Image analysis and mathematical morphology

Preface 
Notation 
PART I. THE TOOLS 
 Chapter I. Principles-Criteria-Models 
  A. How to quantify the description of a structure 
  B. The four principles of quantification 
  C. Mathematical morphology 
  D. Euclidean criteria and algorithms 
  E. Models 
  F. Plan of the book 
  G. \"Pravda\" or \"Istina\"? 
 Chapter II. The Hit or Miss Transformation, Erosion and Opening 
  A. Why this chapter heading? 
  B. \"One, two, three infinity\" 
  C. The Hit or Miss transformation: an algebraic study 
  D. Opening and closing 
  E. Erosions and increasing mappings, morphological and algebraic openings 
  F. A classification of the structuring elements 
  G. Exercises 
 Chapter III. Hit or Miss Topology 
  A. What good is a topology? 
  B. Review of topology 
  C. The Hausdorff metric 
  D. Topological structure for the closed sets of R^n 
  E. Physical consequences of the Hit or Miss topology 
  F. Topological properties of the Hit or Miss transformation 
  G. Exercises 
 Chapter IV. The Convex Set Model 
  A. A basic model 
  B. Set properties of the convex sets 
  C. The global point of view: integral geometry for compact convex 
  D. Minkowski measures 
  E. Convex sets and anisotropies 
  F. Exercises 
 Chapter V. Morphological Parameters and Set Models 
  A. Degrees of irregularity 
  B. The convex ring and its extension 
  C. The regular model 
  D. The class %and fractal dimensions 
  E . Exercises 
PART TWO: PARTIAL KNOWLEDGE 
 Chapter VI. Digital Morphology 
  A. Introduction 
  B. Modules and the associated morphology 
  C. Grids and rotations 
  D. Grids and digital graphs 
  E. Digital metrics and the associated morphology 
  F. Digital morphology in Z^3 
  G. Exercises 
 Chapter VII. Digitalization 
  A. Representations 
  B. The digitalization concept 
  C. Digitalizable transformations for the class (F) 
  D. Homotopy and digitalization 
  E. Convexity and digitalization 
  F. Minkowski functionals and digitalization 
  G. Conclusions 
  H. Exercises 
 Chapter VIII. Random Sampling 
  A. Introduction 
  B. Situation I 
  C. Situation II 
  D. Situation III 
  E. Situation IV 
  F. Situation V 
  G. Conclusion 
  H. Exercises 
PART THREE: THE CRITERIA 
 Chapter IX. The Covariance 
  A. A simple, but effective, tool 
  B. Morphological properties 
  C. A few algorithms 
  D. A few probabilistic models 
  E. A few examples 
  F. Exercises 
 Chapter X. Size Criteria 
  A. What does \"size\" mean? 
  B. 1-D size distributions 
  C. Opening, closing, and size distribution in R^n 
  D. Size distribution and individuals 
  E. Spherical particles 
  F. Theoretical complements 
  G. Exercises 
 Chapter XI. Connectivity Criteria 
  A. introduction 
  B. The skeleton and maximum disks in R^n 
  C. Medial axis and derivations of the skeleton 
  D. Digitalization of the skeleton 
  E. Thinnings and thickenings 
  F. Homotopic thinnings and thickenings 
  G. Connected components analysis 
  H. Examples 
  I. Exercises 
 Chapter XII. Morphology for Grey-tone Functions 
  A. From sets to functions 
  B. General results 
  C. Transformations based on one cross-section 
  D. Transformations based on two cross-sections 
  E. Connectivity criteria 
  F. From functions to sets: segmentation by watersheds 
  G. Convexity and integral geometry 
  H. Random functions 
  I. Exercises 
PART FOUR: THE RANDOM MODELS 
 Chapter XIII. Random Closed Sets 
  A. introduction 
  B. The Boolean model 
  C. Models derived from Boolean sets 
  D. Poisson tesselation 
  E. Other tesselations 
  F. Point models 
  G. Random sets 
  H. The rose of models 
  I. Exercises 
 Chapter XIV. Modelling 
  A. Judicious use of probabilistic models 
  B. Mathematical models in morphology 
  C. Pattern recognition modelling 
APPENDIX 
BIBLIOGRAPHY 
Index