Abstract
The medial axis of a planar shape is the set of points having at least two closest points on the shape boundary. This notion is widely used in computer science. In this paper we propose a mathematical model enabling us to define the notion of a curve skeleton as a 3D generalization of the 2D medial axis. We propose a criterion for comparing various particular methods for the construction of curve skeletons.
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References
H. Blum, “A Transformation for Extracting New Descriptors of Shape,” Models for the Perception of Speech and Visual Form (1967), pp. 362–380.
A. Lieutier, “Any Open Bounded Subset of R n Has the Same Homotopy Type Than Its Medial Axis,” in Proceedings of the 8th ACM Symposium on Solid Modeling and Applications, 2003.
S. I. Mekhedov, “A Multisheet Plane Figure and Its Medial Axis,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 12, 42–53 (2011) [RussianMathematics (Iz. VUZ) 55 (12), 34–43 (2011)].
N. D. Cornea, D. Silver, and P. Min, “Curve-Skeleton Properties, Applications, and Algorithms,” IEEE Transactions on Visualization and Computer Graphics 13(3) 530–548 (2007).
K. Siddiqi and S. M. Pizer, Medial Representations: Mathematics, Algorithms and Applications (Springer, 2008).
L. M. Mestetskii, Continuous Morphology of Binary Images: Shapes, Skeletons, Circulars (Fizmatlit, Moscow, 2009) [in Russian].
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Original Russian Text © D.V. Khromov, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 4, pp. 90–99.
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Khromov, D.V. 3D circular shapes and curve skeletons. Russ Math. 56, 75–83 (2012). https://doi.org/10.3103/S1066369X1204010X
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DOI: https://doi.org/10.3103/S1066369X1204010X