Detection of the non-topology preservation of Ma’s 3D surface-thinning algorithm, by the use of P-simple points

Recently, Wang and Basu [Wang, T., Basu, A., 2007. A note on ‘a fully parallel 3D thinning algorithm and its applications’. Pattern Recognition Lett. 28 (4), 501–506] have written a paper in which they claim that Ma and Sonka’s 3D thinning algorithm [Ma, C., Sonka, M., 1996. A fully parallel 3D thinning algorithm and its applications. Computer Vision and Image Understanding 64 (3), 420–433] does not preserve topology. As they highlight in their paper, a counterexample has been given in Lohou’s thesis [Lohou, C., 2001. Contribution à l’analyse topologique des images: étude d’algorithmes de squelettisation pour images 2D et 3D selon une approche topologie digitale ou topologie discrète. Ph.D. thesis, Univ. de Marne-la-Vallée, France]. In fact, the previous Ma’s algorithm [Ma, C., 1995. A 3D fully parallel thinning algorithm for generating medial faces. Pattern Recognition Lett. 16, 83–87] does not preserve topology. The goal of this paper is to show how P-simple points have guided us towards a proof that Ma’s algorithm does not always preserve topology.