Parts of Visual Form: Computational Aspects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Teddy: a sketching interface for 3D freeform design
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Representation and detection of deformable shapes
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Rectification of the chordal axis transform skeleton and criteria for shape decomposition
Image and Vision Computing
2D Shape Decomposition Based on Combined Skeleton-Boundary Features
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Combinatorial shape decomposition
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
Chordal axis on weighted distance transforms
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
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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.