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Proceedings Paper

Geometry Of Discrete Sets With Applications To Pattern Recognition
Author(s): Divyendu Sinha
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Paper Abstract

In this paper we present a new framework for discrete black and white images that employs only integer arithmetic. This framework is shown to retain the essential characteristics of the framework for Euclidean images. We propose two norms and based on them, the permissible geometric operations on images are defined. The basic invariants of our geometry are line images, structure of image and the corresponding local property of strong attachment of pixels. The permissible operations also preserve the 3x3 neighborhoods, area, and perpendicularity. The structure, patterns, and the inter-pattern gaps in a discrete image are shown to be conserved by the magnification and contraction process. Our notions of approximate congruence, similarity and symmetry are similar, in character, to the corresponding notions, for Euclidean images [1]. We mention two discrete pattern recognition algorithms that work purely with integers, and which fit into our framework. Their performance has been shown to be at par with the performance of traditional geometric schemes. Also, all the undesired effects of finite length registers in fixed point arithmetic that plague traditional algorithms, are non-existent in this family of algorithms.

Paper Details

Date Published: 1 March 1990
PDF: 15 pages
Proc. SPIE 1192, Intelligent Robots and Computer Vision VIII: Algorithms and Techniques, (1 March 1990); doi: 10.1117/12.969734
Show Author Affiliations
Divyendu Sinha, Stevens Institute of Technology (United States)

Published in SPIE Proceedings Vol. 1192:
Intelligent Robots and Computer Vision VIII: Algorithms and Techniques
David P. Casasent, Editor(s)

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