Medial faces from a concise 3D thinning algorithm

We propose in this paper a new 3D fully parallel thinning algorithm that we believe to be the most concise due to its simple characterization. The algorithm is indeed completely defined by a set of five patterns, three removing conditions and two non-removing conditions. These patterns are designed from the two fundamental and compatible constraints usually expected in skeleta: (1) Topology preservation and (2) Medial surface. From these two constraints, the removing patterns (α₁, α₂ and α₃) detect the non-local maxima, whereas the non-removing patterns (β₁ and β₂) prevent any topology change that the removing conditions could imply. We show that the three mentioned constraints are respected. The logical conciseness of our procedure, called MB-3D, makes it to our knowledge the easiest 3D thinning algorithm to implement. Some results are displayed, that illustrate the relevance of our approach.