Abstract
We present a new definition of the 3D curve-skeleton. This definition provides a mathematically strict way to compare and evaluate various approaches to the skeletonization of 3D shapes. The definition is based on the usage of fat curves. A fat curve is a 3D object which allows to approximate tubular fragments of the shape. A set of fat curves is used to approximate the entire shape; such a set can be considered as a generalization of the 2D medial axis. We also present an algorithm which allows to build curve-skeletons according to the given definition. The algorithm is robust and efficient.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Blum, H.: A Transformation for Extracting New Descriptors of Shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual Form, pp. 362–380. MIT Press, Cambridge (1967)
Chang, M.C., Kimia, B.B.: Regularizing 3D medial axis using medial scaffold transforms. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. p. Accepted. IEEE Computer Society, Los Alamitos (2008)
Chuang, J.H., Tsai, C.H., Ko, M.C.: Skeletonization of three-dimensional object using generalized potential field. IEEE Trans. Pattern Anal. Mach. Intell. 22, 1241–1251 (2000), http://dx.doi.org/10.1109/34.888709
Cornea, N.D., Silver, D.: Curve-skeleton properties, applications, and algorithms. IEEE Transactions on Visualization and Computer Graphics 13, 530–548 (2007)
Dey, T.K., Sun, J.: Defining and computing curve-skeletons with medial geodesic function. In: Proceedings of the Fourth Eurographics Symposium on Geometry Processing, pp. 143–152. Eurographics Association, Aire-la-Ville (2006), http://portal.acm.org/citation.cfm?id=1281957.1281975
Giblin, P., Kimia, B.B.: A formal classification of 3d medial axis points and their local geometry. IEEE Trans. Pattern Anal. Mach. Intell. 26, 238–251 (2004), http://dx.doi.org/10.1109/TPAMI.2004.1262192
Palágyi, K., Kuba, A.: A parallel 12-subiteration 3d thinning algorithm to extract medial lines. In: Sommer, G., Daniilidis, K., Pauli, J. (eds.) CAIP 1997. LNCS, vol. 1296, pp. 400–407. Springer, Heidelberg (1997), http://portal.acm.org/citation.cfm?id=648241.752833
Siddiqi, K., Pizer, S.: Medial Representations: Mathematics, Algorithms and Applications, 1st edn. Springer Publishing Company, Incorporated, Heidelberg (2008)
Tagliasacchi, A., Zhang, H., Cohen-Or, D.: Curve skeleton extraction from incomplete point cloud. ACM Trans. Graph. 28, 1–71 (2009), http://doi.acm.org/10.1145/1531326.1531377
Telea, A., van Wijk, J.J.: An augmented fast marching method for computing skeletons and centerlines. In: Proceedings of the Symposium on Data Visualisation, VISSYM 2002, pp. 251–260. Eurographics Association, Aire-la-Ville (2002), http://portal.acm.org/citation.cfm?id=509740.509782
Wang, Y.S., Lee, T.Y.: Curve-skeleton extraction using iterative least squares optimization. IEEE Transactions on Visualization and Computer Graphics 14, 926–936 (2008), http://portal.acm.org/citation.cfm?id=1373109.1373261
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khromov, D. (2011). Curve-Skeletons Based on the Fat Graph Approximation. In: Blanc-Talon, J., Kleihorst, R., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2011. Lecture Notes in Computer Science, vol 6915. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23687-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-23687-7_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23686-0
Online ISBN: 978-3-642-23687-7
eBook Packages: Computer ScienceComputer Science (R0)