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3D Non-rigid Surface Matching and Registration Based on Holomorphic Differentials

  • Wei Zeng
  • Yun Zeng
  • Yang Wang
  • Xiaotian Yin
  • Xianfeng Gu
  • Dimitris Samaras
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5304)

Abstract

3D surface matching is fundamental for shape registration, deformable 3D non-rigid tracking, recognition and classification. In this paper we describe a novel approach for generating an efficient and optimal combined matching from multiple boundary-constrained conformal parameterizations for multiply connected domains (i.e., genus zero open surface with multiple boundaries), which always come from imperfect 3D data acquisition (holes, partial occlusions, change of pose and non-rigid deformation between scans). This optimality criterion is also used to assess how consistent each boundary is, and thus decide to enforce or relax boundary constraints across the two surfaces to be matched. The linear boundary-constrained conformal parameterization is based on the holomorphic differential forms, which map a surface with n boundaries conformally to a planar rectangle with (n - 2) horizontal slits, other two boundaries as constraints. The mapping is a diffeomorphism and intrinsic to the geometry, handles an open surface with arbitrary number of boundaries, and can be implemented as a linear system. Experimental results are given for real facial surface matching, deformable cloth non-rigid tracking, which demonstrate the efficiency of our method, especially for 3D non-rigid surfaces with significantly inconsistent boundaries.

Keywords

Conformal Mapping Connected Domain Iterative Close Point Ricci Flow Surface Match 
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.

Supplementary material

978-3-540-88690-7_1_MOESM1_ESM.wmv (13 mb)
Supplementary material (13,305 KB)

References

  1. 1.
    Campbell, R.J., Flynn, P.J.: A survey of free-form object representation and recognition techniques. Computer Vision and Image Understanding 81, 166–210 (2001)CrossRefzbMATHGoogle Scholar
  2. 2.
    Ruiz-Correa, S., Shapiro, L., Meila, M.: A new paradigm for recognizing 3d object shapes from range data. In: ICCV, pp. 1126–1133 (2003)Google Scholar
  3. 3.
    Huber, D., Kapuria, A., Donamukkala, R., Hebert, M.: Parts-based 3d object classification. In: CVPR, vol. II, pp. 82–89 (June 2004)Google Scholar
  4. 4.
    Vemuri, B., Mitiche, A., Aggarwal, J.: Curvature-based representation of objects from range data. Image and Vision Computing 4, 107–114 (1986)CrossRefGoogle Scholar
  5. 5.
    Xiao, P., Barnes, N., Caetano, T., Lieby, P.: An mrf and gaussian curvature based shape representation for shape matching. In: CVPR (2007)Google Scholar
  6. 6.
    Sun, Y., Abidi, M.: Surface matching by 3d point’s fingerprint. In: ICCV, vol. II, pp. 263–269 (2001)Google Scholar
  7. 7.
    Frome, A., Huber, D., Kolluri, R., Bulow, T., Malik, J.: Recognizing objects in range data using regional point descriptors. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3023, pp. 224–237. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Funkhouser, T., Min, P., Kazhdan, M., Chen, J., Halderman, A., Dobkin, D., Jacobs, D.: A search engine for 3d models. In: ACM TOG, pp. 83–105 (2003)Google Scholar
  9. 9.
    Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape distributions. In: ACM TOG, vol. 21, pp. 807–832 (2002)Google Scholar
  10. 10.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Expression-invariant representations of faces. IEEE Trans. Image Processing 16(1), 188–197 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Starck, J., Hilton, A.: Correspondence labelling for wide-timeframe free-form surface matching. In: ICCV (2007)Google Scholar
  12. 12.
    Lin, W.Y., Wong, K.C., Boston, N., Yu, H.H.: Fusion of summation invariants in 3d human face recognition. In: CVPR (2006)Google Scholar
  13. 13.
    Dalal, P., Munsell, B.C., Wang, S., Tang, J., Oliver, K., Ninomiya, H., Zhou, X., Fujita, H.: A fast 3d correspondence method for statistical shape modeling. In: CVPR (2007)Google Scholar
  14. 14.
    Terzopoulos, D., Witkin, A., Kass, M.: Constraints on deformable models: Recovering 3d shape and nonrigid motion. Artificial Intelligence 35, 91–123 (1988)CrossRefzbMATHGoogle Scholar
  15. 15.
    Huang, X., Paragios, N., Metaxas, D.: Establishing local correspondences towards compact representations of anatomical structures. In: Ellis, R.E., Peters, T.M. (eds.) MICCAI 2003. LNCS, vol. 2878, pp. 926–934. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Malladi, R., Sethian, J.A., Vemuri, B.C.: A fast level set based algorithm for topology-independent shape modeling. JMIV 6(2/3), 269–290 (1996)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhang, D., Hebert, M.: Harmonic maps and their applications in surface matching. In: CVPR 1999, vol. II, pp. 524–530 (1999)Google Scholar
  18. 18.
    Wang, Y., Gupta, M., Zhang, S., Wang, S., Gu, X., Samaras, D., Huang, P.: High resolution tracking of non-rigid 3d motion of densely sampled data using harmonic maps. In: ICCV 2005, vol. I, pp. 388–395 (2005)Google Scholar
  19. 19.
    Gu, X., Wang, Y., Chan, T.F., Thompson, P.M., Yaun, S.: Genus zero surface conformal mapping and its application to brain surface mapping. TMI 23(7) (2004)Google Scholar
  20. 20.
    Levy, B., Petitjean, S., Ray, N., Maillot, J.: Least squares conformal maps for automatic texture atlas generation. In: SIGGRAPH, pp. 362–371 (2002)Google Scholar
  21. 21.
    Sharon, E., Mumford, D.: 2d-shape analysis using conformal mapping. In: CVPR 2004, vol. II, pp. 350–357 (2004)Google Scholar
  22. 22.
    Wang, S., Wang, Y., Jin, M., Gu, X.D., Samaras, D.: Conformal geometry and its applications on 3d shape matching, recognition, and stitching. PAMI 29(7), 1209–1220 (2007)CrossRefGoogle Scholar
  23. 23.
    Gu, X., Wang, S., Kim, J., Zeng, Y., Wang, Y., Qin, H., Samaras, D.: Ricci flow for 3d sahpe analysis. In: ICCV (2007)Google Scholar
  24. 24.
    Lowe, D.: Distinctive image features from scale-invariant keypoints. IJCV 60(2), 91–110 (2004)CrossRefGoogle Scholar
  25. 25.
    Athitsos, V., Alon, J., Sclaroff, S., Kollios, G.: Boostmap: A method for efficient approximate similarity rankings. In: CVPR 2004, vol. II, pp. 268–275 (2004)Google Scholar
  26. 26.
    Yin, X., Dai, J., Yau, S.T., Gu, X.: Slit map: Conformal parameterization for multiply connected surfaces. In: Geometric Modeling and Processing (2008)Google Scholar
  27. 27.
    Gu, X., Vemuri, B.C.: Matching 3d shapes using 2d conformal representations. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 771–780. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  28. 28.
    Lowe, D.: Object recognition from local scale-invariant features. In: ICCV 1999, pp. 1150–1157 (1999)Google Scholar
  29. 29.
    Hernández, C., Vogiatzis, G., Brostow, G.J., Stenger, B., Cipolla, R.: Non-rigid photometric stereo with colored lights. In: ICCV, vol. 1 (2007)Google Scholar
  30. 30.
    Besl, P.J., McKay, N.D.: A method for registration of 3-D shapes. PAMI 14(2), 239–256 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Wei Zeng
    • 1
  • Yun Zeng
    • 1
  • Yang Wang
    • 2
  • Xiaotian Yin
    • 1
  • Xianfeng Gu
    • 1
  • Dimitris Samaras
    • 1
  1. 1.Stony Brook UniversityStony BrookUSA
  2. 2.Carnegie Mellon UniversityPittsburghUSA

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