Rectification of the chordal axis transform skeleton and criteria for shape decomposition

Skeletonization and parts-based decomposition are important to the analysis, characterization, and recognition of shapes. In earlier works we proposed the chordal axis transform (CAT), based on constrained Delaunay triangulations (CDT), for analyzing discrete shapes. In this paper, we refine the CAT skeleton to have smoother branches and stable branch points of any degree based on approximate co-circularity of edge-adjacent triangles. We also introduce new criteria for obtaining visually meaningful shape decompositions using approximate co-circularity and a discrete axial derivative for shapes based on their CDTs.