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Spie Press Book

Hands-on Morphological Image Processing
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Book Description

Morphological image processing, now a standard part of the imaging scientist's toolbox, can be applied to a wide range of industrial applications. Concentrating on applications, this book shows how to analyze a problem and then develop successful algorithms based on the analysis. The book is hands-on in a very real sense: readers can download a demonstration toolbox of techniques and images from the web so they can process the images according to examples in the text.

Book Details

Date Published: 24 July 2003
Pages: 290
ISBN: 9780819447203
Volume: TT59

Table of Contents
SHOW Table of Contents | HIDE Table of Contents
Preface / xi
List of Symbols / xv
1 Binary Erosion and Dilation / 1
1.1 Introduction / 1
1.2 Euclidean and Discrete Binary Images / 2
1.3 Erosion / 5
1.4 Dilation / 10
1.5 Algebraic Properties / 13
1.6 Filter Properties / 16
1.7 Relationship to Set Operations / 18
1.8 Bounded Operators / 19
1.9 Exercises / 23
1.10 Laboratory Experiments / 25
1.11 References / 26
2 Binary Opening and Closing / 29
2.1 Opening / 29
2.2 Closing / 31
2.3 Filter Properties / 33
2.4 Application of Opening and Closing Filters / 35
2.5 Alternating Sequential Filters / 36
2.6 Invariance / 39
2.7 "-Openings / 39
2.8 Demonstration / 43
2.9 Exercises / 47
2.10 Laboratory Experiments / 49
2.11 References / 49
3 Morphological Processing of Binary Images / 51
3.1 Pixel Regions / 51
3.2 Boundary Detection / 54
3.3 Reconstruction / 55
3.4 Conditional Dilation / 59
3.5 Marker Selection in Reconstruction / 62
3.6 Reconstructive "-opening / 65
3.7 Logical Openings / 67
3.8 Logical Structural Filters / 68
3.9 Connected Operators / 70
3.10 Skeletonization / 74
3.11 Distance Transform / 79
3.12 Geodesic Distance Transform / 82
3.13 Exercises / 82
3.14 Laboratory Experiments / 85
3.15 References / 85
4 Hit-or-Miss Transform / 89
4.1 The Transform / 89
4.2 Object Recognition / 91
4.3 Thinning / 92
4.4 Pruning / 94
4.5 Exercises / 98
4.6 Laboratory Experiments / 100
4.7 References / 100
5 Gray-Scale Morphology / 101
5.1 Mathematical Preliminaries / 101
5.2 Gray-Scale Erosion / 105
5.3 Gray-Scale Dilation / 110
5.4 Algebraic Properties / 112
5.5 Filter Properties / 114
5.6 Umbra Transform / 116
5.7 Flat Structuring Elements / 119
5.8 Gray-Scale Morphology for Discrete Images / 122
5.9 Gray-Scale Morphology for Discrete Bounded Signals / 124
5.10 Gray-Scale Opening and Closing / 129
5.11 Exercises / 137
5.12 Laboratory Experiments / 138
5.13 References / 138
6 Morphological Processing of Gray-Scale Images / 143
6.1 Morphological Gradient / 143
6.2 Top-Hat Transform / 144
6.3 Gray-Scale Alternating Sequential Filters / 148
6.4 Gray-Scale Morphological Reconstruction / 151
6.5 Flat Zones and Connected Filters / 156
6.6 Gray-Scale Reconstructive Opening / 157
6.7 Connected Alternating Sequential Filters / 159
6.8 Image Extrema / 161
6.9 Markers From Regional Maxima of Filtered Images / 163
6.10 Extinction Values / 167
6.11 Demonstration / 169
6.12 Exercises / 171
6.13 Laboratory Experiments / 173
6.14 References / 174
7 Morphological Segmentation Watershed / 179
7.1 Watershed From Markers / 182
7.2 Watershed, Voronoi Diagram and SKIZ / 186
7.3 Segmentation of Overlapped Convex Cells / 189
7.4 Inner and Outer Markers / 191
7.5 Hierarchical Watershed Transform / 193
7.6 Watershed Transform Algorithms / 197
7.7 Demonstrations / 201
7.8 Exercises / 207
7.9 Laboratory Experiments / 209
7.10 References / 209
8 Granulometries / 211
8.1 Granulometries Generated by a Single Opening / 211
8.2 Discrete Size Distributions / 214
8.3 The Open and Discrete-Size Transforms / 217
8.4 Granulometries on Random Binary Images / 218
8.5 Granulometric Classification / 222
8.6 General Granulometries / 226
8.7 Logical Granulometries / 229
8.8 Discrete Granulometric Bandpass Filters / 232
8.9 Gray-Scale Granulometries / 236
8.10 Exercises / 240
8.11 Laboratory Experiments / 242
8.12 References / 242
9 Automatic Design of Morphological Operators / 247
9.1 Boolean Functions / 247
9.2 Morphological Representation / 250
9.3 Optimal W-Operators / 253
9.4 Design of Optimal W-Operators / 256
9.5 Optimal Increasing Filters / 260
9.6 Differencing Filters / 265
9.7 Resolution Conversion / 269
9.8 Multiresolution Analysis / 272
9.9 Aperture Filters / 276
9.10 Relation to Pattern Recognition / 280
9.11 Exercises / 283
9.12 References / 284
Index / 289

Preface

Morphological image processing has become a standard part of the imaging scientist's toolbox and today is applied daily to a wide range of industrial applications, including (and certainly not limited to) inspection, biomedical imaging, document processing, pattern recognition, metallurgy, microscopy, and robot vision. Because the morphological operations can serve as a universal language for image processing, their application is only limited by the ability to design effective algorithms and efficient computational implementation.

In the last decade, since the publication of An Introduction to Morphological Image Processing by SPIE Press, there have been many developments in morphological imaging, both in theory and practice. This book concentrates on applications. In keeping with the outlook of the previous book, we aim to provide a handbook that instructs how to analyze a problem and then how to develop successful algorithms based on the analysis. We take a holistic approach by showing how generic methods can be used in combination to solve practical problems. We include demonstrations to show how various morphological techniques can be combined to produce complete and effective algorithms.

In concentrating on applications we have not sacrificed careful definitions and explicit statement of operation properties. Indeed, skillful application requires that one understand the general filtering effects of an operation, and efficient implementation requires that one have knowledge of the operational simplifications available.

Filter properties are integrated into the applications and their relevance is emphasized. We have heard recently the comment that "morphology is an industrial subject." To a great extent this is true, although one should extend this to include research and development laboratories of all kinds. Several months ago, when asked to develop a high-throughput algorithm for analyzing genetic cell arrays, we suggested to our biological colleagues that we would use an algorithm known as the watershed. "Of course," they replied.

The book is hands-on in a very real sense. Most of the techniques used in the book are available in the Morphology Toolbox, and a great majority of the images shown in the text have been processed by the toolbox. These images, along with a demonstration version of the toolbox are downloadable free from the web (http://sourceforge.net/projects/pymorph), so that the reader can actually process the images according to the examples and demonstrations in the text. There is a brief discussion in the first chapter as to how the toolbox correlates to the text, but we do not emphasize this relation throughout the text since we do not want to digress from the imaging essentials. Detailed use of the toolbox can be learned from the downloadable version. To assist the user, each chapter concludes with a list of the toolbox operations used in the chapter, and the detailed demonstration sections include corresponding toolbox implementations. Each chapter also has its own bibliography.

We briefly describe the structure of the book. The first two chapters discuss the basic binary morphological operations, erosion and its dual dilation in the first chapter, and opening and its dual closing in the second. All of morphological image processing rests on these operations. Therefore, we treat them in great detail. The third and fourth chapters discuss the processing of binary images, the third focusing on applications of the primary operators, and the fourth on the hit-or-miss transform, which processes an image directly in terms of the foreground-background relation. We pay particular attention to morphological reconstruction in the third chapter because we believe that it is a very powerful tool for the development of algorithms based on inherent image structure.

Gray-scale morphological operators are discussed in the fifth chapter, and their application is treated in the following chapter. Once again we pay much attention to the role of reconstruction in applications. These tools have been more recently developed and we expect that they will lead to an ever-expanding range of application.

The seventh chapter is devoted to watershed-based segmentation. There are many variants of watershed segmentation. Our approach is to articulate the underlying principles while at the same time providing real-world applications. The key to successful segmentation is marker construction, and this issue is to some extent the focus of the chapter.

In his original (and highly mathematical) work, Random Sets and Integral Geometry, Georges Matheron, who along with Jean Serra founded the subject of mathematical morphology, comments, "Despite the purely mathematical nature of the present treatise, the formulation and the very choice of problems for solution are directly inspired by experimental techniques of texture analysis." It is not surprising, therefore, that morphological imaging is fundamental to a core understanding of texture. The sixth chapter discusses granulometric filters, which play a key role in describing and classifying texture and particle distributions. Whereas Matheron formalized their definition mathematically, granulometric-type methods are well known in sedimentology and the study of porous media.

The final chapter of the book concerns the automatic design of morphological operators. Morphological image processing is based on probing an image with structuring elements, and these determine the relationships within image structure that an algorithm can ascertain. Again quoting Matheron, "In general, the structure of an object is defined as the set of relationships existing between elements or parts of the object. . . Hence, this choice [of relationships]. . . determines the relative worth of the concept of structure at which we will arrive." In many cases it is possible to obtain satisfactory structuring elements by human ingenuity; however, when successful filtering requires hundreds or even thousands of structuring elements, automatic design from training data becomes essential. It is here that morphological image processing meets computational learning. Before closing this preface, we would like to acknowledge some of the people who helped make this book possible: Junior Barrera, Rubens Machado, Roberto Hirata, Jr., Nina S. T. Hirata, Marcel Brun, Yidong Chen, Seungchan Kim, Artyom Grigoryan, Ulisses Braga Neto, and the graduate students who attended the second semester-2002 Morphological Image Analysis course at State University of Campinas, Brazil, testing a preliminary version of this book. We especially thank our wives Terry and Valeria for their ongoing support. Finally, we hope you find this book both enjoyable and useful to your imaging work, in whatever your field.

Edward R. Dougherty
College Station, Texas

Roberto A. Lotufo
Campinas, Brazil


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