- Volume 5 Issue 4
In this paper, we propose a hierarchical method for segmenting a given 3D mesh, which hierarchically clusters sharp vertices of the mesh using the metric of geodesic distance among them. Sharp vertices are extracted from the mesh by analyzing convexity that reflects global geometry. As well as speeding up the computing time, the sharp vertices of this kind avoid the problem of local optima that may occur when feature points are extracted by analyzing the convexity that reflects local geometry. For obtaining more effective results, the sharp vertices are categorized according to the priority from the viewpoint of cognitive science, and the reasonable number of clusters is automatically determined by analyzing the geometric features of the mesh.
Mesh Segmentation;Hierarchical Clustering;Sharp Vertex;Geodesic Distance
- B. Chazelle et al., "Strategies for polyhedral surface decomposition: an experimental study," Computational Geometry: Theory and Applications, Vol. 7, 1997, pp. 327-342. https://doi.org/10.1016/S0925-7721(96)00024-7
- M. Attene, S. Katz, M. Mortara, G. Patane, M. Spagnuolo, and A Tal, "Mesh segmentation - a comparative study," IEEE Int. Conf. on Shape Modeling and Applications, 2006, pp. 14-25.
- D. L. Page, A F. Koschan, and M. A. Abidi, "Perception based 3D triangle mesh segmentation using fast matching watersheds," Conference on Computer Vision and Pattern Recognition, 2003, pp. 27-32. https://doi.org/10.1109/CVPR.2003.1211448
- T. Srinak and C. Kambhamettu, "A novel method for 3D surface mesh segmentation," Proc. of the 6th IASTED International Conference on Computers, Graphics, and Imaging, 2003, pp. 212-217.
- M. Garland, A. Willmott, and P. S. Heckbert, "Hierarchical face clustering on polygonal surfaces," Proc. of the 2001 Symposium on Interactive 3D Graphics, 2001, pp. 49-58.
- S. Katz and A. Tal, "Hierarchical mesh decomposition using fuzzy clustering and cuts," ACM Transactions on Graphics (TOG), Vol.22, No.3, 2003, pp. 954-961. https://doi.org/10.1145/882262.882369
- T. Kanungo, D. M. Mount, N. S. Netanyahu, A. D. Piatko, R. Silverman, and A. Y. Wu, "An efficient -means clustering algorithm: analysis and implementation," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.24, No. 7, 2002, pp. 881-892. https://doi.org/10.1109/TPAMI.2002.1017616
- A. P. Mangan and R. T. Whitaker, "Partitioning 3D surface meshes using watershed segmentation," IEEE Transactions on Visualization and Computer Graphics, Vol.5, No.4, 1999, pp. 308-321. https://doi.org/10.1109/2945.817348
- T. K. Dey, J. Giesen, and S. Goswami, "Shape segmentation and matching with flow discretization," Proc. of the Workshop on Algorithms and Data Structures (WADS), Vol.2748, 2003, pp.25-36. https://doi.org/10.1007/978-3-540-45078-8_3
- K. Wu and M. D. Levine, "3D part segmentation using simulated electrical charge distributions," Proc. of the 1996 IEEE International Conference on Pattern Recognition (ICPR), 1996, pp.14-18. https://doi.org/10.1109/ICPR.1996.545983
- D. Cohen-Steiner, P. Alliez, and M. Desbrun, "Variational shape approximation," Proc. of the 31st Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH), 2004, pp.27-34.
- Y. Zhou and Z. Huang, "Decomposing polygon meshes by means of critical points," Proc. of MMM'04, 2004, pp.187-195. https://doi.org/10.1109/MULMM.2004.1264985
- M. Mortara, G. Panae, M. Spagnuolo, B. Falcidieno, and J. Rossignac, "Blowing bubbles for the multi-scale analysis and decomposition of triangle meshes," Algorithmica, Special Issues on Shape Algorithms, Vol. 38, No. 2, 2004, pp.227-24. https://doi.org/10.1007/s00453-003-1051-4
- S. Katz, G. Leifman, and A. Tal, "Mesh segmentation using feature points and core extraction," Visual Computer Vol.21, 2005, pp.649-658. https://doi.org/10.1007/s00371-005-0344-9
- J. M. Lien and N. M. Amato, "Approximate convex decomposition of polyhedra," Technical Report TR06-002, Dept. of Computer Science, Texas A&M University, 2006.
- D. D. Hoffman and W. A. Richards, "Parts of recognition," Cognition, Vol.18, 1984.
- D. D. Hoffman and M. Singh, "Salience of visual parts," Cognition, Vol.63, 1997.
- F. Yamaguchi, Curves and surfaces in Computer Aided Geometric Design, Springer-Berlag, 1988.
- G. Taubin, "Estimating the tensor of curvatures of a surface from a polyhedral approximation," Proc. of International Conf. on Computer Vision, 1995.
- A. Rosenfeld and E. Johnston, "Angle detection in digital curves," IEEE Transactions on Computers, Vol. 22, 1973, pp.875-878. https://doi.org/10.1109/TC.1973.5009188
- A.D.C. Smith, The Folding of the Human Brain: from Shape to Function, University of London, PhD Dissertations, 1999.
- S. C. Johnson (1967): "Hierarchical Clustering Schemes" Psychometrika, pp. 2:241-254
- E. W. Dijkstra, "A note on two problems in connection with graphs," Numerische Mathematik, Vol. 1, 1959, pp.269-271. https://doi.org/10.1007/BF01386390
- D. Cohen-Steiner and J.M. Morvan, "Restricted Delaunay triangulations and normal cycle", Proc. of 19th Annual ACM Sym. on Computational Geometry, 2003, pp.237-246.
- Computational geometry algorithm library, http://www.cgal.org.
- P. Shilane, M. Kazhdan, P. Min, and T. Funkhouser, "The Princeton shape benchmark," Proc. of Shape Modeling International, 2004.
- Y. J. Park et. al., "Mesh segmentation with the geodesic means of clustering of sharp vertices," IASTED08, 2008.