Pierre Soille

Morphological Image Analysis

Springer-Verlag Berlin Heidelberg GmbH

Pierre Soille

Morphological Image Analysis Principles and Applications

Second Edition Corrected second printing

With 260 Figures

, Springer

Dr. Pierre Soille EC Joint Research Centre Via Enrico Fermi 1, T.P.262 21020 Ispra (Va) ltaly e-mail: Pierre.Soille@jrc.it

Library of Congress Cataloging-in-Publication Data SoiIle, Pierre. (Morphologische Bildverarbeitung. English) Morphological image analysis: principles and applications 1 Pierre SoiIle.-- md ed ISBN 978-3-642-07696-1 ISBN 978-3-662-05088-0 (eBook) DOI 10.1007/978-3-662-05088-0 1. Image analysis. 2. Image processing--Mathematics. 3. Morphisms (Mathematics) I. Title TA1637.S6513 2002 621.36'7--dc21 2002030513

ISBN 978-3-642-07696-1

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To the memory of my father, Andre Soille (1923-2002)

Preface to the second edition

Following the success of the first edition, recent developments in the field of morphological image analysis called for an extended second edition. This was not an easy task because any single modification and extension had to be care­fully evaluated for preserving a coherent structure. The text has been fully revised with the goal of improving its clarity while introducing new concepts of interest to real image analysis applications. The skeleton of the book en­joys one additional bone in the form of a chapter devoted to texture analysis. Flesh around the initial bones has grown by more than 20 percent leading to a total of 391 pages (including 39 additional figures, 3 new tables, 93 extra bibliographical references, as well as 1 supplementary index). This increase has been distributed more or less evenly across all chapters. Main extensions include: discussion about multichannel images and their morphological pro­cessing, ordering relations on image partitions, connected operators and level­lings, homotopy for grey tone images, translation-invariant implementations of erosions and dilations by line segments, reinforced emphasis on rank-based morphological operators, grey tone hit-or-miss, ordered independent homoto­pic thinnings and anchored skeletons, self-dual geodesic transformation and reconstruction, area based self-dual filters, anti-centre, watershed-based tex­ture segmentation, texture models, and a series of new scientific and industrial applications. Chapters on erosions/dilations and openings/closings have been made more concise by moving notions such as the morphological covariance and granulometries to the texture analysis chapter.

The first edition in English has been published in 1999 while I was with the Silsoe Research Institute (SRI) located in Silsoe, England. I am indebted to all members of the image analysis group led by Robin Tillett for intro­ducing me to the captivating world of computer vision applied to agri-food industries. John Marchant from this group deserves special thanks for sug­gestions he made on a draft of the revised 'background notions' chapter. In December 1999, I joined the Space Applications Institute of the EC Joint Research Centre (JRC) established in Ispra, Italy. This opened an avenue for the application of mathematical morphology (MM) to Pan-European geospa­tial data sets. I am very grateful to all JRC staff I have been in contact with since my arrival and especially to all members of the advanced methods sec­tor led by Joannis Kanellopoulos. Martino Pesaresi deserves a special thank

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for sparkling ideas and great enthusiasm for applying MM to earth obser­vation imagery. I have also the pleasure to acknowledge Philippe Caperan, Daniele Ehrlich, and Jurgen Vogt for their interest in the application of MM to their projects. Beyond my colleagues at work, I wish to thank all people interested in image analysis I have been in touch with since the last edition of this book. Their encouragements, suggestions, or simply eager to learn and apply morphological image analysis to real problems have been a constant source of motivation and inspiration for the completion of this second edition. Feedback from readers has always been very much appreciated. In particular, I would like to credit Michel Kocher for regular correspondence and sugges­tions. Special thanks to Dietrich Stoyan for his interest to the first edition of this book including his comments on the first edition in German. The chapter on texture analysis is based on a paper published in a volume of the Lecture Notes in Physics co-edited by Dietrich Stoyan and Klaus Mecke. I am thank­ful to them for their comments and suggestions on the early version of the paper. Many thanks also to Robert Magerle for his openness and interest in applying morphology to atomic force microscopy images, Henk Heijmans for many fruitful discussions at the JRC and CWI, Christian Ronse for his advices, Hugues Talbot for his visit to SRI and the collaborative work we did on directional morphology, Vincent Ranwez for the joint work on order in­dependent thinnings, Laurent Misson for the tree ring project, Paul Whelan for the watermark project, Gunilla Borgefors, Vito Di Gesu, Joachim Ohser, Pramod Rastogi, Gerald Sommer, Michela Spagnuolo, Cesare Valenti, and Rein van den Boomgaard for inviting me to give lectures in conjunction with seminars, conferences, or postgraduate courses.

Finally, the greatest change since the last edition is the arrival of my son Simon in March 2000. He and my wife Sabine motivated me to speed up the production of this second edition during the many sacrificed evenings and holidays. I am enormously thankful to them for their understanding and support. I hope you will appreciate this new edition and find it useful. In any case, I will be very grateful to hear from you for further comments and suggestions.

Preface to the first edition

In 1992, by the time I was finishing my doctorate thesis jointly at the Ecole des Mines de Paris and the Universite catholique de Louvain, my former colleague Jean-Franc;ois Rivest and I have had the opportunity to organise a tutorial course about morphological image processing during an interna­tional conference held in The Hague. The success of this course as well as others organised later in Sydney, Delft, Quebec City, and Brisbane rapidly convinced me that there was a need for an application-oriented book present­ing the principles and latest developments of morphological image analysis. The intent of the present book is to fulfil this need.

The book is self-contained in the sense that it is accessible to engineers, scientists, and practitioners having no prior experience with morphology. In addition, most necessary background notions about digital image processing are covered. The emphasis being put on the techniques useful for solving prac­tical problems rather than the theory underlying mathematical morphology, no special knowledge about set theory and topology is required. Neverthe­less, the book goes well beyond an introduction to mathematical morpho­logy. Indeed, starting from the fundamental transformations, more elaborate methods which have proved their practical usefulness are explained. This is achieved through a step by step process pursued until the most recent ad­vances.

The successful completion of this book has been very challenging because there are now many teams around the world participating to the fruitful de­velopment of morphology and working on a wide variety of topics ranging from the definition of new filters to the design of novel algorithmic tech­niques. Inevitably, some subjects are more detailed than others due to my own experience and research activities. Bibliographical notes and references are included at the end of each chapter to help the reader finding further readings on a specific theme. The total number of distinct references equals 364. Each chapter dealing with a well defined topic, only 30 of references appear on more than one chapter.

Acknowledgements are due to all people involved with image analysis and whom I met since 1988 when I begun my research activities in this fascinating field. Their dedication to both applied and theoretical research has been a constant source of inspiration for the writing of this book. Naming all these

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people would be a very difficult and dangerous exercise since I would surely forget some of them. Nevertheless, I wish to express my deep acknowledge­ments to Jean Serra's group of the Centre de Morphologie Mathematique of the Ecole des Mines de Paris which I worked with during four years. This book would never have been published without the very fruitful discussions and joint research projects I have had with the group members and the many people who visited the Centre during my stay. Mark Berman's image analysis group of the Commonwealth Scientific and Industrial Research Organisation, Mathematical and Information Sciences (Sydney) which I visited in 1992-1993 and September 1997 also deserves special thanks. The comments and suggestions of all group members concerning preliminary versions of this book helped me a lot. Moreover, their constant interest in my book project motiv­ated me to pursue it. The pattern recognition department of the Fraunhofer­Institut fur Produktionsanlagen und Konstruktionstechnik (Berlin) which I visited in 1993 and 1995 has been a real chance for me to be confronted with the many technical aspects regarding the application of image analysis to industrial applications. Thanks a lot to Bertram Nickolay and all members of his department. I am also indebted to Tilman Jochems for many advises and helpful discussions following the reading of a draft copy of this book. Piero Zamperoni from the Technische Universitiit Braunschweig deserves my deep gratitude for its kind encouragements, the very careful reading of the German version of this book, and the many discussions and thorough sugges­tions. Thanks are also due to Bernd Jiihne from the Universitiit Heidelberg and Paul Whelan from the Dublin City University for their interest in my book project. In addition, I wish to acknowledge the Ecole des Mines d'Ales and its Laboratoire de Genie Informatique et d'Ingenierie de la Production, site EERIE (Nimes) where I have been lecturing and pursuing my research activities during the period 1995-1998.

I would like to conclude in gratitude to Sabine Miiller who shared with me the necessary motivation for successfully achieving this book. In addition, the former German version of this book would never have been written without her help. For comments and suggestions aiming at improving and extending the present book, I would like to thank all readers in advance.

Contents

1. Introduction.............................................. 1 1.1 Origin of mathematical morphology. . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Scope of morphological image analysis .................... 4

1.2.1 Image filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Image segmentation .............................. 6 1.2.3 Image measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.4 Some other tasks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Book organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11 1.4 Bibliographical notes and references ...................... 12

2. Background Notions.. . . . . . .. .. .. . . .. . . .. . . .. .. .... .. . .. .. 15 2.1 From continuous to discrete spaces ....................... 15 2.2 Discrete images ........................................ 17

2.2.1 Binary image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 2.2.2 Grey tone image ................................. 18 2.2.3 Multichannel image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21

2.3 Image to image transformations . . . . . . . . . . . . . . . . . . . . . . . . .. 22 2.3.1 Point image transformations. . . . . . . . . . . . . . . . . . . . . .. 23 2.3.2 Neighbourhood image transformations. . . . . . . . . . . . .. 24

2.4 Set operators applied to images .......................... 26 2.5 Ordering relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29

2.5.1 On pixel intensity values .......................... 29 2.5.2 On images and image transformations.. . . . . . . . . . . . .. 30 2.5.3 On set partitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31 2.5.4 Links to lattice theory ............................ 32

2.6 Discrete geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32 2.6.1 Graphs.......................................... 32 2.6.2 Grids and connectivity. . . . . . . . . . . . . . . . . . . . . . . . . . .. 35 2.6.3 Discrete boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38 2.6.4 Discrete lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40 2.6.5 Convexity....................................... 43

2.7 Discrete distances and distance functions. . . . . . . . . . . . . . . . .. 45 2.7.1 Definitions ...................................... 45 2.7.2 Computation.................................... 47

2.8 Image transformation properties. . . . . . . . . . . . . . . . . . . . . . . . .. 49 2.9 Bibliographical notes and references ...................... 57

xii Contents

3. Erosion and Dilation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63 3.1 Structuring element. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 64 3.2 Erosion............................................... 65 3.3 Dilation............................................... 68 3.4 Properties............................................. 70 3.5 Links with other transformations . . . . . . . . . . . . . . . . . . . . . . . .. 74

3.5.1 Distance function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75 3.5.2 Distance between sets. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75 3.5.3 Minkowski operators. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 76 3.5.4 Rank filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77

3.6 Extensions to graphs and multichannel images ............. 78 3.6.1 Morphology for arbitrary graphs ................... 78 3.6.2 Morphology for multichannel images . . . . . . . . . . . . . . .. 78

3.7 On the structuring element choice. . . . . . . . . . . . . . . . . . . . . . .. 80 3.7.1 Elementary symmetric. . . . . . . . . . . . . . . . . . . . . . . . . . .. 80 3.7.2 Digital approximations of the disc. . . . . . . . . . . . . . . . .. 80 3.7.3 Pair of points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82 3.7.4 Digital approximations of line segments .... . . . . . . . .. 82 3.7.5 Adaptive........................................ 83 3.7.6 Composite....................................... 84 3.7.7 Miscellaneous.................................... 84

3.8 First words: morphological gradients. . . . . . . . . . . . . . . . . . . . .. 84 3.8.1 Basic morphological gradients. . . . . . . . . . . . . . . . . . . . .. 85 3.8.2 Half gradients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86 3.8.3 Thick gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 87 3.8.4 Directional gradients. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88

3.9 Computation of erosions and dilations. . . . . . . . . . . . . . . . . . . .. 89 3.9.1 Line segments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89 3.9.2 Periodic lines ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92 3.9.3 Moving histogram technique. . . . . . . . . . . . . . . . . . . . . .. 92 3.9.4 Fast binary erosions and dilations ....... . . . . . . . . . .. 96

3.10 Bibliographical notes and references ...................... 97

4. Opening and Closing . .................................... 105 4.1 Morphologicalopening .................................. 105 4.2 Morphological closing ................................... 108 4.3 Properties ............................................. 109 4.4 Algebraic opening and closing ............................ 112

4.4.1 Trivial and attribute openings ..................... 112 4.4.2 Area opening .................................... 113 4.4.3 Parametric opening ............................... 114 4.4.4 Annular opening ................................. 115 4.4.5 Convex hull closing ............................... 116

4.5 Top-hats .............................................. 121 4.5.1 Definitions ...................................... 121

Contents xiii

4.5.2 Application to the correction of uneven illumination .. 124 4.5.3 Application to contrast enhancement ............... 126

4.6 Multiscale gradient ..................................... 127 4.7 An industrial application ................................ 130 4.8 Computation of openings and closings ..................... 132

4.8.1 Structural openings ............................... 132 4.8.2 Attribute openings ............................... 132 4.8.3 Closing by a half-plane ............................ 133

4.9 Bibliographical notes and references ...................... 135

5. Hit-Dr-miss and Skeletons ................................. 139 5.1 Hit-or-miss transform ................................... 140

5.1.1 Binary case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 140 5.1.2 Grey scale extensions ............................. 142 5.1.3 Applications ..................................... 146 5.1.4 Hit-or-miss opening ............................... 149 5.1.5 Rank hit-or-miss ................................. 150

5.2 Thinning and thin-fit ................................... 150 5.2.1 Generic definitions ................................ 151 5.2.2 Homotopic thinning .............................. 152

5.3 Thickening and thick-miss ............................... 155 5.3.1 Generic definitions ................................ 155 5.3.2 Examples ....................................... 157

5.4 Euclidean skeletons ..................................... 158 5.4.1 Grass-fire or wavefront propagation ................. 159 5.4.2 Distance function ................................. 159 5.4.3 Maximal discs ................................... 159 5.4.4 Minimal paths ................................... 160 5.4.5 Openings ........................................ 160

5.5 Discrete skeletons ...................................... 161 5.5.1 Openings ........................................ 161 5.5.2 Homotopic sequential thinnings .................... 162 5.5.3 Order independent homotopic thinnings ............. 163 5.5.4 Distance function ................................. 168 5.5.5 Skeleton pruning ................................. 169 5.5.6 Skeleton by influence zones ........................ 170 5.5.7 Two practical applications ......................... 173

5.6 Computation of HMTs and skeletons ...................... 175 5.6.1 Look-up-table implementation of binary HMTs ....... 175 5.6.2 Skeletonisation algorithms ......................... 176

5.7 Bibliographical notes and references ...................... 177

xiv Contents

6. Geodesic Transformations ................................ 183 6.1 Elementary geodesic transformations ...................... 183

6.1.1 Geodesic dilation ................................. 183 6.1.2 Geodesic erosion ................................. 185 6.1.3 Self-dual geodesic transformation ................... 188

6.2 Morphological reconstruction ............................ 189 6.2.1 Definitions ...................................... 190 6.2.2 Implementation .................................. 194 6.2.3 On the choice of the mask and marker images ........ 196

6.3 Reconstruction based operators .......................... 196 6.3.1 Blob analysis .................................... 197 6.3.2 Double threshold ................................. 199 6.3.3 Regional extrema ................................. 201 6.3.4 Extended and h-extrema .......................... 203 6.3.5 Depth or dynamic of an image extremum ............ 204 6.3.6 Minima imposition ............................... 206 6.3.7 Fillhole ......................................... 208 6.3.8 Ultimate eroded set ............................... 208 6.3.9 Opening/closing by reconstruction .................. 210 6.3.10 Top-hat by reconstruction ......................... 212

6.4 Interpolation of contour data ............................ 212 6.5 Bibliographical notes and references ...................... 216

7. Geodesic Metrics . ........................................ 219 7.1 Geodesic distance ...................................... 219

7.1.1 Definitions ...................................... 219 7.1.2 Use for interpolation .............................. 221

7.2 Operators based on geodesic distance ..................... 222 7.2.1 Lower complete transformation ..................... 222 7.2.2 Geodesic skeleton by influence zones ................ 227 7.2.3 Propagation function ............................. 227

7.3 Generalised geodesy .................................... 231 7.3.1 Geodesic time .................................... 231 7.3.2 Geodesic dissimilarity ............................. 232 7.3.3 Dilation, erosion, and influence zone ................ 233 7.3.4 Application to minimal path detection .............. 233

7.4 Computation of geodesic distances and times ............... 234 7.4.1 Geodesic distance function ......................... 235 7.4.2 Geodesic time function ............................ 237

7.5 Bibliographical notes and references ...................... 238

Contents xv

8. Filtering .................................................. 241 8.1 Morphological filter definition ............................ 242

8.1.1 Necessary and sufficient properties .................. 242 8.1.2 Further properties ................................ 243

8.2 Design of a morphological filter ........................... 244 8.2.1 Parallel combinations ............................. 245 8.2.2 Sequential combinations ........................... 245 8.2.3 Iterative combinations ............................ 248

8.3 Alternating sequential filters ............................. 249 8.3.1 Definition ....................................... 249 8.3.2 Example ........................................ 251

8.4 Self-dual filters ......................................... 251 8.5 Toggle mappings ....................................... 255

8.5.1 Centre .......................................... 255 8.5.2 Anti-centre ...................................... 259 8.5.3 Toggle contrast .................................. 259

8.6 A practical application .................................. 260 8.7 Bibliographical notes and references ...................... 263

9. Segmentation ............................................. 267 9.1 Image segmentation techniques ........................... 268 9.2 The watershed transformation ............................ 268

9.2.1 Definition in terms of flooding simulations ........... 269 9.2.2 Definition in terms of generalised geodesy ........... 272 9.2.3 Computation of watersheds ........................ 274

9.3 Marker-controlled segmentation .......................... 277 9.3.1 Principle ........................................ 277 9.3.2 On the choice of marker and segmentation functions .. 279 9.3.3 Direct computation of watersheds with markers ...... 281

9.4 Case studies ........................................... 281 9.4.1 Separation of overlapping blobs .................... 282 9.4.2 Reconstruction of the boundaries of convex regions ... 285 9.4.3 Watersheds on topographic data ................... 285 9.4.4 Fringe segmentation .............................. 286

9.5 Bibliographical notes and references ...................... 290

10. Classification ............................................. 293 10.1 Pixel-based classification techniques ....................... 294 10.2 Watershed-based clustering .............................. 295

10.2.1 Principle ........................................ 295 10.2.2 Histogram filtering ............................... 296 10.2.3 Sensitivity to feature scalings ...................... 299

10.3 Subsequent spatial segmentation ......................... 302 10.3.1 Principle ........................................ 302 10.3.2 Partitioning of satellite images ..................... 306

xvi Contents

10.3.3 Discussion ....................................... 310 10.4 Bibliographical notes and references ...................... 313

11. Texture analysis .......................................... 317 11.1 Granulometry .......................................... 318

11.1.1 Principle ........................................ 318 11.1.2 Texture classification using global granulometries ..... 321 11.1.3 Texture segmentation using local granulometries ..... 322 11.1.4 Discrete line segments and discs .................... 323

11.2 Morphological covariance ................................ 328 11.2.1 Principle ........................................ 328 11.2.2 Applications ..................................... 328

11.3 Orientation of directional structures ...................... 329 11.3.1 Global orientation information ..................... 330 11.3.2 Local orientation information (orientation field) ...... 332

11.4 Multiscale area measurements ............................ 334 11.4.1 Fractal or noninteger dimensions ................... 335 11.4.2 Morphological fractal dimension .................... 336

11.5 Some other techniques .................................. 338 11.5.1 Extrema analysis and watershed segmentation ....... 338 11.5.2 Connectivity number ............................. 340 11.5.3 Texture models .................................. 340

11.6 Summary table ......................................... 342 11.7 Bibliographical notes and references ...................... 342

12. Application Fields ........................................ 347 12.1 Geoscience and remote sensing ........................... 347 12.2 Materials science ....................................... 350 12.3 Biological and medical imaging ........................... 351 12.4 Industrial applications .................................. 356 12.5 Identification and security control ........................ 358 12.6 Document processing ................................... 359 12.7 Image coding .......................................... 360 12.8 Other applications ...................................... 361 12.9 Further links and references .............................. 362

List of Symbols ............................................... 369

N arne index .................................................. 371

Citation index ................................................ 377

Subject index ................................................. 382