Piecewise Approximation of Pictures Using Maximal Neighborhoods

Suppose that we are given a picture having approximately piecewise constant gray leveL Each point P has a largest neighborhood N(P) that is entirely contained in one of the constant regions, and the set of maximal N(P)\´s (i.e., N(P)\´s not contained in other N(P)\´s) constitutes an economical description of the picture, generalizing the Blum "skeleton" or medial axis transformation. This description can be used to construct approximations to the picture (e.g., by discarding small N(P)\´s). The picture can be smoothed, without excessive blurring, by averaging over each N(P). By taking differences between pairs of touching maximal N(P)\´s, the edges between the regions can be detected; since this edge detection scheme is not based on symmetrical detection operators, it is not handicapped when two adjacent regions differ greatly in size.