Laurent Najman is Professor in the Informatics Department of ESIEE, Paris and a member of the Institut Gaspard Monge, Paris-Est Marne-la-Vallée University in France. His current research interest is discrete mathematical morphology. Hugues Talbot is Associate Professor at ESIEE, Paris, France. His research interests include mathematical morphology, image segmentation, thin feature analysis, texture analysis, discrete and continuous optimization and associated algorithms.

• Preface xvPART I. FOUNDATIONS 1Chapter 1. Introduction to Mathematical Morphology 3Laurent NAJMAN, Hugues TALBOT1.1. First steps with mathematical morphology: dilations and erosions 41.2. Morphological filtering 121.3. Residues 221.4. Distance transform, skeletons and granulometric curves 241.5. Hierarchies and the watershed transform 301.6. Some concluding thoughts 33Chapter 2. Algebraic Foundations of Morphology 35Christian RONSE, Jean SERRA2.1. Introduction 352.2. Complete lattices 362.3. Examples of lattices 422.4. Closings and openings 512.5. Adjunctions 562.6. Connections and connective segmentation 642.7. Morphological filtering and hierarchies 75Chapter 3.Watersheds in Discrete Spaces 81Gilles BERTRAND, Michel COUPRIE, Jean COUSTY, Laurent NAJMAN3.1. Watersheds on the vertices of a graph 823.2. Watershed cuts: watershed on the edges of a graph 903.3. Watersheds in complexes 101PART II. EVALUATING AND DECIDING 109Chapter 4. An Introduction to Measurement Theory for Image Analysis 111Hugues TALBOT, Jean SERRA, Laurent NAJMAN4.1. Introduction 1114.2. General requirements 1124.3. Convex ring and Minkowski functionals 1134.4. Stereology and Minkowski functionals 1194.5. Change in scale and stationarity 1214.6. Individual objects and granulometries 1224.7. Gray-level extension 1284.8. As a conclusion 130Chapter 5. Stochastic Methods 133Christian LANTUÉJOUL5.1. Introduction 1335.2. Random transformation 1345.3. Random image 138Chapter 6. Fuzzy Sets and Mathematical Morphology 155Isabelle BLOCH6.1. Introduction 1556.2. Background to fuzzy sets 1566.3. Fuzzy dilations and erosions from duality principle 1606.4. Fuzzy dilations and erosions from adjunction principle 1656.5. Links between approaches 1676.6. Application to the definition of spatial relations 1706.7. Conclusion 176PART III. FILTERING AND CONNECTIVITY 177Chapter 7. Connected Operators based on Tree Pruning Strategies 179Philippe SALEMBIER7.1. Introduction 1797.2. Connected operators 1817.3. Tree representation and connected operator 1827.4. Tree pruning 1877.5. Conclusions 198Chapter 8. Levelings 199Jean SERRA, Corinne VACHIER, Fernand MEYER8.1. Introduction 1998.2. Set-theoretical leveling 2008.3. Numerical levelings 2098.4. Discrete levelings 2148.5. Bibliographical comment 227Chapter 9. Segmentation,Minimum Spanning Tree and Hierarchies 229Fernand MEYER, Laurent NAJMAN9.1. Introduction 2299.2. Preamble: watersheds, floodings and plateaus 2309.3. Hierarchies of segmentations 2379.4. Computing contours saliency maps 2529.5. Using hierarchies for segmentation 2559.6. Lattice of hierarchies 258PART IV. LINKS AND EXTENSIONS 263Chapter 10. Distance, Granulometry and Skeleton 265Michel COUPRIE, Hugues TALBOT10.1. Skeletons 26510.2. Skeletons in discrete spaces 26910.3. Granulometric families and skeletons 27010.4. Discrete distances 27510.5. Bisector function 27910.6. Homotopic transformations 28010.7. Conclusion 289Chapter 11. Color and Multivariate Images 291Jesus ANGULO, Jocelyn CHANUSSOT11.1. Introduction 29111.2. Basic notions and notation 29211.3. Morphological operators for color filtering 29911.4. Mathematical morphology and color segmentation 31211.5. Conclusion 320Chapter 12. Algorithms for Mathematical Morphology 323Thierry GÉRAUD, Hugues TALBOT, Marc VAN DROOGENBROECK12.1. Introduction 32312.2. Translation of definitions and algorithms 32412.3. Taxonomy of algorithms 32912.4. Geodesic reconstruction example 33412.5. Historical perspectives and bibliography notes 34412.6. Conclusions 352PART V. APPLICATIONS 355Chapter 13. Diatom Identification with Mathematical Morphology 357Michael WILKINSON, Erik URBACH, Andre JALBA, Jos ROERDINK13.1. Introduction 35713.2. Morphological curvature scale space 35813.3. Scale-space feature extraction 35913.4. 2D size-shape pattern spectra 35913.5. Datasets 36413.6. Results 36413.7. Conclusions 365Chapter 14. Spatio-temporal Cardiac Segmentation 367Jean COUSTY, Laurent NAJMAN, Michel COUPRIE14.1.Which objects of interest? 36814.2. How do we segment? 36914.3. Results, conclusions and perspectives 372Chapter 15. 3D Angiographic Image Segmentation 375Benoît NAEGEL, Nicolas PASSAT, Christian RONSE15.1. Context 37515.2. Anatomical knowledge modeling 37615.3. Hit-or-miss transform 37815.4. Application: two vessel segmentation examples 37815.5. Conclusion 383Chapter 16. Compression 385Beatriz MARCOTEGUI, Philippe SALEMBIER16.1. Introduction 38516.2. Morphological multiscale decomposition 38516.3. Region-based decomposition 38916.4. Conclusions 391Chapter 17. Satellite Imagery and Digital ElevationModels 393Pierre SOILLE17.1. Introduction 39317.2. On the specificity of satellite images 39417.3. Mosaicing of satellite images 39817.4. Applications to digital elevation models 40017.5. Conclusion and perspectives 405Chapter 18. Document Image Applications 407Dan BLOOMBERG, Luc VINCENT18.1. Introduction 40718.2. Applications 409Chapter 19. Analysis and Modeling of 3D Microstructures 421Dominique JEULIN19.1. Introduction 42119.3. Models of random multiscale structures 43119.4. Digital materials 44019.5. Conclusion 444Chapter 20. Random Spreads and Forest Fires 445Jean SERRA20.1. Introduction 44520.2. Random spread 44820.3. Forecast of the burnt zones 45120.4. Discussion: estimating and choosing 45320.5. Conclusions 454Bibliography 457List of Authors 499Index 501

Laurent Najman is Professor in the Informatics Department of ESIEE, Paris and a member of the Institut Gaspard Monge, Paris-Est Marne-la-Vallée University in France. His current research interest is discrete mathematical morphology. Hugues Talbot is Associate Professor at ESIEE, Paris, France. His research interests include mathematical morphology, image segmentation, thin feature analysis, texture analysis, discrete and continuous optimization and associated algorithms.

• Preface xvPART I. FOUNDATIONS 1Chapter 1. Introduction to Mathematical Morphology 3Laurent NAJMAN, Hugues TALBOT1.1. First steps with mathematical morphology: dilations and erosions 41.2. Morphological filtering 121.3. Residues 221.4. Distance transform, skeletons and granulometric curves 241.5. Hierarchies and the watershed transform 301.6. Some concluding thoughts 33Chapter 2. Algebraic Foundations of Morphology 35Christian RONSE, Jean SERRA2.1. Introduction 352.2. Complete lattices 362.3. Examples of lattices 422.4. Closings and openings 512.5. Adjunctions 562.6. Connections and connective segmentation 642.7. Morphological filtering and hierarchies 75Chapter 3.Watersheds in Discrete Spaces 81Gilles BERTRAND, Michel COUPRIE, Jean COUSTY, Laurent NAJMAN3.1. Watersheds on the vertices of a graph 823.2. Watershed cuts: watershed on the edges of a graph 903.3. Watersheds in complexes 101PART II. EVALUATING AND DECIDING 109Chapter 4. An Introduction to Measurement Theory for Image Analysis 111Hugues TALBOT, Jean SERRA, Laurent NAJMAN4.1. Introduction 1114.2. General requirements 1124.3. Convex ring and Minkowski functionals 1134.4. Stereology and Minkowski functionals 1194.5. Change in scale and stationarity 1214.6. Individual objects and granulometries 1224.7. Gray-level extension 1284.8. As a conclusion 130Chapter 5. Stochastic Methods 133Christian LANTUÉJOUL5.1. Introduction 1335.2. Random transformation 1345.3. Random image 138Chapter 6. Fuzzy Sets and Mathematical Morphology 155Isabelle BLOCH6.1. Introduction 1556.2. Background to fuzzy sets 1566.3. Fuzzy dilations and erosions from duality principle 1606.4. Fuzzy dilations and erosions from adjunction principle 1656.5. Links between approaches 1676.6. Application to the definition of spatial relations 1706.7. Conclusion 176PART III. FILTERING AND CONNECTIVITY 177Chapter 7. Connected Operators based on Tree Pruning Strategies 179Philippe SALEMBIER7.1. Introduction 1797.2. Connected operators 1817.3. Tree representation and connected operator 1827.4. Tree pruning 1877.5. Conclusions 198Chapter 8. Levelings 199Jean SERRA, Corinne VACHIER, Fernand MEYER8.1. Introduction 1998.2. Set-theoretical leveling 2008.3. Numerical levelings 2098.4. Discrete levelings 2148.5. Bibliographical comment 227Chapter 9. Segmentation,Minimum Spanning Tree and Hierarchies 229Fernand MEYER, Laurent NAJMAN9.1. Introduction 2299.2. Preamble: watersheds, floodings and plateaus 2309.3. Hierarchies of segmentations 2379.4. Computing contours saliency maps 2529.5. Using hierarchies for segmentation 2559.6. Lattice of hierarchies 258PART IV. LINKS AND EXTENSIONS 263Chapter 10. Distance, Granulometry and Skeleton 265Michel COUPRIE, Hugues TALBOT10.1. Skeletons 26510.2. Skeletons in discrete spaces 26910.3. Granulometric families and skeletons 27010.4. Discrete distances 27510.5. Bisector function 27910.6. Homotopic transformations 28010.7. Conclusion 289Chapter 11. Color and Multivariate Images 291Jesus ANGULO, Jocelyn CHANUSSOT11.1. Introduction 29111.2. Basic notions and notation 29211.3. Morphological operators for color filtering 29911.4. Mathematical morphology and color segmentation 31211.5. Conclusion 320Chapter 12. Algorithms for Mathematical Morphology 323Thierry GÉRAUD, Hugues TALBOT, Marc VAN DROOGENBROECK12.1. Introduction 32312.2. Translation of definitions and algorithms 32412.3. Taxonomy of algorithms 32912.4. Geodesic reconstruction example 33412.5. Historical perspectives and bibliography notes 34412.6. Conclusions 352PART V. APPLICATIONS 355Chapter 13. Diatom Identification with Mathematical Morphology 357Michael WILKINSON, Erik URBACH, Andre JALBA, Jos ROERDINK13.1. Introduction 35713.2. Morphological curvature scale space 35813.3. Scale-space feature extraction 35913.4. 2D size-shape pattern spectra 35913.5. Datasets 36413.6. Results 36413.7. Conclusions 365Chapter 14. Spatio-temporal Cardiac Segmentation 367Jean COUSTY, Laurent NAJMAN, Michel COUPRIE14.1.Which objects of interest? 36814.2. How do we segment? 36914.3. Results, conclusions and perspectives 372Chapter 15. 3D Angiographic Image Segmentation 375Benoît NAEGEL, Nicolas PASSAT, Christian RONSE15.1. Context 37515.2. Anatomical knowledge modeling 37615.3. Hit-or-miss transform 37815.4. Application: two vessel segmentation examples 37815.5. Conclusion 383Chapter 16. Compression 385Beatriz MARCOTEGUI, Philippe SALEMBIER16.1. Introduction 38516.2. Morphological multiscale decomposition 38516.3. Region-based decomposition 38916.4. Conclusions 391Chapter 17. Satellite Imagery and Digital ElevationModels 393Pierre SOILLE17.1. Introduction 39317.2. On the specificity of satellite images 39417.3. Mosaicing of satellite images 39817.4. Applications to digital elevation models 40017.5. Conclusion and perspectives 405Chapter 18. Document Image Applications 407Dan BLOOMBERG, Luc VINCENT18.1. Introduction 40718.2. Applications 409Chapter 19. Analysis and Modeling of 3D Microstructures 421Dominique JEULIN19.1. Introduction 42119.3. Models of random multiscale structures 43119.4. Digital materials 44019.5. Conclusion 444Chapter 20. Random Spreads and Forest Fires 445Jean SERRA20.1. Introduction 44520.2. Random spread 44820.3. Forecast of the burnt zones 45120.4. Discussion: estimating and choosing 45320.5. Conclusions 454Bibliography 457List of Authors 499Index 501

Laurent Najman is Professor in the Informatics Department of ESIEE, Paris and a member of the Institut Gaspard Monge, Paris-Est Marne-la-Vallée University in France. His current research interest is discrete mathematical morphology. Hugues Talbot is Associate Professor at ESIEE, Paris, France. His research interests include mathematical morphology, image segmentation, thin feature analysis, texture analysis, discrete and continuous optimization and associated algorithms.

• Preface xvPART I. FOUNDATIONS 1Chapter 1. Introduction to Mathematical Morphology 3Laurent NAJMAN, Hugues TALBOT1.1. First steps with mathematical morphology: dilations and erosions 41.2. Morphological filtering 121.3. Residues 221.4. Distance transform, skeletons and granulometric curves 241.5. Hierarchies and the watershed transform 301.6. Some concluding thoughts 33Chapter 2. Algebraic Foundations of Morphology 35Christian RONSE, Jean SERRA2.1. Introduction 352.2. Complete lattices 362.3. Examples of lattices 422.4. Closings and openings 512.5. Adjunctions 562.6. Connections and connective segmentation 642.7. Morphological filtering and hierarchies 75Chapter 3.Watersheds in Discrete Spaces 81Gilles BERTRAND, Michel COUPRIE, Jean COUSTY, Laurent NAJMAN3.1. Watersheds on the vertices of a graph 823.2. Watershed cuts: watershed on the edges of a graph 903.3. Watersheds in complexes 101PART II. EVALUATING AND DECIDING 109Chapter 4. An Introduction to Measurement Theory for Image Analysis 111Hugues TALBOT, Jean SERRA, Laurent NAJMAN4.1. Introduction 1114.2. General requirements 1124.3. Convex ring and Minkowski functionals 1134.4. Stereology and Minkowski functionals 1194.5. Change in scale and stationarity 1214.6. Individual objects and granulometries 1224.7. Gray-level extension 1284.8. As a conclusion 130Chapter 5. Stochastic Methods 133Christian LANTUÉJOUL5.1. Introduction 1335.2. Random transformation 1345.3. Random image 138Chapter 6. Fuzzy Sets and Mathematical Morphology 155Isabelle BLOCH6.1. Introduction 1556.2. Background to fuzzy sets 1566.3. Fuzzy dilations and erosions from duality principle 1606.4. Fuzzy dilations and erosions from adjunction principle 1656.5. Links between approaches 1676.6. Application to the definition of spatial relations 1706.7. Conclusion 176PART III. FILTERING AND CONNECTIVITY 177Chapter 7. Connected Operators based on Tree Pruning Strategies 179Philippe SALEMBIER7.1. Introduction 1797.2. Connected operators 1817.3. Tree representation and connected operator 1827.4. Tree pruning 1877.5. Conclusions 198Chapter 8. Levelings 199Jean SERRA, Corinne VACHIER, Fernand MEYER8.1. Introduction 1998.2. Set-theoretical leveling 2008.3. Numerical levelings 2098.4. Discrete levelings 2148.5. Bibliographical comment 227Chapter 9. Segmentation,Minimum Spanning Tree and Hierarchies 229Fernand MEYER, Laurent NAJMAN9.1. Introduction 2299.2. Preamble: watersheds, floodings and plateaus 2309.3. Hierarchies of segmentations 2379.4. Computing contours saliency maps 2529.5. Using hierarchies for segmentation 2559.6. Lattice of hierarchies 258PART IV. LINKS AND EXTENSIONS 263Chapter 10. Distance, Granulometry and Skeleton 265Michel COUPRIE, Hugues TALBOT10.1. Skeletons 26510.2. Skeletons in discrete spaces 26910.3. Granulometric families and skeletons 27010.4. Discrete distances 27510.5. Bisector function 27910.6. Homotopic transformations 28010.7. Conclusion 289Chapter 11. Color and Multivariate Images 291Jesus ANGULO, Jocelyn CHANUSSOT11.1. Introduction 29111.2. Basic notions and notation 29211.3. Morphological operators for color filtering 29911.4. Mathematical morphology and color segmentation 31211.5. Conclusion 320Chapter 12. Algorithms for Mathematical Morphology 323Thierry GÉRAUD, Hugues TALBOT, Marc VAN DROOGENBROECK12.1. Introduction 32312.2. Translation of definitions and algorithms 32412.3. Taxonomy of algorithms 32912.4. Geodesic reconstruction example 33412.5. Historical perspectives and bibliography notes 34412.6. Conclusions 352PART V. APPLICATIONS 355Chapter 13. Diatom Identification with Mathematical Morphology 357Michael WILKINSON, Erik URBACH, Andre JALBA, Jos ROERDINK13.1. Introduction 35713.2. Morphological curvature scale space 35813.3. Scale-space feature extraction 35913.4. 2D size-shape pattern spectra 35913.5. Datasets 36413.6. Results 36413.7. Conclusions 365Chapter 14. Spatio-temporal Cardiac Segmentation 367Jean COUSTY, Laurent NAJMAN, Michel COUPRIE14.1.Which objects of interest? 36814.2. How do we segment? 36914.3. Results, conclusions and perspectives 372Chapter 15. 3D Angiographic Image Segmentation 375Benoît NAEGEL, Nicolas PASSAT, Christian RONSE15.1. Context 37515.2. Anatomical knowledge modeling 37615.3. Hit-or-miss transform 37815.4. Application: two vessel segmentation examples 37815.5. Conclusion 383Chapter 16. Compression 385Beatriz MARCOTEGUI, Philippe SALEMBIER16.1. Introduction 38516.2. Morphological multiscale decomposition 38516.3. Region-based decomposition 38916.4. Conclusions 391Chapter 17. Satellite Imagery and Digital ElevationModels 393Pierre SOILLE17.1. Introduction 39317.2. On the specificity of satellite images 39417.3. Mosaicing of satellite images 39817.4. Applications to digital elevation models 40017.5. Conclusion and perspectives 405Chapter 18. Document Image Applications 407Dan BLOOMBERG, Luc VINCENT18.1. Introduction 40718.2. Applications 409Chapter 19. Analysis and Modeling of 3D Microstructures 421Dominique JEULIN19.1. Introduction 42119.3. Models of random multiscale structures 43119.4. Digital materials 44019.5. Conclusion 444Chapter 20. Random Spreads and Forest Fires 445Jean SERRA20.1. Introduction 44520.2. Random spread 44820.3. Forecast of the burnt zones 45120.4. Discussion: estimating and choosing 45320.5. Conclusions 454Bibliography 457List of Authors 499Index 501