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Vision Geometry
Edited by: Robert A. Melter, Azriel Rosenfeld, and Prabir Bhattacharya

Contemporary Mathematics
1991; 237 pp; softcover
Volume: 119
ISBN-10: 0-8218-5125-X
ISBN-13: 978-0-8218-5125-8
List Price: US$110
Member Price: US$88
Order Code: CONM/119
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Since its genesis more than thirty-five years ago, the field of computer vision has been known by various names, including pattern recognitions, image analysis, and image understanding. The central problem of computer vision is obtaining descriptive information by computer analysis of images of a scene. Together with the related fields of image processing and computer graphics, it has become an established discipline at the interface between computer science and electrical engineering.

This volume contains fourteen papers presented at the AMS Special Session on Geometry Related to Computer Vision, held in Hoboken, New Jersey in October 1989. This book makes the results presented at the Special Session, which previously had been available only in the computer science literature, more widely available within the mathematical sciences community.

Geometry plays a major role in computer vision, since scene descriptions always involve geometrical properties of, and relations among, the objects or surfaces in the scene. The papers in this book provide a good sampling of geometric problems connected with computer vision. They deal with digital lines and curves, polygons, shape decompositions, digital connectedness and surfaces, digital metrics, and generalizations to higher-dimensional and graph-structured "spaces." Aimed at computer scientists specializing in image processing, computer vision, and pattern recognition--as well as mathematicians interested in applications to computer science--this book will provide readers with a view of how geometry is currently being applied to problems in computer vision.

Table of Contents

  • A. M. Bruckstein -- Self-similarity properties of digitized straight lines
  • J. Czyzowicz, I. Rival, and J. Urrutia -- Galleries and light matchings: Fat cooperative guards
  • M. Díaz and J. O'Rourke -- Chord centers for convex polygons
  • L. Dorst and A. W. M. Smeulders -- Discrete straight line segments: Parameters, primitives, and properties
  • P. K. Ghosh -- Vision, geometry, and Minkowski operators
  • G. T. Herman -- Discrete multidimensional Jordan surfaces
  • R. A. Melter -- A survey of digital metrics
  • D. Mount and R. Silverman -- Combinatorial and computational aspects of Minkowski decompositions
  • A. Rosenfeld and T. Y. Kong -- Connectedness of a set, its complement, and their common boundary
  • A. Rosenfeld and A. Y. Wu -- "Digital geometry" on graphs
  • D. Shaked, J. Koplowitz, and A. M. Bruckstein -- Star-shapedness of digitized planar shapes
  • R. Silverman and A. H. Stein -- Algorithms for the decomposition of convex polygons
  • A. W. M. Smeulders and L. Dorst -- Decomposition of discrete curves into piecewise straight segments in linear time
  • I. Stojmenović and R. Tošić -- Digitization schemes and the recognition of digital straight lines, hyperplanes, and flats in arbitrary dimensions
  • G. T. Toussaint -- Computational geometry and computer vision
  • D. Wood, G. J. E. Rawlins, and S. Schuierer -- Convexity, visibility, and orthogonal polygons
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