General neighborhood sequences in Z

Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in Z 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.