Abstract
A new skeletonization algorithm is presented to compute the curvilinear skeleton of 3D objects. The algorithm is based on the use of the <3,4,5> distance transform, on the detection of suitable anchor points, and on iterated topology preserving voxel removal. The obtained skeleton is topologically correct, is symmetrically placed within the object and its structure reflects the morphology of the represented object.
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References
Siddiqi, K., Pizer, S.M. (eds.): Medial Representations. Springer, Heidelberg (2008)
De Floriani, L., Spagnuolo, M. (eds.): Shape Analysis and Structuring. Springer, Heidelberg (2008)
Arcelli, C., Sanniti di Baja, G.: A width-independent fast thinning algorithm. IEEE Trans. on PAMI 7, 463–474 (1985)
Klein, F.: Euclidean skeletons. In: Proc. 5th Scandinavian Conf. Image Anal., pp. 443–450 (1987)
Arcelli, C., Sanniti di Baja, G.: A one-pass two-operations process to detect the skeletal pixels on the 4-distance transform. IEEE Trans. PAMI 11, 411–414 (1989)
Xia, Y.: Skeletonization via the realization of the fire front’s propagation and extinction in digital binary shapes. IEEE Trans. PAMI 11(10), 1076–1086 (1989)
Arcelli, C., Sanniti di Baja, G.: Euclidean skeleton via center-of-maximal-disc extraction. Image and Vision Computing 11, 163–173 (1993)
Kimmel, R., Shaked, D., Kiryati, N.: Skeletonization via distance maps and level sets. Computer Vision and Image Understanding 62(3), 382–391 (1995)
Sanniti di Baja, G., Thiel, E.: Skeletonization algorithm running on path-based distance maps. Image and Vision Computing 14, 47–57 (1996)
Pudney, C.: Distance-ordered homotopic thinning: a skeletonization algorithm for 3D digital images. Computer Vision and Image Understanding 72(3), 404–413 (1998)
Zhou, Y., Kaufman, A., Toga, A.W.: Three-dimensional skeleton and centerline generation based on an approximate minimum distance field. The Visual Computer 14(7), 303–314 (1998)
Borgefors, G., Nystrom, I., Sanniti di Baja, G.: Computing skeletons in three dimensions. Pattern Recognition 32(7), 1225–1236 (1999)
Sanniti di Baja, G., Svensson, S.: Surface skeletons detected on the d6 distance transform. In: Amin, A., Pudil, P., Ferri, F., Iñesta, J.M. (eds.) SPR 2000 and SSPR 2000. LNCS, vol. 1876, pp. 387–396. Springer, Heidelberg (2000)
Blum, H.: Biological shape and visual science. Journal of Theoretical Biology 38, 205–287 (1973)
Leymarie, F., Levine, M.D.: Simulating the grassfire transform using an active contour model. IEEE Trans. PAMI 14(1), 56–75 (1992)
Kimia, B.B., Tannenbaum, A., Zucker, S.W.: Shape, shocks, and deformations I: the components of two-dimensional shape and the reaction-diffusion space. International Journal of Computer Vision 15, 189–224 (1995)
Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.W.: Hamilton-Jacobi skeletons. International Journal of Computer Vision 48(3), 215–231 (2002)
Dimitrov, P., Damon, J.N., Siddiqi, K.: Flux invariants for shape. In: Proc. IEEE Conf. CVPR 2003, Madison, WI, vol. 1, pp. 835–841 (2003)
Giblin, P.J., Kimia, B.B.: A formal classification of 3D medial axis points and their local geometry. IEEE Trans. PAMI 26(2), 238–251 (2004)
Saha, P.K., Chaudhuri, B.B.: Detection of 3D simple points for topology preserving transformations with application to thinning. IEEE Trans. PAMI 16(10), 1028–1032 (1994)
Bertrand, G., Malandain, G.: A new characterization of three-dimensional simple points. Pattern Recognition Letters 15(2), 169–175 (1994)
Borgefors, G.: Digital distance transforms in 2D, 3D, and 4D. In: Chen, C.H., Wang, P.P.S. (eds.) Handbook of Pattern Recognition and Computer Vision, pp. 157–176. World Scientific, Singapore (2005)
Svensson, S., Sanniti di Baja, G.: Using distance transforms to decompose 3D discrete objects. Image and Vision Computing 20, 529–540 (2002)
Shaked, D., Bruckstein, A.M.: Pruning medial axes. Computer Vision and Image Understanding 69(2), 156–169 (1998)
Svensson, S., Sanniti di Baja, G.: Simplifying curve skeletons in volume images. Computer Vision and Image Understanding 90(3), 242–257 (2003)
AIM@SHAPE Shape Repository, http://shapes.aimatshape.net/viewmodels.php
Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton Shape Benchmark. In: Shape Modeling International, Genova, Italy (June 2004)
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Arcelli, C., Sanniti di Baja, G., Serino, L. (2009). The <3,4,5> Curvilinear Skeleton. In: Brlek, S., Reutenauer, C., Provençal, X. (eds) Discrete Geometry for Computer Imagery. DGCI 2009. Lecture Notes in Computer Science, vol 5810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04397-0_35
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DOI: https://doi.org/10.1007/978-3-642-04397-0_35
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