Powerful Parallel Symmetric 3D Thinning Schemes Based on Critical Kernels

The main contribution of the present article consists of new 3D parallel and symmetric thinning schemes which have the following qualities: - They are effective and sound, in the sense that they are guaranteed to preserve topology. This guarantee is obtained thanks to a theorem on critical kernels; - They are powerful, in the sense that they remove more points, in one iteration, than any other symmetric parallel thinning scheme; - They are versatile, as conditions for the preservation of geometrical features (e.g., curve extremities or surface borders) are independent of those accounting for topology preservation; - They are efficient: we provide in this article a small set of masks, acting in the grid Z3, that is sufficient, in addition to the classical simple point test, to straightforwardly implement them