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.
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References
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)
Ruiz-Correa, S., Shapiro, L., Meila, M.: A new paradigm for recognizing 3d object shapes from range data. In: ICCV, pp. 1126–1133 (2003)
Huber, D., Kapuria, A., Donamukkala, R., Hebert, M.: Parts-based 3d object classification. In: CVPR, vol. II, pp. 82–89 (June 2004)
Vemuri, B., Mitiche, A., Aggarwal, J.: Curvature-based representation of objects from range data. Image and Vision Computing 4, 107–114 (1986)
Xiao, P., Barnes, N., Caetano, T., Lieby, P.: An mrf and gaussian curvature based shape representation for shape matching. In: CVPR (2007)
Sun, Y., Abidi, M.: Surface matching by 3d point’s fingerprint. In: ICCV, vol. II, pp. 263–269 (2001)
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)
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)
Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape distributions. In: ACM TOG, vol. 21, pp. 807–832 (2002)
Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Expression-invariant representations of faces. IEEE Trans. Image Processing 16(1), 188–197 (2007)
Starck, J., Hilton, A.: Correspondence labelling for wide-timeframe free-form surface matching. In: ICCV (2007)
Lin, W.Y., Wong, K.C., Boston, N., Yu, H.H.: Fusion of summation invariants in 3d human face recognition. In: CVPR (2006)
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)
Terzopoulos, D., Witkin, A., Kass, M.: Constraints on deformable models: Recovering 3d shape and nonrigid motion. Artificial Intelligence 35, 91–123 (1988)
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)
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)
Zhang, D., Hebert, M.: Harmonic maps and their applications in surface matching. In: CVPR 1999, vol. II, pp. 524–530 (1999)
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)
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)
Levy, B., Petitjean, S., Ray, N., Maillot, J.: Least squares conformal maps for automatic texture atlas generation. In: SIGGRAPH, pp. 362–371 (2002)
Sharon, E., Mumford, D.: 2d-shape analysis using conformal mapping. In: CVPR 2004, vol. II, pp. 350–357 (2004)
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)
Gu, X., Wang, S., Kim, J., Zeng, Y., Wang, Y., Qin, H., Samaras, D.: Ricci flow for 3d sahpe analysis. In: ICCV (2007)
Lowe, D.: Distinctive image features from scale-invariant keypoints. IJCV 60(2), 91–110 (2004)
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)
Yin, X., Dai, J., Yau, S.T., Gu, X.: Slit map: Conformal parameterization for multiply connected surfaces. In: Geometric Modeling and Processing (2008)
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)
Lowe, D.: Object recognition from local scale-invariant features. In: ICCV 1999, pp. 1150–1157 (1999)
Hernández, C., Vogiatzis, G., Brostow, G.J., Stenger, B., Cipolla, R.: Non-rigid photometric stereo with colored lights. In: ICCV, vol. 1 (2007)
Besl, P.J., McKay, N.D.: A method for registration of 3-D shapes. PAMI 14(2), 239–256 (1992)
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Zeng, W., Zeng, Y., Wang, Y., Yin, X., Gu, X., Samaras, D. (2008). 3D Non-rigid Surface Matching and Registration Based on Holomorphic Differentials. In: Forsyth, D., Torr, P., Zisserman, A. (eds) Computer Vision – ECCV 2008. ECCV 2008. Lecture Notes in Computer Science, vol 5304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88690-7_1
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DOI: https://doi.org/10.1007/978-3-540-88690-7_1
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