Digital connectivity and extended well-composed sets for gray images

In this paper, we propose a new definition of digital connectivity for gray images on a 2D space for arbitrary grid systems. We extend a digital version of the Jordan curve theorem and its converse proved earlier by Rosenfeld for the rectangular grid system. We also extend in two directions the concept of well-composed sets introduced by Latecki et al. (1995, Comput. Vision Image Understanding 61, 70-83), First, we extend the definition of well-composed sets from the quadratic grid system to an arbitrary grid system, Then, by using the concept of parameter-dependent connected components introduced by us in a previous work, we allow the pixels in a connected component of a well-composed set to have different gray values so that the connectivity of connected components accommodates a wider meaning. (C) 1997 Academic Press.