RELATION BETWEEN PARALLEL AND SEQUENTIAL TRANSFORMATIONS ON DIGITAL IMAGES.

A discussion is presented of the relation between parallel and sequential transformations of the image from the following two viewpoints: (1) the power of the parallel and the sequential transformations are compared, where the neighborhood degree is used as the parameter. The neighborhood degree is defined in such a way that the point under consideration is counted as the first neighborhood; (2) the condition is sought for the equivalence between parallel and sequential transformations. The following results are obtained: the set of parallel transformations and the set of sequential transformation realizable with the neighborhood degree m, respectively, form the hierarchical structure with respect to m.