정보처리학회논문지A (The KIPS Transactions:PartA)

한국정보처리학회 (Korea Information Processing Society)
권호 표지
DOI QR코드

DOI QR Code

전역 및 국부 기하 특성을 반영한 메쉬 분할

A Mesh Segmentation Reflecting Global and Local Geometric Characteristics

  • 임정훈 (충북대학교 컴퓨터교육과) ;
  • 박영진 (충북대학교 정보산업공학과) ;
  • 성동욱 (충북대학교 정보통신공학과) ;
  • 하종성 (우석대학교 게임콘텐츠학과) ;
  • 유관희 (충북대학교 정보산업공학과 및 컴퓨터교육과)
  • 발행 : 2007.12.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 3D 메쉬 모델의 텍스쳐 매핑, 단순화, 모핑, 압축, 형상정합 등 다양한 분야에 응용될 수 있는 메쉬분할 문제를 다룬다. 메쉬 분할은 주어진 메쉬를 서로 떨어진 집합(disjoint sets)으로 나누는 과정으로서, 본 논문에서는 메쉬의 전역적 및 국부적 기하 특성을 동시에 반영하여 메쉬를 분할하는 방법을 제시하고자 한다. 먼저 주어진 메쉬의 국부적 기하 특성인 곡률 정보와 전역적 기하 특성인 볼록성을 이용하여 메쉬 정점들 중 첨예정점(sharp vertex)을 추출하고, 모든 첨예정점들 간의 유클리디언 거리에 기반한 $\kappa$-평균군집화 기법[26]을 적용하여 첨예 정점들을 분할한다. 분할된 첨예정점에 속하지 않는 나머지 정점들에 대해서는 유클리디언 거리상 가까운 군집으로 병합하여 최종적인 메쉬분할이 이루어진다. 또한 본 논문에서 제안한 메쉬분할 방법을 구현하여 여러 메쉬 모델에 대해 실험 결과를 보여준다.

This paper is concerned with the mesh segmentation problem that can be applied to diverse applications such as texture mapping, simplification, morphing, compression, and shape matching for 3D mesh models. The mesh segmentation is the process of dividing a given mesh into the disjoint set of sub-meshes. We propose a method for segmenting meshes by simultaneously reflecting global and local geometric characteristics of the meshes. First, we extract sharp vertices over mesh vertices by interpreting the curvatures and convexity of a given mesh, which are respectively contained in the local and global geometric characteristics of the mesh. Next, we partition the sharp vertices into the $\kappa$ number of clusters by adopting the $\kappa$-means clustering method [29] based on the Euclidean distances between all pairs of the sharp vertices. Other vertices excluding the sharp vertices are merged into the nearest clusters by Euclidean distances. Also we implement the proposed method and visualize its experimental results on several 3D mesh models.

키워드

참고문헌

  1. B. Chazelle, et al., 'Strategies for polyhedral surface decomposition: an experimental study,' Computational Geometry: Theory and Applications, 7, pp.327-342, 1997 https://doi.org/10.1016/S0925-7721(96)00024-7
  2. 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, pp.14-25, 2006
  3. A. Shamir, 'A formulation of boundary mesh segmentation,' Proc. of 2nd Int. Sym. on 3D Data Processing, Visualization and Transmission (3DPVT'04), pp.82-89, 2004
  4. 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, pp.27-32, 2003
  5. 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, pp.212-217, 2003
  6. M. Garland, A. Willmott, and P. S. Heckbert, 'Hierarchical face clustering on polygonal surfaces,' Proc. of the 2001 Symposium on Interactive 3D Graphics, pp.49-58, 2001
  7. S. Katz and A. Tal, 'Hierarchical mesh decomposition using fuzzy clustering and cuts,' ACM Transactions on Graphics (TOG), Vol.22, No.3, pp.954-961, 2003 https://doi.org/10.1145/882262.882369
  8. T. Kanungo, D. M. Mount, N. S. Netanyahu, A. D. Piatko, R. Silverman, and A. Y. Wu, 'An efficient k-means clustering algorithm: analysis and implementation,' IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.24, No.7, pp.881-892, 2002 https://doi.org/10.1109/TPAMI.2002.1017616
  9. 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, pp.308-321, 1999 https://doi.org/10.1109/2945.817348
  10. 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, pp.25-36, 2003
  11. 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), pp.14-18, 1996
  12. D. Cohen Steiner, P. Alliez, and M. Desbrun, 'Variational shape approximation,' Proc. of the 31st Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH), pp.27-34, 2004
  13. D. D. Hoffman and W.A. Richards, 'Parts of recognition,' Cognition 18, 1984
  14. D. D. Hoffman and M. Singh, 'Salience of visual parts,' Cognition 63, 1997
  15. Y. Zhou and Z. Huang, 'Decomposing polygon meshes by means of critical points,' Proc. of MMM'04, 2004
  16. M. Mortara, G. Panae, M. Spagnuolo, B. Falcidieno and J. Rossignac, 'Blowing bubbles for the multi-scale analysis and decomposition of traingle meshes,' Algorithmica, Special Issues on Shape Algorithms, Vol. 38, No.2, pp.227-24, 2004 https://doi.org/10.1007/s00453-003-1051-4
  17. S. Katz, G. Leifman and A. Tal, 'Mesh segmentation using feature points and core etxraction,' Visual Computer Vol.21, 2005
  18. 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
  19. Y.J. Lee, S.Y. Lee, A. Shamir, D. Cohen-Or and H.-P. Seidel, Intelligent mesh scissoring using 3d snakes, Proc. of Pacific Graphics, pp. 279-287, 2004
  20. Kwan-Hee Yoo and Jong-Sung Ha, User-steered methods for extracting geometric features over 3D Meshes,' Computer-Aided Design and Applications, Vol.2, No.1-4, 2005
  21. Kwan-Hee Yoo, Geometric livewire and geometric livelane for 3d meshes,' Journal of KIPS, Vol.2, No.1-4, 2005
  22. F. Yamaguchi, Curves and surfaces in Computer Aided Geometric Design, Springer-Berlag, 1988
  23. G. Taubin, 'Estimating the tensor of curvatures of a surface from a polyhedral approximation,' Proc. of International Conf. on Computer Vision, 1995
  24. A. Rosenfeld and E. Johnston, 'Angle detection in digital curves,' IEEE Transactions on Computers, Vol.22, pp.875-878, 1973 https://doi.org/10.1109/TC.1973.5009188
  25. A.D.C. Smith, The Folding of the Human Brain: from Shape to Function, University of London, PhD Dissertations, 1999
  26. G. Turk, 'Re-tiling polygonal surfaces,' ACM Computer Graphics (Proc. of SIGGRAPH '92), Vol.26, No.2, pp.55-64, 1992
  27. D. Cohen-Steiner and J.M. Morvan, 'Restricted Delaunay triangulations and normal cycle', Proc. of 19th Annual ACM Sym. on Computational Geometry, pp.237-246, 2003
  28. 하종성, '삼차원 제조성에 응용할 수 있는 다면체 단조성 의 특성화', 한국정보과학회 논문지(A), 제24권 11호, pp. 1051-1058, 1997
  29. T. Kanungo, et al., 'An efficient k-means clustering algorithm: analysis and implementation,' IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 881-892
  30. Computational geometry algorithm library, http://www.cgal.org
  31. P. Shilane, M. Kazhdan, P. Min and T. Funkhouser, 'The Princeton shape benchmark,' Proc. of Shape Modeling International, 2004