Cellular Skeletons: a New Approach to Topological Skeletons with Geometric Features

Aldo Gonzalez-Lorenzo (1, 2, 3) , Alexandra Bac (2, 3) , Jean-Luc Mari (2, 3) , Pedro Real (1)

1 Universidad de Sevilla = University of Seville
2 GMOD-LSIS - GMOD-LSIS
3 AMU - Aix Marseille Université

This paper introduces a new kind of skeleton for binary volumes called the cellular skeleton. This skeleton is not a subset of voxels of a volume nor a subcomplex of a cubical complex: it is a chain complex together with a reduction from the original complex. Starting from the binary volume we build a cubical complex which represents it regarding 6 or 26-connectivity. Then the complex is thinned using the proposed method based on elementary collapses, which preserves significant geometric features. The final step reduces the number of cells using Discrete Morse Theory. The resulting skeleton is a reduction which preserves the homology of the original complex and the geometrical information of the output of the previous step. The result of this method, besides its skeletonization content, can be used for computing the homology of the original complex, which usually provides well shaped homology generators.

Domaines: Informatique [cs]; Synthèse d'image et réalité virtuelle [cs.GR]; Géométrie algorithmique [cs.CG]; Autre [cs.OH]

Aldo Gonzalez-Lorenzo, Alexandra Bac, Jean-Luc Mari, Pedro Real. Cellular Skeletons: a New Approach to Topological Skeletons with Geometric Features. 16th International Conference on Computer Analysis of Images and Patterns (CAIP 2015), Sep 2015, La Valette, Malta. pp.616-627, ⟨10.1007/978-3-319-23117-4_53⟩. ⟨hal-01341037⟩