Geometry Of Discrete Sets With Applications To Pattern Recognition
Divyendu Sinha · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1990
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.