Abstract
We introduce a parallel thinning algorithm with directional substeps based on the collapse operation, which is guaranteed to preserve topology and to provide a thin result. Then, we propose two variants of a surface-preserving thinning scheme, based on this parallel directional thinning algorithm. Finally, we propose a methodology to produce filtered surface skeletons, based on the above thinning methods and the recently introduced discrete λ-medial axis.
This work has been partially supported by the “ANR BLAN07–2_184378 MicroFiss” project.
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References
Attali, D., Boissonnat, J.-D., Edelsbrunner, H.: Stability and computation of the medial axis — a state-of-the-art report. In: Möller, T., Hamann, B., Russell, B. (eds.) Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. LNCS, pp. 1–19. Springer, Heidelberg (to appear, 2009)
Attali, D., Lachaud, J.O.: Delaunay conforming iso-surface, skeleton extraction and noise removal. Computational Geometry: Theory and Applications 19, 175–189 (2001)
Attali, D., Montanvert, A.: Modelling noise for a better simplification of skeletons. In: Proc. International Conference on Image Processing (ICIP), vol. 3, pp. 13–16 (1996)
Bertrand, G.: On critical kernels. Comptes Rendus de l’Académie des Sciences, Série Math. I(345), 363–367 (2007)
Bertrand, G., Couprie, M.: Two-dimensional parallel thinning algorithms based on critical kernels. Journal of Mathematical Imaging and Vision 31(1), 35–56 (2008)
Bertrand, G., Couprie, M.: A new 3D parallel thinning scheme based on critical kernels. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 580–591. Springer, Heidelberg (2006)
Bertrand, G., Couprie, M.: On parallel thinning algorithms: minimal non-simple sets, P-simple points and critical kernels. Journal of Mathematical Imaging and Vision 35(1), 23–35 (2009)
Borgefors, G., Ragnemalm, I., Sanniti di Baja, G.: The Euclidean distance transform: finding the local maxima and reconstructing the shape. In: Proc. of the 7th Scandinavian Conference on Image Analysis, vol. 2, pp. 974–981 (1991)
Chaussard, J., Couprie, M., Talbot, H.: A discrete lambda-medial axis. In: Brlek, S., Reutenauer, C., Provençal, X. (eds.) DGCI 2009. LNCS, vol. 5810, pp. 421–433. Springer, Heidelberg (2009)
Chazal, F., Lieutier, A.: The lambda medial axis. Graphical Models 67(4), 304–331 (2005)
Couprie, M., Bertrand, G.: New characterizations of simple points in 2D, 3D and 4D discrete spaces. IEEE Trans. on Pattern Analysis and Machine Intelligence 31(4), 637–648 (2009)
Davies, E.R., Plummer, A.P.N.: Thinning algorithms: a critique and a new methodology. Pattern Recognition 14, 53–63 (1981)
Ge, Y., Fitzpatrick, J.M.: On the generation of skeletons from discrete Euclidean distance maps. IEEE Trans. on Pattern Analysis and Machine Intelligence 18(11), 1055–1066 (1996)
Hesselink, W.H., Roerdink, J.B.T.M.: Euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform. IEEE Trans. on Pattern Analysis and Machine Intelligence 30(12), 2204–2217 (2008)
Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Computer Vision, Graphics and Image Processing 48, 357–393 (1989)
Kong, T.Y., Litherland, R., Rosenfeld, A.: Problems in the topology of binary digital images. In: Open problems in topology, pp. 376–385. Elsevier, Amsterdam (1990)
Kovalevsky, V.A.: Finite topology as applied to image analysis. Computer Vision, Graphics and Image Processing 46, 141–161 (1989)
Liu, L.: 3d thinning on cell complexes for computing curve and surface skeletons. Master’s thesis, Washington University in Saint Louis (May 2009)
Malandain, G., Fernández-Vidal, S.: Euclidean skeletons. Image and Vision Computing 16, 317–327 (1998)
Ogniewicz, R.L., Kübler, O.: Hierarchic Voronoi skeletons. Pattern Recognition 28(33), 343–359 (1995)
Pudney, C.: Distance-ordered homotopic thinning: a skeletonization algorithm for 3D digital images. Computer Vision and Image Understanding 72(3), 404–413 (1998)
Rémy, E., Thiel, E.: Exact medial axis with Euclidean distance. Image and Vision Computing 23(2), 167–175 (2005)
Rosenfeld, A.: A characterization of parallel thinning algorithms. Information and Control 29, 286–291 (1975)
Serra, J.: Image analysis and mathematical morphology. Academic Press, London (1982)
Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.: The Hamilton-Jacobi skeleton. In: International Conference on Computer Vision (ICCV), pp. 828–834 (1999)
Soille, P.: Morphological image analysis. Springer, Heidelberg (1999)
Talbot, H., Vincent, L.: Euclidean skeletons and conditional bisectors. In: Proc. VCIP 1992, SPIE, vol. 1818, pp. 862–876 (1992)
Vincent, L.: Efficient computation of various types of skeletons. In: Proc. Medical Imaging V, SPIE, vol. 1445, pp. 297–311 (1991)
Whitehead, J.H.C.: Simplicial spaces, nuclei and m-groups. Proceedings of the London Mathematical Society 45(2), 243–327 (1939)
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Chaussard, J., Couprie, M. (2009). Surface Thinning in 3D Cubical Complexes. In: Wiederhold, P., Barneva, R.P. (eds) Combinatorial Image Analysis. IWCIA 2009. Lecture Notes in Computer Science, vol 5852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10210-3_11
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DOI: https://doi.org/10.1007/978-3-642-10210-3_11
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