Rectification of the Chordal Axis Transform and a New Criterion for Shape Decomposition

In an earlier work we proposed the chordal axis transform (CAT) as a more useful alternative to the medial axis transform (MAT) for obtaining skeletons of discrete shapes. Since then, the CAT has benefited various applications in 2D and 3D shape analysis. In this paper, we revisit the CAT to address its deficiencies that are artifacts of the underlying constrained Delaunay triangulation (CDT). We introduce a valuation on the internal edges of a discrete shape's CDT based on a concept of approximate co-circularity. This valuation provides a basis for suppression of the role of certain edges in the construction of the CAT skeleton. The result is a rectified CAT skeleton that has smoother branches as well as branch points of varying degrees, unlike the original CAT skeleton whose branches exhibit oscillations in tapered sections of shapes and allows only degree-3 branch points. Additionally, the valuation leads to a new criterion for parsing shapes into visually salient parts that closely resemble the empirical decompositions of shapes by human subjects as recorded in experiments by M. Singh, G. Seyranian, and D. Hoffman.