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