Two symmetrical thinning algorithms for 3D binary images, based on PP-simple points

In this paper, we propose two 3D symmetrical thinning algorithms based on the parallel deletion of PP-simple points. The first one permits surface skeletons to be obtained. The second one permits curve skeletons to be extracted, and as far as we know, this is the only symmetrical curve thinning algorithm which preserves topology.These algorithms have been conceived in order to obtain precise results on simple specific objects (parallelepipeds). Consequently, we can predict the number of deletion iterations, the number of deleted points, and the skeleton of these objects obtained by the two algorithms, which is hardly ever possible to assess with other algorithms even on these simple objects.