in vivo (57 subjects) with and without nerve removal. In the three enucleated eyes, there was no significant difference between keratocyte density measured by automated counting with nerve removal and by histologic methods (P equals 0.75). However, in the 57 normal corneas, use of the nerve-removal algorithm reduced estimates of density by 57.0 +/- 164.6 cells/mm³ (mean +/- SD, p < 0.038) in the anterior two-thirds of the stroma.

This paper deals with human motion analysis without using markers. It presents a new approach of human motion tracking in three sequence of images acquired simultaneously by a calibrated vision system. The analysis process leads to the three-dimensional reconstruction of a superquadric-based model representing the human body. The motion on the images is first computed with an optical flow method; it is followed by a crest line detection and by the classification of the parts of the superquadric with a Least Median of Squares algorithm. The results presented in the following concern more specifically the analysis of movement disabilities of a human leg during the gait.

Heart wall motion abnormalities are the very sensitive indicators of common heart diseases, such as myocardial infarction and ischemia. Regional strain analysis is especially important in diagnosing local abnormalities and mechanical changes in the myocardium. In this work, we present a complete method for the analysis of cardiac motion and the evaluation of regional strain in the left ventricular wall. The method is based on the generalized spline models and tagged magnetic resonance images (MRI) of the left ventricle. The whole method combines dynamical tracking of tag deformation, simulating cardiac movement and accurately computing the regional strain distribution. More specifically, the analysis of cardiac motion is performed in three stages. Firstly, material points within the myocardium are tracked over time using a semi-automated snake-based tag tracking algorithm developed for this purpose. This procedure is repeated in three orthogonal axes so as to generate a set of one-dimensional sample measurements of the displacement field. The 3D-displacement field is then reconstructed from this sample set by using a generalized vector spline model. The spline reconstruction of the displacement field is explicitly expressed as a linear combination of a spline kernel function associated with each sample point and a polynomial term. Finally, the strain tensor (linear or nonlinear) with three direct components and three shear components is calculated by applying a differential operator directly to the displacement function. The proposed method is computationally effective and easy to perform on tagged MR images. The preliminary study has shown potential advantages of using this method for the analysis of myocardial motion and the quantification of regional strain.

A maximum likelihood-expectation maximization (ML-EM) reconstruction algorithm has been developed that allows random coincidence correction for the phantom we used and the reconstructed images are better than those obtained by convolution backprojection (CBP) for positron emission tomography (PET) studies in terms of spatial resolution, image artifacts and noise. With our algorithm reconstruct the true coincidence events and random coincidence events were reconstructed separately. We also calculated the random ratio from the measured projection data (singles) using line and cylindrical phantoms, respectively. From cylindrical phantom experiments, the random event ratio was 41.8% to 49.1% in each ring. These results are close to the ratios obtained from geometric calculation, which range from 45.0% to 49.5%. The random ratios and the patterns of random events provide insightful information for random correction. This information is particularly valuable when the delay window correction is not available as in the case of our PET system.

Low-contrast features such as thrombus, dissection, and even stents can be difficult to detect in coronary x-ray images or angiograms. For these reasons we propose to improve the clinical visualization of low-contrast structures using layer decomposition. Our method for layer decomposition models the cone-beam projections through the chest as a set of superposed layers moving with translation, rotation, and scaling. We solve for the layer motions using phase correlation methods. We solve for the layer densities by averaging along moving trajectories and subtracting new layer densities from previous layer estimates. We apply layer decomposition to clinical coronary angiograms with and without contrast material. The reconstructed vessel layer represents a motion-compensated temporal average of structures co-moving with the vessel. Subtraction of background layers from the original image sequence yields a tracked background-subtracted sequence which has no vessel-motion artifacts and almost no increase in noise, unlike standard background substraction techniques. Layer decomposition improves vessel definition and visibility of low-contrast objects in cine x-ray image sequences.

A template-matching approach to registration of volumetric images is described. The process automatically selects about a dozen highly detailed and unique templates (cubic or spherical subvolumes) from the target volume and locates the templates in the reference volume. The centroids of the 'best' four correspondences are then used to determine the transformation matrix that resamples the target volume to overlay the reference volume. Different similarity measures used in template matching are discussed and preliminary results are presented. The proposed registration method produces a median error of 2.8 mm when registering Venderbilt image data sets, with average registration time of 2.5 minutes on a 400 MHz PC.

Dynamic imaging is used in magnetic resonance imaging examinations when several shots of the same anatomical cross section need be acquired at a much high temporal resolution than what normal scan procedures would allow. Present techniques improve the temporal resolution by reducing the number of samples required to reconstruct the dynamic images. This comes at the expense of a reduction in either the spatial resolution or the signal-to-noise ratio. In this work, a new technique is presented for improving both the temporal and spatial resolutions without sacrificing the signal-to-noise ratio. The technique is based on modeling individual lines of the reconstructed images with a series of super-resolution rectangular pulses. The dynamic changes of the object can be determined by estimating the parameters of these pulses at the different shots. In particular, a robust estimation is achieved by using linear associative memories, which have been classically used in pattern recognition applications. The technique starts by acquiring a full resolution image for the imaged slice, from which accurate initial values of the parameters are computed. These values are used to train the linear associative memory system to establish the mapping between a few acquired samples of a certain dynamic image and its model parameters. Results on simulated images demonstrated the value of the technique to accurately reconstruct high spatial resolution dynamic images at a significantly reduced scanning time.

The goal of this work was to develop a warping technique for mapping a brain image to another image or atlas data, with minimum user interaction and independent of gray level information. We have developed and tested three different methods for warping MR brain images. We utilize a deformable contour to extract and warp the boundaries of the two images. A mesh-grid coordinate system is constructed for each brain, by applying a distance transformation to the resulting contours, and scaling. In the first method (MGC), the first image is mapped to the second image based on a one-to-one mapping between different layers defined by the mesh-grid. In the second method (IDW), the corresponding pixels in the two images are found using the above mesh-grid system and a local inverse-distance weights interpolation. In the third proposed method (TSB), a subset of grid points is used for finding the parameters of a spline transformation, which defines the global warping. The warping methods were applied to clinical MR consisting of diffusion weighted and T2 weighted images of the human brain. The IDW and TSB methods were superior in ranking of diagnostic quality of the warped MR images to the MGC (p less than 0.01) as defined by a neuroradiologist. The deformable contour warping produced excellent diagnostic quality for the diffusion-weighted images co-registered and warped to T2 weighted images.

The quality and quantitative accuracy of transmission CT images are affected by artifacts due to truncation of the projection data. In this study, the effect of data sampling on the quantitative accuracy of transmission CT images reconstructed from truncated projections has been investigated. Parallel-beam projections with different sets of acquisition and data sampling parameters were simulated. In deciding whether a set of parameters provided sufficient data sampling, use was made of the condition number obtained from the singular value decomposition of the projection matrix. The results of the study indicate that for noise-free data the truncation artifacts which are present in images reconstructed using iterative algorithms can be reduced or completely eliminated provided that the data sampling is sufficient, and an adequate number of iterations is performed. However, when a null space is present in the singular value decomposition, the iterative reconstruction methods fail to recover the object. The convergence of the reconstructed attenuation maps depends on the sampling and is faster as the number of angles and/or the number of projection bins is increased. Furthermore, the higher the degree of truncation the larger is the number of iterations required in order to obtain accurate attenuation maps. In the presence of noise, the number of iterations required for the best compromise of noise and image detail is decreased with increased noise level and higher degree of truncation, resulting in inferior reconstructions. Finally, the use of the body contour as support in the reconstructions resulted in quantitatively superior reconstructed images.

The advent of large (40 cm X 40 cm) flat panel x-ray detection devices has ushered in a new era of synthetically generating tomographic image sets for many diagnostic applications. Tomosynthetic image sets correspond to focal planes passing through an imaged object and are commonly generated by algebraically reconstructing (backprojecting) a set of two-dimensional (2D) projections. Tomosynthetic image sets typically contain a significant amount of cross-sectional blur. This paper describes a system for modeling the tomosynthesis process and proposes a methodology for quantitatively and qualitatively evaluating erroneous intensity values in reconstructed three-dimensional (3D) tomosynthetic image sets.

For the analysis of renal function, sequences of 90 magnet resonance images of the abdominal region showing both kidneys are taken in intervals of two seconds after a contrast medium was applied. Respiration of the patients during the acquisition of the images leads to organ movements throughout the series. These displacements are corrected by using an extended cepstral technique. To minimize registration errors caused by inhomogeneous movements of organs and tissues during respiration, the cepstrum-relevant part of the images is limited to small regions of interest around both kidneys. Even organ movements of sub-pixel range can be detected. After correction, the kidneys are the same position throughout the sequence. The regions of interest marked in one image are projected to all other images. To archive diagnostic results, dynamic contrast medium evaluations for different tissues of the kidneys are computed with signal-intensity-time graphs. Using a-priori knowledge about parameters of the SIT-graph for a whole kidney and about organ shape and structure, pixels of the kidney-segment are divided into the three classes renal cortex, medulla and pelvis. As a result, precise graphs can be computed for each tissue. The evaluation of the system is in progress, time save is more than one hour per patient.

Medical image data contain several types of uncertain or vague information. Therefore, the knowledge about the data is also vague. Consequently, for the segmentation and classification of the image data the use of vague knowledge should be allowed. Finally, the optimization of such systems dealing with vague information should also be done automatically. Using fuzzy descriptions for the segmentation and analysis of medical image data has provided better results than the exclusive use of standard methods. More often, structures can be segmented and classified more adequately. Applications have been developed to segment brain structures and tumors in MRI- data. By applying neural networks, good results for the step of image improvement (pre-processing) and determination of regions of interest (ROI) in image data were obtained. Even more the classification of structures with neural networks has shown also good results. The optimization of the knowledge base was done with evolution strategies. Therefore, the optimization time was reduced to a fraction of the time needed for a manual optimization.

The study of coronary arteries has evolved from examining gross anatomy and morphology to scrutinizing micro-anatomy and cellular composition. Technological advances such as high- resolution digital microscopes and high precision cutting devices have allowed examination of coronary artery morphology and pathology at micron resolution. We have developed a software toolkit to analyze histological sections. In particular, we are currently engaged in examining normal coronary arteries in order to provide the foundation for study of remodeled tissue. The first of two coronary arteries was stained for elastin and collagen. The second coronary artery was sectioned and stained for cellular nuclei and smooth muscle. High resolution light microscopy was used to image the sections. Segmentation was accomplished initially with slice- to-slice thresholding algorithms. These segmentation techniques choose optimal threshold values by modeling the tissue as one or more distributions. Morphology and image statistics were used to further differentiate the thresholded data into different tissue categories therefore refine the results of the segmentation. Specificity/sensitivity analysis suggests that automatic segmentation can be very effective. For both tissue samples, greater than 90% specificity was achieved. Summed voxel projection and maximum intensity projection appear to be effective 3-D visualization tools. Shading methods also provide useful visualization, however it is important to incorporate combined 2-D and 3-D displays. Surface rendering techniques (e.g. color mapping) can be used for visualizing parametric data. Preliminary results are promising, but continued development of algorithms is needed.

Nonlinear anisotropic diffusion filtering is a procedure based on nonlinear evolution partial differential equations which seeks to improve images qualitatively by removing noise while preserving details and even enhancing edges. However, well known implementations are sensitive to parameters which are necessarily tuned to sharpen a narrow range of edge slopes; otherwise, edges are either blurred or staircased. In this work, nonlinear anisotropic diffusion filters have been developed which sharpen edges over a wide range of slopes and which reduce noise conservatively with dissipation purely along feature boundaries. Specifically, the range of sharpened edge slopes is widened as backward diffusion normal to level sets is balanced with forward diffusion tangent to level sets. Also, noise is reduced by selectively altering the balance toward diminishing normal backward diffusion and particularly toward total variation filtering. The theoretical motivation for the proposed filters is presented together with computational results comparing them with other nonlinear anisotropic diffusion filters on both phantom images and magnetic resonance images.

Optical Tomography (OT) can provide useful information about the interior distribution of optical properties in various body parts, such as the brain, breast, or finger joints. This novel medical imaging modality uses measured transmission intensities of near infrared light that are detected on accessible surfaces. Image reconstruction schemes compute from the measured data cross sectional images of the optical properties throughout the body. The image quality and the computational speed largely depend on the employed reconstruction method. Of considerable interest are currently so-called model-based iterative image reconstruction schemes, in which the reconstruction problem is formulated as an optimization problem. The correct image equals the spatial distribution of optical properties that leads to a minimum of a user-defined objective function. In the past several groups have developed steepest-gradient-descent (SGD) techniques and conjugate-gradient (CG) methods, which start from an initial guess and search for the minimum. These methods have shown some good initial results, however, they are known to be only slowly converging. To alleviate this disadvantage we have implemented in this work a quasi-Newton (QN) method. We present numerical results that show that QN algorithms are superior to CG techniques, both in terms of conversion time and image quality.

We have been developing a temporal subtraction technique to assist radiologists in the detection of interval changes of pulmonary abnormalities on digital chest radiographs. By subtracting a previous image from a current one, a temporal subtraction image is obtained, in which the lesions can be enhanced because skeletal structures such as ribs and clavicles are eliminated. Although the quality of the subtraction images obtained with our previous technique is relatively good, minor misregistration artifacts were observed in many cases because of the use of polynomial fitting of shift values. In this study, we employed three new techniques to reduce the misregistration artifacts in the temporal subtraction images. The first was a rib edge matching technique which was used to align the rib structures approximately in the two images. The second was an increase in the number of template and search area regions of interest (ROIs) in the two images. The third was the use of an elastic matching technique for the replacement of the polynomial fitting technique employed in the previous subtraction technique. With the new techniques, the quality of subtraction images was improved significantly. In particular, the number of subtraction images with excellent quality was greatly increased from 37% to 57%.

The distinct feature of data acquisition for magnetic resonance imaging (MRI) was that the data were sampled on frequency domain instead of spatial domain. Therefore, the acquired data must be inverse Fourier transformed to generate images. To apply fast Fourier transform (FFT) algorithm, the data were usually acquired on rectilinear grid. However, acquiring data on rectilinear grid was not very efficient in MRI. A spiral trajectory that started at the origin of the frequency domain and span out to higher spatial frequency was more efficient and faster than the conventional method. Since the spiral trajectory did not sample on rectilinear grid, raw data must be re-interpolated onto rectilinear grid prior to inverse FFT. This re-gridding process was done using an off- line reconstruction program. When the platforms to run the program grew, the efforts required on maintaining the program became prohibitive. This problem could be solved through the platform-independent Java programming language. In this paper, we reported on our attempt to implement the spiral MR image reconstruction program in Java. We showed that the performance was not significantly impacted and it was practical to use a platform-independent reconstruction program.

Shading is a prominent phenomenon in microscopy, reflecting the inherent imperfections of the image formation process and manifesting itself via spurious intensity variations not present in the original scene. The elimination of shading effects is frequently necessary for subsequent image processing tasks, especially if quantitative analysis is the final goal. In this paper a novel method for retrospective shading correction is proposed. First, the image formation process and the corresponding shading effects are described by a linear image formation model, consisting of an additive and a multiplicative shading component that are modeled by the parametric polynomial surfaces. Second, shading correction is performed by the inverse of the image formation model, whose shading components are estimated retrospectively by minimizing the entropy of the acquired images. The method was qualitatively and quantitatively evaluated by using artificial and real microscopical images of muscle fibers. A number of qualitative results confirmed that entropy is an appropriate measure for shading correction. Quantitative results indicate that the method does not introduce additional intensity variations but only reduces them if they exist. In conclusion, the proposed method uses all the information available in the images, it enables the optimization of arbitrarily complex image formation models, and as such may have applications in and beyond the field of microscopical imaging, for example, in MRI.

Women who have large breast area that is mammographically dense are greater risk of breast cancer than women with less mammographically dense breasts. It is a labor-intensive task to generate such a breast cancer risk information with the conventional screen film mammography. We have developed an automatic method to segment dense breast tissue areas using images acquired from full-field digital mammography systems. To evaluate its performance, a study was conducted to compare the segmentation results between the automatic method and a manually contouring method. A quantitative measurement, (delta) , is defined as the proportion of the segmented areas within a breast. The evaluation results indicate that there are 12 images whose (delta) difference between the automatic method and the manual method is less than 5%. Forty-nine images are between 5% and 10% and twenty images are within 15% in difference. On average, the process time required for the automatic method is approximately 18 seconds per image and 33 seconds per image for the manual method. The performance of our automatic method is comparable with the manual method. Yet, the automatic method does not require human intervention with the computer. We believe the automatic dense breast tissue segmentation method can be an effective tool to conduct studies of risk for breast cancer using FFDM images.

Thanks to its ability to yield functionally-based information, the SPECT imagery technique has become a great help in the diagnostic of cerebrovascular diseases. Nevertheless, due to the imaging process, SPECT images are blurred and consequently their interpretation by the clinician is often difficult. In order to improve the spatial resolution of these images and then to facilitate their interpretation, we propose herein to implement a deconvolution procedure relying on an accurate distribution mixture parameter estimation procedure. Parameters of this distribution mixture are efficiently exploited in order to prevent overfitting of the noisy data or to determine the support of the object to be deconvolved when this one is needed. In this context, we compare the deconvolution results obtained by the Lucy-Richardson method and by the recent blind deconvolution technique called the NAS-RIF algorithm on real and simulated brain SPECT images. The NAS-RIF performs the best and shows significant contrast enhancement with little mottle (noise) amplification.

The purpose of this work was to evaluate three volumetric registration methods in terms of technique, user-friendliness and time requirements. CT and SPECT data from 11 patients were interactively registered using: a 3D method involving only affine transformation; a mixed 3D - 2D non-affine (warping) method; and a 3D non-affine (warping) method. In the first method representative isosurfaces are generated from the anatomical images. Registration proceeds through translation, rotation, and scaling in all three space variables. Resulting isosurfaces are fused and quantitative measurements are possible. In the second method, the 3D volumes are rendered co-planar by performing an oblique projection. Corresponding landmark pairs are chosen on matching axial slice sets. A polynomial warp is then applied. This method has undergone extensive validation and was used to evaluate the results. The third method employs visualization tools. The data model allows images to be localized within two separate volumes. Landmarks are chosen on separate slices. Polynomial warping coefficients are generated and data points from one volume are moved to the corresponding new positions. The two landmark methods were the least time consuming (10 to 30 minutes from start to finish), but did demand a good knowledge of anatomy. The affine method was tedious and required a fair understanding of 3D geometry.

The accurate comparison of inter-individual 3D image brain datasets requires non-affine transformation techniques (warping) to reduce geometric variations. Constrained by the biological prerequisites we use in this study a landmark-based warping method with weighted sums of displacement vectors, which is enhanced by an optimization process. Furthermore, we investigate fast automatic procedures for determining landmarks to improve the practicability of 3D warping. This combined approach was tested on 3D autoradiographs of Gerbil brains. The autoradiographs were obtained after injecting a non-metabolized radioactive glucose derivative into the Gerbil thereby visualizing neuronal activity in the brain. Afterwards the brain was processed with standard autoradiographical methods. The landmark-generator computes corresponding reference points simultaneously within a given number of datasets by Monte-Carlo-techniques. The warping function is a distance weighted exponential function with a landmark- specific weighting factor. These weighting factors are optimized by a computational evolution strategy. The warping quality is quantified by several coefficients (correlation coefficient, overlap-index, and registration error). The described approach combines a highly suitable procedure to automatically detect landmarks in autoradiographical brain images and an enhanced point-based warping technique, optimizing the local weighting factors. This optimization process significantly improves the similarity between the warped and the target dataset.

Objective: Metabolic activity in trabecular bone is an important indicator in the therapy of bone diseases like osteoporosis. It is reflected by the amount of osteoid (young, not yet mineralized bone) and young calcified tissue (YCT). Our aim was to replace standard 2D histomorphometry with a 3D approach for osteoid and YCT measurement. Measurement Methods: Excised lumbar vertebrae of 5 ovariectomized (OVX) and 5 control rats were 3D-scanned with computed micro-tomography ((mu) CT, isotropic spatial resolution 20 micrometer³) and laser scanning confocal microscopy (LSCM, 20X magnification, 1X1X2 micrometer³ spatial resolution). (mu) CT shows trabecular bone structure; LSCM shows osteoid and YCT by fluorescent light. Image Processing Methods: The fraction of bone to tissue volume (BV/TV) and the number of trabeculae (Tb.N) were calculated from globally thresholded (mu) CT images. LSCM images were enhanced using top-hat transform, globally thresholded and morphologically closed. Separate regions were labeled by volume growing. We measured feature volume to background volume ratio and number of features per unit volume. Results and Conclusions: In the specimens obtained from the OVX rats, a significant increase in the volume fractions of osteoid and YCT could be seen. The (mu) CT-LSCM approach presents a significant improvement over time-consuming, standard histomorphometry. The image processing for both modalities could be achieved automatically.

Maximum Likelihood (ML) estimation based Expectation Maximization (EM) reconstruction algorithm has shown to provide good quality reconstruction for PET. Our previous work introduced the multigrid EM (MGEM) and multiresolution (MREM) and Wavelet based Multiresolution EM (WMREM) algorithm for PET image reconstruction. This paper investigates the use of various wavelets in the new Wavelet based Multiresolution EM (WMREM) algorithm. The wavelets are used to construct a multiresolution data space, which is then used in the estimation process. The beauty of the wavelet transform to provide localized frequency-space representation of the data allows us to perform the estimation using these decomposed components. The advantage of this method lies with the fact that the noise in the acquired data becomes localized in the high-high or diagonal frequency bands and not using these bands for estimation at coarser resolution helps speed up the recovery of various frequency components with reduced noise estimation. Different wavelet bases result in different reconstructions. Custom wavelets are designed for the reconstruction process and these wavelets provide better results than the commonly known wavelets. The WMREM reconstruction algorithm is implemented to reconstruct simulated phantom data and real data.

We have developed a weighted optical flow algorithm for the extraction of instantaneous blood velocity from dynamic digital x-ray images of blood vessels. We have carried out in- vitro validation of this technique. A pulsatile physiological blood flow circuit was constructed using sections of silicone tubing to simulate blood vessels with whole blood as the fluid. Instantaneous recording of flow from an electromagnetic flow meter (EMF) provided the gold standard measurement. Biplanar dynamic digital x-ray images of the blood vessel with injection of contrast medium were acquired at 25 fps using a PC frame capture card. Imaging of a Perspex calibration cube allowed 3D reconstruction of the vessel and determination of true dimensions. Blood flow waveforms were calculated off-line on a Sun workstation using the new algorithm. The correlation coefficient between instantaneous blood flow values obtained from the EMF and the x-ray method was r equals 0.871, n equals 1184, p less than 0.0001. The correlation coefficient for average blood flow was r equals 0.898, n equals 16, p less than 0.001. We have successfully demonstrated that our new algorithm can measure pulsatile blood flow in a vessel phantom. We aim to use this algorithm to measure blood flow clinically in patients undergoing vascular interventional procedures.

Flow images generated with Echo-Planar Imaging (EPI) show a poor Signal-to-Noise Ratio (SNR). To improve the resolution of EPI flow maps, so a better SNR can be obtained without loss of spatial resolution and with minimal sacrifice of motion effects. The continuous transform of Coiflets wavelet is applied to 2D velocity maps to enhance image SNR. Wavelet coefficients of velocity maps of the cardiac chambers and the descending aorta were calculated. These velocity maps were earlier obtained by Half Fourier Echo-Planar Imaging (HF-EPI). Wavelet coefficient images and contour maps are shown. The enhanced images are compared with previous velocity maps. Cardiac contour maps show hemodynamic patterns in cardiac chambers and descending aorta. Improvement of image quality with other wavelets, such as Mexican Hat, Morlet, Meyer, Daubechies, is briefly discussed.

The generation of magnitude magnetic resonance images comprises a sequence of data encodings or transformations, from detection of an analog electrical signal to a digital phase/frequency k-space to a complex image space via an inverse Fourier transform and finally to a magnitude image space via a magnitude transformation and rescaling. Noise present in the original signal is transformed at each step of this sequence. Denoising MR images from low field strength scanners is important because such images exhibit low signal to noise ratio. Algorithms that perform denoising of magnetic resonance images may be usefully classified according to the data domain on which they operate (i.e. at which step of the sequence of transformations they are applied) and the underlying statistical distribution of the noise they assume. This latter dimension is important because the noise distribution for low SNR images may be decidedly non-Gaussian. Examples of denoising algorithms include 2D wavelet thresholding (operates on the wavelet transform of the magnitude image; assumes Gaussian noise), Nowak's 2D wavelet filter (operates on the squared wavelet transform of the magnitude image; assumes Rician noise), Alexander et. al.'s complex 2D filters (operates on the wavelet transform of the complex image space; assumes Gaussian noise), wavelet packet denoising (wavelet packet transformation of magnitude image; assumes Rician noise) and anisotropic diffusion filtering (operates directly on magnitude image; no assumptions on noise distribution). Effective denoising of MR images must take into account both the availability of the underlying data, and the distribution of the noise to be removed. We classify a number of recently published denoising algorithms and compare their performance on images from a 0.35T permanent magnet MR scanner.

This paper presents a new method for automated detection of stents. The method consists of three sequential steps. At first, a 3D to 2D projection procedure is applied to find the global stent location. A local search strategy was designed, using a combination of characteristic image features to extract the sampling point candidates of the stent in each of the original cross-sectional images. Finally, the preselected points are accepted or rejected depending on a set of a priori criteria for position and shape. Using the resulting stent points, geometrical parameters of the stent are automatically calculated and a wire frame model is generated for 3D surface reconstruction. Thus, in combination with our algorithms for automated detection of the lumen cross-sectional area, the new method is an essential component for 3D visualization of stents and the automated quantification of the degree of in- stent restenosis. The evaluation is based on in vitro and in vivo recordings. The results show that the new algorithm is well-suited to replace time consuming manual segmentation and measurements.

Small pellets are often used as fiducial markers in a calibration phantom to estimate the geometrical parameters in 3D (three-dimensional) reconstruction. But calibration accuracy depends on the accuracy of locating the pellet centers. Here we describe a technique for fast and accurate detection of these centers. The phantom consists of tungsten carbide pellets arranged in a helical trajectory. The plastic holder mounting the pellets may cause unequal distribution of attenuation around edge pellets compared to the center ones. After log subtraction with flood frames the grayscale gradient in the background is derived within the mask for every point for a reliable background correction. The pellets are identified from the amplitude projections of each frame and a mask is used to refine its position. The grayscale gradient of the background is suitably estimated at each point by the equation of a plane. The center obtained after gradient filter correction is compared with manual measurement, and to measurement using a single background value for each mask. Gradient correction gives centers within 0.3 +/- 0.1 pixel of the manual measurements for the edge pellets, while a single value for background correction yields results within 0.6 +/- 0.3 pixel.

Digital subtraction angiographic image sequences of a calibration phantom are acquired at 30 frames per second from a C-arm gantry covering an angular arc of more than 180 degrees rotating at 40 degrees/s. For each frame, after XRII distortion correction, the relation between the source and its image plane orientation in 3D space is estimated from fiducial markers in the calibration phantom. This gives a mapping between the three-dimensional calibration object and its two- dimensional projection at each gantry angle. We derive eleven mapping coefficients as a function of gantry angle. We use the coefficients to backproject the contribution to any physical voxel. Thus the wobble correction is incorporated directly into cone-beam backprojection. In the absence of gantry wobble, this method is equivalent to the short-scan Feldkamp algorithm, any deviation of the coefficients from those perfect values can be taken as a measure of the gantry wobble. The mapping method requires no special knowledge of the system geometry and any wobble, twisting of the C-arm or XRII during rotation is automatically included. A phantom with tungsten- carbide beads is reconstructed. Accuracy is obtained by comparing reprojections of the center of the tungsten beads with their known values.

The focus of this paper is to evaluate the clinical performance of the image processing technique which we have developed for computed radiography x-rays. This algorithm, which was presented at the SPIE '99 medical imaging conference, uses iterative deconvolution with a measured point spread function to reduce the effect of scatter. Wavelet denoising is also carried out after each iteration to remove effects due to noise. A random selection of chest x-rays were processed using the algorithm. Both the raw and processed images were presented to the radiologists in a random order. They scored the images with regard to the visibility of anatomical detail and image quality as outlined in the european guidelines on quality criteria for diagnostic radiographic images. The most notable result of the technique is seen in the reduction of noise in the processed image.

The electrical activity of the brain can be monitored using ElectroEncephaloGraphy (EEG). From the positions of the EEG electrodes, it is possible to localize focal brain activity. Thereby, the accuracy of the localization strongly depends on the accuracy with which the positions of the electrodes can be determined. In this work, we present an automatic, simple, and accurate scheme that detects EEG electrode markers from 3D MR data of the human head.

During a Magnetic Resonance (MR) sequence, simultaneously acquired ElectroEncephaloGraphy (EEG) data are compromised by severe pollution due to artifacts originating from the switching of the magnetic field gradients. In this work, it is shown how these artifacts can be strongly reduced or even removed through application of an adaptive artifact restoration scheme. The method has proved to be fully automatic and to retain high frequency EEG information, which is indispensable for many EEG applications.

We present a method for exploring the relationship between the image segmentation results obtained by an optimal feature space method and the MRI protocols used. The steps of the work accomplished are as follows. (1) Three patients with brain tumors were imaged by a 1.5T General Electric Signa MRI System, using multiple protocols (T1- and T2-weighted spin- echo and FLAIR). T1-weighted images were acquired before and after Gadolinium (Gd) injection. (2) Image volumes were co- registered, and images of a slice through the center of the tumor were selected for processing. (3) Nine sets of images were defined by selecting certain MR images (e.g., 4T2's + 1T1, 4T2's + FLAIR, 2T2's + 1T1). (4) Using the images in each set, the optimal feature space was generated and images were segmented into normal tissues and different tumor zones. (5) Segmentation results obtained using different MRI sets were compared. We found that the locations of the clusters for the tumor zones and their corresponding regions in the image domain changed to some extent as a function of the MR images (MRI protocols) used. However, the segmentation results for the total lesion and normal tissues remained almost unchanged.

In this paper, we present a method to register medical images non-rigidly and to determine critical structures using a model-based segmentation. We present our method in the case of 2D and 3D magnetic resonance images (MRI) of the brain. In our approach, we first use an existing algorithm for rigid matching of medical images by Mutual Information maximization for the initialization of our registration. Then we apply our gray level based non-rigid matching algorithm to match the contours of the model on acquired medical images. We have also added an elastic internal energy term to our algorithm, so that the contour deformations are elastically propagated throughout the whole object to be matched. We present this non-rigid and iterative method in the context of inter-patient matching and of deforming an elastic brain atlas on medical images for automatic localization and identification of brain structures in medical images. The main advantages of our implementation are its very low computational cost in comparison to other methods and the fact that it can be applied directly on a synthetic atlas without passing through a corresponding medical image. We present preliminary results, we mention some existing limitations of our method and indicate future work.

This paper presents a new approach for the evaluation of Doppler flow velocity diagrams, obtained during brachial artery flow mediated dilatation (FMD) studies. The velocity diagrams are stored as image sequences on VCR tape. For this reason standard signal processing methods can not be used. A method for determination of blood velocity envelopes from image data is reported that uses Doppler-data specific heuristic to achieve high accuracy and robustness. The approach was tested in 40 Doppler blood flow images. Comparisons with manually defined independent standards demonstrated a very good correlation in determined peak velocity values (r equals 0.993) and flow envelope areas (r equals 0.996). The method is currently tested in a large volume clinical study.

The proposed approach overcomes the shortcomings of previous deformable models in segmenting magnetic resonance images (MRI). In previous models, definition of the initial contour is left to the operator. In addition, previous models show poor convergence towards boundary concavities. The new method consists of the following steps. (1) An adaptive K-means clustering algorithm generates uniform regions with inaccurate boundaries for the tissues in the image. (2) Boundaries of the desired tissue are extracted from the regions generated in the Step 1. Certain points on the boundaries are considered as the vertices of the initial contour. (3) Since the results of Step 1 may not include detail boundary information in some regions, a correction algorithm using neighborhood information is applied. (4) Dynamic contour model of Lobregt and Viergever is applied, but in defining the external forces, a deflection in the radial direction is implemented in the manner defined by Prince and Xu. This uses the idea of solenoidal external forces to help track boundary concavities. By convergence of this step, through diminishing velocity and acceleration of all vertices, the procedure is completed. Experimental results show that the proposed method tracks the concavities quite well. In addition, the initial contours for tissues with closed boundaries are obtained automatically, thereby no initial contour needs to be defined by the operator.

The 3D acquisition data from positron coincidence detection on a gamma camera, can be stored in list-mode or histogram format. The standard processing of the list mode-data is Single Slice Rebinning (with a maximum acceptance angle) to 2D histogrammed projections followed by Ordered Subsets Expectation Maximization reconstruction. This method has several disadvantages: sampling accuracy is lost by histogramming events, axial resolution degrades with increasing distance from the center of rotation and useful events, with angle bigger than the acceptance angle, are not included in the reconstruction. Therefore an iterative reconstruction algorithm, operating directly on list-mode data, has been implemented. The 2D and 3D version of this iterative list-mode algorithm have been compared with the aforementioned standard reconstruction method. A higher number of events is used in the reconstruction, which results in a lower standard deviation. Resolution is fairly constant over the Field of View. The use of a fast projector and backprojector reduces the reconstruction time to clinical acceptable times.

This paper presents a novel algorithm for automatically extracting 3D contour edges, which are points of maximum surface curvature in a surface range image. The 3D image data are represented as a surface polygon mesh. The algorithm transforms the range data, obtained by scanning a dental plaster cast, into a 2D gray scale image by linearly converting the z-value of each vertex to a gray value. The Canny operator is applied to the median-filtered image to obtain the edge pixels and their orientations. A vertex in the 3D object corresponding to the detected edge pixel and its neighbors in the direction of the edge gradient are further analyzed with respect to their n-curvatures to extract the real 3D contour edges. This algorithm provides a fast method of reducing and sorting the unwieldy data inherent in the surface mesh representation. It employs powerful 2D algorithms to extract features from the transformed 3D models and refers to the 3D model for further analysis of selected data. This approach substantially reduces the computational burden without losing accuracy. It is also easily extended to detect 3D landmarks and other geometrical features, thus making it applicable to a wide range of applications.

In radiographic images the actual region of interest (ROI), i.e. the collimation field, is often smaller than the overall image detector area. Collimation devices (shutters) and lead aprons confine the X-ray beam to the anatomically relevant region. Therefore, large shuttered areas with low radiation intensity may exist in the image. This background may however show strong radiation scatter features, so that simple thresholding or histogram analysis approaches fail. Automated recognition of the collimation field is necessary with respect to optimal contrast adjustment of the monitor and film-printer representation, and accelerates the workflow in comparison to manual ROI settings. In our approach we first identify several hundreds of shutter edge candidates by means of a Hough transform. Then several thousand ROI hypotheses are checked. The objective is to maximize at the same time the enclosed area, the enclosed image intensity, and the enclosed second derivative (Laplace value) of the intensity. The maximization of the Laplace area integral has been found to be the single most powerful feature for finding the true collimation field. The approach was successfully tested on image sets from clinical routine.

Existing lossless coding models yield only up to 3:1 compression. However, a much higher lossless compression can be achieved for certain medical images when the images are segmented prior to applying integer to integer wavelet transform and lossless coding. The methodology used in this research work is to apply a contour detection scheme to segment the image first. The segmented image is then wavelet transformed with integer to integer mapping to obtain a lower weighted entropy than the original. An adaptive arithmetic model is then applied to code the transformed image losslessly. For the male visible human color image set, the overall average lossless compression using the above scheme is around 10:1 whereas the compression ratio of an individual slice can be as high as 16:1. The achievable compression ratio depends on the actual bit rate of the segmented images attained by lossless coding as well as the compression obtainable from segmentation alone. The computational time required by the entire process is fast enough for application on large medical images.

Three-dimensional geometric modeling of the human cochlea not only provides a basis for preoperative planning and postoperative evaluation of cochlear implantation, but also facilitates medical education and training. In this paper, the three-dimensional geometric modeling method of the cochlea has been developed. The central path of the cochlea is extracted from a spiral CT image volume by segmenting the cochlea and tracking through the cochlear canal. The central path is modeled by a helico-spiral. The first component in the helico- spiral model represents the projected central path onto a plane perpendicular to the modiolar axis, while the second component depicts the longitudinal stretching of the central path. A non-linear least square minimization based algorithm is devised for the identification of intrinsic and extrinsic parameters of the helico-spiral representation of the cochlea. Numerical phantoms with added different noise levels up to standard deviation of 2 mm are synthesized according to the average parameters of the human cochlea to evaluate the accuracy. In real human cochlear studies, our model fits into the modiolar axis and the central path very well, allowing the calculation of length, height and angular positions needed for frequency mapping of multi-channel cochlear implant electrodes.

Image processing algorithms that automatically locate patterns in digital images have application to medical image enhancement processing and computer-aided diagnosis (CAD). A flexible and computationally efficient detection and classification algorithm has been developed that can be readily adapted for any specified anatomical structure or imaging modality. The algorithm makes use of image pattern filters and eigenvector analysis. The algorithm was optimized and tested for the detection of the class of cylindrical bones in digital projection radiography. Gradient-based edge detection is used to locate candidate bone edge pixels. For each candidate pixel, the bone image profile (i.e., the code values on a line segment that cross the bone perpendicular to the bone edge) is analyzed to identify indicators of bone location. Shape constraints of the image profile are used to refine the selection of candidate profiles. An eigenvector representation for the cylindrical bone profiles is then constructed. The algorithm then automatically classifies structures in the imagery that matches the eigenvector representation of the cylindrical bone profile. Using an eigenvector representation of a cylindrical bone profile constructed from a set of training images, the algorithm correctly classified 91 humerus bone profiles that were tested.

Accurate reconstruction of the human cerebral cortex from magnetic resonance (MR) images is important for brain morphometric analysis, image-guided surgery, and functional mapping. Previously, we have implemented a cortical surface reconstruction method that employs fuzzy segmentation, isosurfaces and deformable surface models. The accuracy of the fuzzy segmentation has been well-studied using simulated brain images. However, global quantitative validation of the cortical surface model has not been feasible due to the lack of a true representation of the cortical surface. In this paper, we have alternately validated the deformable surface model used in one cortical surface reconstruction method by using a metasphere computational phantom. A metasphere is a mathematically defined three-dimensional (3-D) surface that has convolutions similar to the cortex. We simulated 500 image volumes using metaspheres with various numbers and degrees of convolutions. Different levels of Gaussian noise were also incorporated. Quantification of the differences between the reconstructed surfaces and the true metasphere surfaces provides a measure of the deformable model accuracy in relation to the properties of the modeled object and data quality.

Real-time volume ultrasound imaging of the heart is a new trend, and the registration of acquired volume framesets is clinically important. This registration may be accomplished by processing a selected pair of volume frames having identical cardiac phase (preferably end diastolic) from two framesets. The registration solves for the optimal rigid transformation between selected volumes through maximization of mutual information, a voxel similarity measure. The accuracy of registration was estimated through retrieval of an artificially introduced misalignment. Two volume frames, belonging to the same frameset and separated in time by 250 ms, were selected. The secondary volume was translated by seven voxels along each axis and rotated by seven degrees about each axis relative to the primary prior to registration. The translational mismatch upon registration was within one voxel and the rotational mismatch less than two degrees. Reduction of the speckle noise by spatio-temporal averaging followed by intensity binning was a key step in successful application of mutual information approach to ultrasound imaging. The application of our method to nine framesets arising from four different patients demonstrates the feasibility of using of mutual information for automatic registration of cardiac ultrasound data.

An automated image analysis tool is being developed for estimation of mammographic breast density, which may be useful for risk estimation or for monitoring breast density change in a prevention or intervention program. A mammogram is digitized using a laser scanner and the resolution is reduced to a pixel size of 0.8 mm X 0.8 mm. Breast density analysis is performed in three stages. First, the breast region is segmented from the surrounding background by an automated breast boundary-tracking algorithm. Second, an adaptive dynamic range compression technique is applied to the breast image to reduce the range of the gray level distribution in the low frequency background and to enhance the differences in the characteristic features of the gray level histogram for breasts of different densities. Third, rule-based classification is used to classify the breast images into several classes according to the characteristic features of their gray level histogram. For each image, a gray level threshold is automatically determined to segment the dense tissue from the breast region. The area of segmented dense tissue as a percentage of the breast area is then estimated. In this preliminary study, we analyzed the interobserver variation of breast density estimation by two experienced radiologists using BI-RADS lexicon. The radiologists' visually estimated percent breast densities were compared with the computer's calculation. The results demonstrate the feasibility of estimating mammographic breast density using computer vision techniques and its potential to improve the accuracy and reproducibility in comparison with the subjective visual assessment by radiologists.

Patient motion plays a major role in the degradation of image quality provided with magnetic resonance imaging (MRI). This effect is called motion artifact. In this work, we address the problem of MRI artifact arising from a 3-D affine motion. We show that the effect of such a motion is imposing phase error, amplitude distortion, and non uniform sampling to the Fourier domain (k-space) of the acquired MR data. Based on the previous works, a reconstruction algorithm is proposed to reduce the corresponding MRI artifact. In order to investigate the problem and proposed solution, the Poisson and Gaussian probability density functions (PDF) are used to randomly generate the location, amplitude, and number of a subject displacements during data acquisition. Then, the effect of 3-D affine motion parameters on creating MRI artifact and also the performance of the employed technique to suppress the resultant artifact are reported in the paper.

This paper describes how to validate image processing algorithms when the algorithm has been designed to produce a numerical output that optimizes a given scalar criterion function having all first and second partial derivatives. The validation technique analyzes the statistical behavior of the algorithm under small random perturbations of its input. This paper gives the theory for the computation of the covariance matrix of the output when the input is perturbed by small random input perturbations. A statistical test is done examining the algorithm output under multiple instances of simulated perturbations and comparing these outputs with the ideal output and the analytically derived covariance matrix. A second level of simulations can be done that examines the test statistics of the hypothesis of the statistical test to determine whether in fact it is distributed in accordance with statistical theory. If the hypothesis is rejected that the output perturbations do not have the analytically predicted covariance matrix, then the image analysis software fails validation.

Modern imaging techniques in medicine have revolutionized the study of anatomy and physiology in man. A central factor in the success and increasingly widespread application of imaging-based approaches in clinical and basic research has been the emergence of sophisticated computational methods for extracting salient information from image data. The utility of image processing has prompted the development of numerous algorithms for medical data, but these have largely remained research tools and few have been incorporated into a clinical workflow. A primary cause of this poor track record is the lack of validation of these methods. A workshop was held at this year's Image Processing Conference to discuss and stimulate developments in performance characterization research for medical image processing algorithms. This report presents highlights from the workshop presentations and from the panel discussion with the audience.

There has been a significant increase in commercial products using imaging analysis techniques to solve real-world problems in diverse fields such as manufacturing, medical imaging, document analysis, transportation and public security, etc. This has been accelerated by various factors: more advanced algorithms, the availability of cheaper sensors, and faster processors. While algorithms continue to improve in performance, a major stumbling block in translating improvements in algorithms to faster deployment of image analysis systems is the lack of characterization of limits of algorithms and how they affect total system performance. The research community has realized the need for performance analysis and there have been significant efforts in the last few years to remedy the situation. Our efforts at SCR have been on statistical modeling and characterization of modules and systems. The emphasis is on both white-box and black box methodologies to evaluate and optimize vision systems. In the first part of this paper we review the literature on performance characterization and then provide an overview of the status of research in performance characterization of image and video understanding systems. The second part of the paper is on performance evaluation of medical image segmentation algorithms. Finally, we highlight some research issues in performance analysis in medical imaging systems.