A duality theorem for two connectivity-preserving parallel shrinking transformations

Authors:
Hiroshi Umeo;Giancarlo Mauri
Affiliations:
Osaka Electro-Communication University, Graduate School of Engineering, Faculty of Information Science and Technology, Department of Engineering Informatics, Neyagawa-shi, Hatsu-cho, 18-8, 572-853 ...;Università degli Studi di Milano--Bicocca, Dipartimento di Informatica, Sistemistica e Comunicazione, Via Bicocca degli Arcimboldi 8, 20126 Milan, Italy
Venue:
Future Generation Computer Systems - Cellular automata CA 2000 and ACRI 2000
Year:
2002

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Abstract

We study two classical connectivity-preserving parallel shrinking algorithms proposed to recognize and label two-dimensional connected components of binary images. The algorithms we consider were developed by Beyer [Recognition of topological invariants by iterative arrays, Ph.D. Thesis, MIT, 1969, p. 144] and Levialdi [Commun. ACM 15 (1) (1972) 7] independently for the purpose of shrinking 4-connected and 8-connected components of binary images in linear time, respectively. It is shown that those two independently developed algorithms are closely related and in a sense they are in a dual relation such that, for any initially given binary image and its inverted one, one algorithm produces, simultaneously, an image which is dual of the one produced by the other, step-by-step.