Advertisement

Non-manifold Medial Surface Reconstruction from Volumetric Data

  • Takashi Michikawa
  • Hiromasa Suzuki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6130)

Abstract

We present a method for medial surface reconstruction from volumetric data of thin-plate objects including junctions. Given medial voxels and distance fields computed from binarized volumes, we polygonize medial voxels by covering them with spherical supports and connecting the center points of the supports. These spherical supports are constructed by distributing spheres depending on the topological type of the voxels so that junction and boundary voxels are distributed first. Triangular meshes are built from Voronoi diagrams on medial voxels. This improvement builds correct junctions, whereas conventional voxel-based methods tend to result in small cavities around them. This paper also demonstrates several results computed from CT-scanned engineering objects.

Keywords

Voronoi Diagram Medial Surface Medial Axis Volumetric Data Polygonal Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3d surface construction algorithm. In: SIGGRAPH 1987: Proceedings of the 14th annual conference on Computer graphics and interactive techniques, pp. 163–169. ACM, New York (1987)CrossRefGoogle Scholar
  2. 2.
    Ju, T., Losasso, F., Schaefer, S., Warren, J.: Dual contouring of hermite data. In: SIGGRAPH 2002: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, pp. 339–346. ACM, New York (2002)CrossRefGoogle Scholar
  3. 3.
    Fujimori, T., Suzuki, H., Kobayashi, Y., Kase, K.: Contouring medial surface of thin plate structure using local marching cubes. In: International Conference on Shape Modeling and Applications, pp. 297–306 (2004)Google Scholar
  4. 4.
    Prohaska, S., Hege, H.C.: Fast visualization of plane-like structures in voxel data. In: Proceedings of the conference on Visualization 2002, Washington, DC, USA, pp. 29–36. IEEE Computer Society, Los Alamitos (2002)Google Scholar
  5. 5.
    Suzuki, H., Fujimori, T., Michikawa, T., Miwata, Y., Sadaoka, N.: Skeleton surface generation from volumetric models of thin plate structures for industrial applications. In: Martin, R., Sabin, M.A., Winkler, J.R. (eds.) Mathematics of Surfaces 2007. LNCS, vol. 4647, pp. 442–464. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Ohtake, Y., Belyaev, A., Seidel, H.P.: An integrating approach to meshing scattered point data. In: SPM 2005: Proceedings of the 2005 ACM symposium on Solid and physical modeling, pp. 61–69. ACM, New York (2005)CrossRefGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Toriwaki, J., Mori, K.: Distance transformation and skeletonization of 3d pictures and their applications to medical images. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 412–428. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Ju, T., Baker, M.L., Chiu, W.: Computing a family of skeletons of volumetric models for shape description. Computer Aided Design 39(5), 352–360 (2007)CrossRefGoogle Scholar
  11. 11.
    Tsao, Y.F., Fu, K.S.: A parallel thinning algorithm for 3-d pictures. Computer Graphics and Image Processing 17(4), 315–331 (1981)CrossRefGoogle Scholar
  12. 12.
    Manzanera, A., Bernard, T., Preteux, F., Longuet, B.: Medial faces from a concise 3d thinning algorithm. In: IEEE International Conference on Computer Vision, vol. 1, p. 337 (1999)Google Scholar
  13. 13.
    Borgefors, G., Nystrom, I., Baja, G.S.D.: Computing skeletons in three dimensions. Pattern Recognition 32(7), 1225–1236 (1999)CrossRefGoogle Scholar
  14. 14.
    Michikawa, T., Nakazaki, S., Suzuki, H.: Efficiend medial voxel extraction from large volumetric models. In: Proceeding of WSCG 2009, pp. 169–176 (2009)Google Scholar
  15. 15.
    Dey, T.K., Li, K., Ramos, E.A., Wenger, R.: Isotopic reconstruction of surfaces with boundaries. Computer Graphics Forum 28(5), 1371–1382 (2009)CrossRefGoogle Scholar
  16. 16.
    Attali, D., Montanvert, A.: Computing and simplifying 2d and 3d continuous skeletons. Computer Vision and Image Understanding 67(3), 261–273 (1997)CrossRefGoogle Scholar
  17. 17.
    Etzion, M., Rappoport, A.: Computing the voronoi diagram of a 3-d polyhedron by separate computation of its symbolic and geometric parts. In: SMA 1999: Proceedings of the fifth ACM symposium on Solid modeling and applications, pp. 167–178. ACM, New York (1999)CrossRefGoogle Scholar
  18. 18.
    Amenta, N., Choi, S., Kolluri, R.K.: The power crust. In: SMA 2001: Proceedings of the sixth ACM symposium on Solid modeling and applications, pp. 249–266. ACM, New York (2001)CrossRefGoogle Scholar
  19. 19.
    Dey, T.K., Zhao, W.: Approximate medial axis as a voronoi subcomplex. In: SMA 2002: Proceedings of the seventh ACM symposium on Solid modeling and applications, pp. 356–366. ACM, New York (2002)CrossRefGoogle Scholar
  20. 20.
    Foskey, M., Lin, M.C., Manocha, D.: Efficient computation of a simplified medial axis. In: SM 2003: Proceedings of the eighth ACM symposium on Solid modeling and applications, pp. 96–107. ACM, New York (2003)CrossRefGoogle Scholar
  21. 21.
    Sud, A., Foskey, M., Manocha, D.: Homotopy-preserving medial axis simplification. In: SPM 2005: Proceedings of the 2005 ACM symposium on Solid and physical modeling, pp. 39–50. ACM, New York (2005)CrossRefGoogle Scholar
  22. 22.
    Shimada, K., Gossard, D.C.: Bubble mesh: automated triangular meshing of non-manifold geometry by sphere packing. In: SMA 1995: Proceedings of the third ACM symposium on Solid modeling and applications, pp. 409–419. ACM, New York (1995)CrossRefGoogle Scholar
  23. 23.
    Masuda, H.: Topological operators and boolean operations for complex-based nonmanifold geometric models. Computer-Aided Disign 25(2), 119–129 (1993)zbMATHCrossRefGoogle Scholar
  24. 24.
    Malandain, G., Bertrand, G., Ayache, N.: Topological segmentation of discrete surfaces. International Journal of Computer Vision 10(2), 183–197 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Takashi Michikawa
    • 1
  • Hiromasa Suzuki
    • 1
  1. 1.The University of TokyoTokyoJapan

Personalised recommendations