ON TOPOLOGY PRESERVATION IN 3D THINNING

Topology preservation is a major concern of parallel thinning algorith ms for 2D and 3D binary images. To prove that a parallel thinning algo rithm preserves topology, one must show that it preserves topology for all possible images. But it would be difficult to check all images, s ince there are too many possible images. Efficient sufficient conditio ns which can simplify such proofs for the 2D case were proposed by Ron se [Discrete Appl. Math. 21, 1988, 69-79]. By Ronse's results, a 2D pa rallel thinning algorithm can be proved to be topology preserving by c hecking a rather small number of configurations. This paper establishe s sufficient conditions for 3D parallel thinning algorithms to preserv e topology. (C) 1994 Academic Press, Inc.