Computational Morphology: A Computational Geometric Approach to the Analysis of FormG.T. Toussaint Elsevier, 28 հնս, 2014 թ. - 273 էջ Computational Geometry is a new discipline of computer science that deals with the design and analysis of algorithms for solving geometric problems. There are many areas of study in different disciplines which, while being of a geometric nature, have as their main component the extraction of a description of the shape or form of the input data. This notion is more imprecise and subjective than pure geometry. Such fields include cluster analysis in statistics, computer vision and pattern recognition, and the measurement of form and form-change in such areas as stereology and developmental biology.This volume is concerned with a new approach to the study of shape and form in these areas. Computational morphology is thus concerned with the treatment of morphology from the computational geometry point of view. This point of view is more formal, elegant, procedure-oriented, and clear than many previous approaches to the problem and often yields algorithms that are easier to program and have lower complexity. |
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Chapter 3 Circular Separability of Planar Point Sets | 25 |
CHAPTER 4 SYMMETRY FINDING ALGORITHMS | 41 |
CHAPTER 5 COMPUTING THE RELATIVE NEIGHBOUR DECOMPOSITION OF A SIMPLE POLYGON | 53 |
Chapter 6 Polygonal Approximations of a Curve Formulations and Algorithms | 71 |
CHAPTER 7 ON POLYGONAL CHAIN APPROXIMATION | 87 |
CHAPTER 8 UNIQUENESS OF ORTHOGONAL CONNECTTHEDOTS | 97 |
CHAPTER 9 ON THE SHAPE OF A SET OF POINTS | 105 |
CHAPTER 10 ORTHOCONVEXITY AND ITS GENERALIZATIONS | 137 |
Chapter 11 Guard Placement in Rectilinear Polygons | 153 |
CHAPTER 12 REALIZABILITY OF POLYHEDRONS FROM LINE DRAWINGS | 177 |
CHAPTER 13 VORONOI AND RELATED NEIGHBORS ON DIGITIZED TWODIMENSIONAL SPACE WITH APPLICATIONS TO TEXTURE A... | 207 |
CHAPTER 14 A GRAPHTHEORETICAL PRIMAL SKETCH | 229 |
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Common terms and phrases
angle approximation problems arcs Art Gallery Theorem Assumption boundary bounded chain clusters complexity Computational Geometry computational morphology Computer Vision connected components consider construct contains convex hull convex polygons convex quadrilateral convex set decomposition defined denote determine diagonal diagram endpoints eroded pyramid Figure finite Gabriel graph Hence IEEE Image Processing Imai incidence structure input intersection labels Lemma line drawing line segments logn MDVD method minimum number monotone polygon monotone rectilinear polygons O-convex O'Rourke O(n log object obtained orthogonal polygons pairs parallel Pattern Recognition picture plane piecewise linear pixels planar point set polyhedra polyhedron projection Proof properties pyramidal tour realizability problem rectangles with width rectilinear polygon relative neighbourhood graph result separating circle set of points shape simple polygon solved spatial analysis stack star-shaped Step subset Sugihara symmetries texture Theorem triangle vertex vertices view direction view point visible Voronoi Voronoi diagram