3D circular shapes and curve skeletons. (English. Russian original) Zbl 1254.65030
Russ. Math. 56, No. 4, 75-83 (2012); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 4, 90-99 (2012).
In the paper under review a notion of a curve skeleton as a 3D generalization of the 2D medial axis is proposed. It is based on the definition of the concept of fat curve which is very similar to that of canal surface.
Reviewer: Juan Monterde (Burjasot)
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
References:
| [1] | H. Blum, ”A Transformation for Extracting New Descriptors of Shape,” Models for the Perception of Speech and Visual Form (1967), pp. 362–380. |
| [2] | 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. |
| [3] | 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)]. · Zbl 1253.53009 |
| [4] | 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). · doi:10.1109/TVCG.2007.1002 |
| [5] | K. Siddiqi and S. M. Pizer, Medial Representations: Mathematics, Algorithms and Applications (Springer, 2008). · Zbl 1151.00014 |
| [6] | L. M. Mestetskii, Continuous Morphology of Binary Images: Shapes, Skeletons, Circulars (Fizmatlit, Moscow, 2009) [in Russian]. |
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