Some results concerning connected fuzzy digital pictures

A fuzzy digital picture is called 'connected' if it has only one connected component of constant fuzzy level that is maximal. In this paper, we prove three theorems concerning the connectedness of fuzzy digital pictures. The first theorem proves that colored three-pebble acceptors can determine whether a given fuzzy digital picture is connected. The second one proves that one-way parallel/sequential acceptors can also recognize the connectedness of fuzzy digital pictures. The third is a theorem on continuous functions on fuzzy digital pictures. We define 'continuous' functions on fuzzy digital pictures. Then, it is shown that for a function @? mapping fuzzy digital pictures to fuzzy digital ones @? is continuous iff @? takes connected fuzzy digital pictures into connected ones.