Detection of the non-topology preservation of Mas 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), 501506] have written a paper in which they claim that Ma and Sonkas 3D thinning algorithm [Ma, C., Sonka, M., 1996. A fully parallel 3D thinning algorithm and its applications. Computer Vision and Image Understanding 64 (3), 420433] does not preserve topology. As they highlight in their paper, a counterexample has been given in Lohous thesis [Lohou, C., 2001. Contribution  lanalyse topologique des images: tude dalgorithmes de squelettisation pour images 2D et 3D selon une approche topologie digitale ou topologie discrte. Ph.D. thesis, Univ. de Marne-la-Valle, France]. In fact, the previous Mas algorithm [Ma, C., 1995. A 3D fully parallel thinning algorithm for generating medial faces. Pattern Recognition Lett. 16, 8387] does not preserve topology. The goal of this paper is to show how P-simple points have guided us towards a proof that Mas algorithm does not always preserve topology.
digital topology 3d parallel thinning algorithm topology preservation