Geodesic
3D circular shapes and curve skeletons
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 90-99.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: medial axis, curve skeleton, fat curve. 
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D. V. Khromov. 3D circular shapes and curve skeletons. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 90-99. http://geodesic.mathdoc.fr/item/IVM_2012_4_a9/

[1] Blum H., “A transformation for extracting new descriptors of shape”, Models for the Perception of Speech and Visual Form, 1967, 362–380

[2] Lieutier A., “Any open bounded subset of $R^n$ has the same homotopy type than its medial axis”, Proceedings of the eighth ACM symposium on Solid modeling and applications, 2003

[3] Mekhedov I. S., “Mnogolistnaya ploskaya figura i ee sredinnaya os”, Izv. vuzov. Matem., 2011, no. 12, 42–53

[4] Cornea N. D., Silver D., Min P., “Curve-skeleton properties, applications, and algorithms”, IEEE Transactions on Visualization and Computer Graphics, 13:3 (2007), 530–548 | DOI

[5] Siddiqi K., Pizer S. M., Medial representations: mathematics, algorithms and applications, Springer, 2008 | MR

[6] Mestetskii L. M., Nepreryvnaya morfologiya binarnykh izobrazhenii: figury, skelety, tsirkulyary, Fizmatlit, M., 2009