General neighborhood sequences in Zn

Authors:
András Hajdu;Lajos Hajdu;Robert Tijdeman
Affiliations:
Faculty of Informatics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary;Number Theory Research Group of the Hungarian Academy of Sciences, and Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary;Mathematical Institute, Leiden University, Postbus 9512, NL-2300 RA Leiden, The Netherlands
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 13
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Abstract

Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in Z^n only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretical criteria for certain important (e.g. metrical) properties of the sequences. Our results are valid for several types of classical neighborhood sequences and for generated distance functions (e.g. octagonal and chamfer distances) which are widely applied in digital image processing. We conclude the paper by showing how our results contribute to the theory of distance transformations.