Abstract
A thinning algorithm must `preserve topology,' but in the case of a parallel thinning algorithm it can be hard to prove that it does so. Ronse has given sufficient conditions which can be used to simplify such proofs in the 2D case. By Ronse's results, the fact that a parallel thinning algorithm is topology preserving can be verified by checking only a rather small number of configurations. This paper introduces Ronse-like sufficient conditions for 3D binary images.
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