This paper aims at reviewing the recent published works dealing with industrial applications of wavelet and, more generally speaking, multiresolution analysis. After a quick recall in a simple overview of the basics of wavelet transform and of its main variations, some of its applications are reviewed domain by domain, beginning with signal processing, continuous and discrete wavelet transform proceeding with image processing and applications. More than 150 recent papers are presented in these two sections.

We try to measure lithography line edge roughness (LER) from a noisy SEM image using wavelet analysis. First, we evaluated the edge detection performance of the wavelet multiscale edge detection method without and with denoising by applying them to a modeled secondary electron (SE) signal of photoresist without and with noise. As denoising, the method called soft thresholding was used. Many modulus maxima lines with short lengths for a modeled SE signals with low SNR such as 3 appears and characteristic modulus maxima lines with long lengths do not come out. After denoising, the characteristic modulus maxima lines come out. When SNR was larger than 10, the standard deviation was less than 1 pixel and the average position converged to a point. Then we applied the wavelet multiscale edge detection method to a noisy SEM image of photoresist. LERs (1 sigma evaluated along a distance) along ninety scan lines were measured with the number of average line scans as a parameter. The measured LER for one scan line was determined to be reliable from results of averaging effects and LER for this photoresist pattern was about 3 pixels.

Image degradation is a frequently encountered problem in different imaging systems, like microscopy, astronomy, digital photography, etc. The degradation is usually modeled as a convolution with a blurring kernel (or Point Spread Function, psf) followed by noise addition. Based on the combined knowledge about the image degradation and the statistical features of the original images, one is able to compensate at least partially for the degradation using so-called image restoration algorithms and thus retrieve information hidden for the observer. One problem is that often this blurring kernel is unknown, and has to be estimated before actual image restoration can be performed. In this work, we assume that the psf can be modeled by a function with a single parameter, and we estimate the value of this parameter. As an example of such a single-parametric psf, we have used a Gaussian. However, the method is generic and can be applied to account for more realistic degradations, like optical defocus, etc.

Belt filter presses represent an economical means to dewater the residual sludge generated in wastewater treatment plants. In order to assure maximal water removal, the raw sludge is mixed with a chemical conditioner prior to being fed into the belt filter press. When the conditioner is properly dosed, the sludge acquires a coarse texture, with space between flocs. This information was exploited for the development of a software sensor, where digital images are the input signal, and the output is a numeric value proportional to the dewatered sludge dry content. Three families of features were used to characterize the textures. Gabor filtering, wavelet decomposition and co-occurrence matrix computation were the techniques used. A database of images, ordered by their corresponding dry contents, was used to calibrate the model that calculates the sensor output. The images were separated in groups that correspond to single experimental sessions. With the calibrated model, all images were correctly ranked within an experiment session. The results were very similar regardless of the family of features used. The output can be fed to a control system, or, in the case of fixed experiment conditions, it can be used to directly estimate the dewatered sludge dry content.

The 3D reconstruction of a scene with 2D images requires several scene acquisitions or the use of specific lighting (structured light). The solution choice depends on the scene to be reconstructed. Unfortunately in the case of face reconstruction, health standards forbid the use of structured light; the elaboration of a multi-sensor system, such as stereovision is then required. In this paper, primary results about depth reconstruction from defocused images are presented. The used method relies on inverse ray tracing and provides results better than those obtained by using the conventional gradient based method.

In this paper, an objective criterion on wavelet filters in proposed. Wavelet transforms are used in number of important signal and image industrial processing tasks including image coding and denoising. The choice of the wavelet filter bank is is very important and is directly linked to the efficiency of the application. Some criteria have been proposed such as regularity, size of the support of the wavelet and number of vanishing moments. The size of the wavelet support increases with the number of vanishing moments. The wavelet regularity is important to reduce the artifacts. The choice of an optimal wavelet is thus the result of a trade-off between the number of vanishing moments and artifacts. But there is only a partial correlation between filter regularity and reconstructed image quality. The proposed criterion is composed of two indexes. The first one is a frequency index computed from the aliasing of the filters. The second is a spatial index computed from the spread of the coefficients in spatial domain. From these indexes a filter set can be represented by a point in a criteria-plan. The abscissa is given by the frequency index and the ordinate by the spatial index. The quality of a wavelet filter bank is a trade-off between frequency and spatial quality. So the quality of a wavelet filter bank can be assessed from the position of the corresponding point in the criteria-plan. The coding and denoising performances are estimated for various filters (including orthogonal splines and Daubechies). These performances are connected to the indexes of each filter bank. The results show that the two proposed indexes allow : 1/ a good estimation of the coding and denoising performances of the wavelet filters, and 2/ an objective comparison of the filters. Some clues on the connection between our indexes and the kernel size in the Heisenberg-Gabor formula are also given.

In this paper we develop an advanced spatio-temporal wavelet domain filtering algorithm which is suitable for hardware implementation, we implement it in the Field Programmable Gate Arrays (FPGA) and report the results of real-time processing. The wavelet decomposition in our implementation is non-decimated with three decomposition levels and with a Daubechies' minimum phase orthogonal wavelet. Noise reduction is implemented with spatially adaptive Bayesian wavelet shrinkage. In the next filtering stage, a motion detector controls selective, recursive averaging of pixel intensities over time. The algorithm is customized for the hardware implementation and is realized in FPGA. The standard composite television video stream is digitalized and used as source for real-time video sequences. The results demonstrate the effectiveness of the developed scheme for real time video processing.

Error protection and concealment of motion vectors are of prime concern when video is transmitted over variable-bandwidth error-prone channels, such as wireless channels. In this paper, we investigate the influence of corrupted motion vectors in video coding based on motion-compensated temporal filtering, and develop various error protection and concealment mechanisms for this class of codecs. The experimental results show that our proposed motion vector coding technique significantly increases the robustness against transmission errors and generates performance gains of up to 7 dB compared with the original coding technique at the cost of less than 4% in terms of rate. It is also shown that our proposed spatial error-concealment mechanism leads to additional performance gains of up to 4 dB.

Real time delivery of video over best-effort and error-prone networks requires compression systems that dynamically adapt the rate to the available channel capacity and exhibit robustness to loss of some data as retransmission is often impractical. Error resiliency, however, significantly lowers the coding performance when rigid design is performed based on a worst-case scenario. This paper presents a scalable video coding scheme that couples the compression efficiency of the open-loop architecture with the robustness of multiple description source coding. The use of embedded multiple description quantization and a novel channel-aware rate-allocation allows for shaping on-the fly the output bit-rate and the degree of resiliency without resorting to channel coding. As a result, robustness to data losses is traded for better visual quality when transmission occurs over reliable channels, while error resilience is introduced when noisy links are involved. The advantage of our proposal is demonstrated in the context of packet-lossy networks comparing the performance of similar instantiations of the video codec employing non-scalable redundancy.

Many vision applications require robust point detection as a preliminary task. This can be efficiently done in Gaussian scale-space, with Harris-Laplacian or Lindeberg detectors. Yet, such a uniform smoothing may be a drawback for some applications. Continuous wavelet or curvelet domains have shown to be well adapted to 1D and 2D singularity detection and are therefore an alternative to Gaussian scale-space. Discretization makes the wavelet transform loose its translation and dilation invariance, which is particularly true for critically sampled transforms. In this paper, we investigate discrete wavelet transforms for points detection, show that a redundant transform such as contourlet transform yield to more robust points than a critically sampled one, and compare results with Harris-Laplacian and Lindeberg point detectors.

In the recent past years, scaling, random multiplicative cascades, multifractal stochastic processes became common paradigms used to analyse a large variety of different empirical times series characterised by scale invariance phenomena or properties. Scale invariance implies that no characteristic scale can be identified in data or equivalently that all scales are equally important. It also means that all scales are in relation ones with the others, hence the connection to multiplicative cascades, which, by construction, tie together a wide range of scales. Data with scale invariance are also often characterised by a high irregularity of their sample path. This variability is usually accounted for by Multifractal analysis. Hence, in applications, the three notions, scaling, multiplicative cascade and multifractal are often used ones for the others and even confusingly mixed up. These assimilations, that turned out to be fruitful in the early stages of the study of scaling, are now often responsible for misleading analysis and erroneous conclusions. Wavelet coefficients have long been used with relevance to analyse scaling. However, very recently, it has been shown that the analysis of multifractal properties can be significantly improved both conceptually and practically by the use of quantities referred to as wavelet leaders. The goals of this article are to introduce the wavelet leader based multifractal analysis, to detail its qualities and to show how it enables an insightful visit of the relationships between scaling, multifractal and multiplicative cascades.

Recently, scalable video codecs based upon motion compensated temporal filtering (MCTF) have received a lot of attention. These video coding schemes perform on par with H.264, the current state-of-the-art video coding standard, while providing quality, resolution and frame-rate scalability. In this paper we aim to evaluate the rate-distortion performance of MCTF-based codecs when applied to volumetric data sets. In our experiments the lossy coding efficiency of an MCTF-based codec is compared to that of the 3D QT-L codec, which represents the state-of-the-art in volumetric coding. The results show that the MCTF-based coder does not provide better PSNR performance than the 3D QT-L codec. However, if the rate spent to code the motion vector information is not taken into account, the performance of the MCTF-based codec at low rates is on par or better than the performance of the 3D QT-L. This leads us to conclude that possible distortion improvements obtained by using MCTF instead of a regular wavelet-transform in the temporal direction do not outweigh the extra rate needed to encode the motion vector information.

This paper compares wavelet and short time Fourier transform based techniques for single channel speech signal noise reduction. Despite success of wavelet denoising of images, it has not yet been widely used for removal of noise in speech signals. We explored how to extend this technique to speech denoising, and discovered some problems in this endeavor. Experimental comparison with large amount test data has been performed. Our results have shown that although the Fourier domain methods still has the superiority, wavelet based alternatives can be very close, and enormous different configurations can still be tried out for possible better solutions.

Recent advances in scanning and acquisition technologies allow the construction of complex models from real world scenes. However, the data of those models are generally corrupted by measurement errors. This paper describes an efficient single pass algorithm for denoising irregular meshes of scanned 3D model surfaces. In this algorithm, the frequency content of the model is assessed by a multiresolution analysis that requires only 1-ring neighbourhood without any particular parameterization of the model faces. Denoising is achieved by applying the soft thresholding method to the detail coefficients given by the multiresolution analysis. Our method is suitable for irregular meshes with appearance attributes such as normal vectors and colors. Some results of real world scene models denoised with the proposed algorithm are given to demonstrate its efficiency.

In the last decade, the accessibility of inexpensive and powerful computers has allowed true digital holography to be used for industrial inspection using microscopy. This technique allows capturing a complex image of a scene (i.e. containing magnitude and phase), and reconstructing the phase and magnitude information. Digital holograms give a new dimension to texture analysis since the topology information can be used as an additional way to extract features. This new technique can be used to extend previous work on image segmentation of patterned wafers for defect detection. This paper presents a comparison between the features obtained using Gabor filtering on complex images under illumination and focus variations.

An original statistical approach making it possible to accurately model video sequences in the wavelet domain as Gaussian laws is presented. By partitioning the wavelet coefficients into classes with independent elements, we rigorously handle the dependency existing among the successive frames in the video sequence. Further on, four statistical tests are applied to each class in the partition, with the following purposes: (1) to check up the Gaussian law; (2) to validate the data partition and (3) to reveal a homogeneity behaviour among the classes in the partition. Finally, the obtained results are fusioned so as to provide a global information characterising the whole sequence. At the same time, an a posteriori proof concerning an ergodicity behaviour for video sequences is obtained. We integrated these results within a robust video watermarking scheme. The mark is generated according to a CDMA (Code Division Multiple Access) procedure, starting from a 64 bit message (a serial number, a logo, etc). The embedding procedure is a weighted addition of the watermark into the wavelet coefficients featuring the Gaussian behaviour. The detection procedure is based on matched filters, the optimality of which is ensured under the considered framework. The experiments feature firm results concerning all the requirements stated nowadays: obliviousness, transparency, robustness, and probability of false alarm.

The application of the steerable pyramid transform in image watermarking has many useful properties. In this paper, we will try to address some properties of steerable pyramid transform that are relevant for use in image watermarking; these properties include: (1) invariance properties; (2) multiresolution aspect; (3) capture of multi-scale and multiresolution structures in the image. All the above mentioned properties make this steerable pyramid transform appropriate for the design of a robust watermarking scheme. This paper proposes an image watermarking scheme based on steerable pyramid transform to embed invisible and robust watermark. We can summarize the basic principles of our method as follow: a host image is first transformed by the steerable pyramid transform. The different features are then extracted by thresolding the different subbands. The watermark sequence is inserted into disjoint blocks centered on the extracted feature points. The original host image is needed in watermark detection mainly for extracting the featured coefficients necessary for robust detection and determining the value of one bit of the watermark spread into a block. It has been confirmed by experiments and comparisons with many existing non-blind techniques that the watermark information embedded by the proposed technique is robust to JPEG compression, additive noise, and median filtering.