Computational Morphology : a Computational Geometric Approach to the Analysis of Form

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Front Cover; Computational Morphology: A Computational Geometric Approach to the Analysis of Form; Copyright Page; Table of Contents; Preface; Chapter 1. Computational Complexity of Restricted Polygon Decompositions; 1. Introduction; 2. Restricted Convex and Spiral Decompositions; 3. Computing Restricted Star-Shaped Decompositions; CHAPTER 2. COMPUTING MONOTONE SIMPLE CIRCUITS IN THE PLANE; 1. INTRODUCTION; 2. PYRAMIDAL TOURS AND MONOTONE CIRCUITS; 3. DISCUSSION; REFERENCES; Chapter 3. Circular Separability of Planar Point Sets; 1. Introduction; 2. Geometric properties of S(S1,S2). 3. Algorithm CIRCULAR and its worst-case analysis4. Smallest and largest separating circles; 5. Conclusions; REFERENCES; CHAPTER 4. SYMMETRY FINDING ALGORITHMS; 1. Introduction; 2. Algorithms in Two Dimensions; 3. Three Dimensions; 4. Optimality; 5. Final Remarks: ""Near"" Symmetry; References; CHAPTER 5. COMPUTING THE RELATIVE NEIGHBOUR DECOMPOSITION OF A SIMPLE POLYGON; 1. INTRODUCTION; 2. THE RND PROBLEM; 3. PROOF OF PLANARITY; 4. ALGORITHMS; 5. CONCLUDING REMARKS; REFERENCES; Chapter 6. Polygonal Approximations of a Curve

Formulations and Algorithms; 1. Introduction. 2. Approximation problems for a piecewise linear function3. The approximation problems for a general piecewise linear curve; 4. Concluding Remarks; Acknowledgment; References; CHAPTER 7. ON POLYGONAL CHAIN APPROXIMATION; 1. INTRODUCTION; 2. THE ALGORITHM; REFERENCES; CHAPTER 8. UNIQUENESS OF ORTHOGONAL CONNECT-THE-DOTS; 1. INTRODUCTION; 2. TWO DIMENSIONS; 3. THREE DIMENSIONS; 4. DISCUSSION; REFERENCES; CHAPTER 9. ON THE SHAPE OF A SET OF POINTS; 1. Introduction; 2. Motivation for Studying Form; 3. Properties of a Point Set; 4. Methods of Point Pattern Analysis; 5. Notions of Shape. 6. Decompositions That Characterize Form7. Discussion; REFERENCES; CHAPTER 10. ORTHO-CONVEXITY AND ITS GENERALIZATIONS; 1. Introduction; 2. Characterizations of ortho-convexity; 3. A second definition of orthogonal convexity; 4. Ortho-convex hulls; 5. Restricted-Orientation Convexity; 6. Generalized convexity; 7. Future directions; 8. References; Chapter 11. Guard Placement in Rectilinear Polygons; 1. INTRODUCTION; 2. OVERVIEW OF ALGORITHM; 3. QUADRILATERIZING PYRAMIDS; 4. QUADRILATERIZING MONOTONE POLYGONS; 5. QUADRILATERIZING RECTILINEAR POLYGONS; OPEN PROBLEMS; ACKNOWLEDGEMENTS; REFERENCES. CHAPTER 12. REALIZABILITY OF POLYHEDRONS FROM LINE DRAWINGS1. INTRODUCTION; 2. REALIZABILITY PROBLEMS; 3. PERSPECTIVE, OBLIQUE, OR ORTHOGRAPHIC; 4. LABELING SCHEME; 5. GRADIENT SPACE AND RECIPROCAL FIGURES; 6. LINEAR-ALGEBRAIC APPROACH; 7. FLEXIBLE JUDGMENT OF THE REALIZABILITY; 8. REALIZABILITY OF RECTANGULAR OBJECTS; 9. CONCLUDING REMARKS; ACKNOWLEDGMENTS; REFERENCES; CHAPTER 13. VORONOI AND RELATED NEIGHBORS ON DIGITIZED TWO-DIMENSIONAL SPACE WITH APPLICATIONS TO TEXTURE ANALYSIS; 1. Introduction; 2. Definition of Modified Digital Voronoi Diagram; 3. Algorithm to Obtain the MDVD