iccv iccv2013 iccv2013-140 iccv2013-140-reference knowledge-graph by maker-knowledge-mining
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Author: Emanuele Rodolà, Andrea Torsello, Tatsuya Harada, Yasuo Kuniyoshi, Daniel Cremers
Abstract: We consider a parametrized relaxation of the widely adopted quadratic assignment problem (QAP) formulation for minimum distortion correspondence between deformable shapes. In order to control the accuracy/sparsity trade-off we introduce a weighting parameter on the combination of two existing relaxations, namely spectral and game-theoretic. This leads to the introduction of the elastic net penalty function into shape matching problems. In combination with an efficient algorithm to project onto the elastic net ball, we obtain an approach for deformable shape matching with controllable sparsity. Experiments on a standard benchmark confirm the effectiveness of the approach.
[1] S. Boyd and L. Vandenberghe. Convex Optimization. Cam-
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12] bridge Univ. Press, New York, USA, 2004. A. Bronstein, M. Bronstein, U. Castellani, et al. Shrec 2010: Robust correspondence benchmark. In Eurographics Workshop on 3D Object Retrieval, 2010. A. Bronstein, M. Bronstein, and R. Kimmel. Generalized multidimensional scaling: a framework for isometryinvariant partial surface matching. Proc. National Academy of Science (PNAS), 103(5): 1168–1 172, 2006. M. Bronstein and I. Kokkinos. Scale-invariant heat kernel signatures for non-rigid shape recognition. In Proc. CVPR, pages 1704 –171 1, 2010. J. Dattorro. Convex Optimization & Euclidean Distance Geometry. Meboo Publ., Palo Alto, CA, USA, 2005. S. Gold and A. Rangarajan. A graduated assignment algorithm for graph matching. IEEE Trans. Patt. Analysis and Machine Intelligence, 18:377–388, 1996. P. Gong, K. Gai, and C. Zhang. Efficient euclidean projections via piecewise root finding and its application in gradient projection. Neurocomp. , 74:2754 – 2766, 2011. M. Leordeanu and M. Hebert. A spectral technique for correspondence problems using pairwise constraints. In Proc. CVPR, volume 2, pages 1482–1489, 2005. Y. Lipman and T. Funkhouser. Mobius voting for surface correspondence. ACM Trans. on Graphics, 28(3), 2009. J. Mairal, F. Bach, J. Ponce, and G. Sapiro. Online learning for matrix factorization and sparse coding. J. Mach. Learn. Res., 11:19–60, 2010. F. M ´emoli. Gromov-Wasserstein distances and the metric approach to object matching. Found. Comput. Math., 11:417–487, 2011. F. M ´emoli and G. Sapiro. A theoretical and computational
[13]
[14]
[15]
[16]
[17]
[18] framework for isometry invariant recognition of point cloud data. Found. Comput. Math., 5:3 13–346, 2005. M. Ovsjanikov, Q.-X. Huang, and L. J. Guibas. A condition number for non-rigid shape matching. Comput. Graph. Forum, pages 1503–15 12, 2011. E. Rodol `a, A. Bronstein, A. Albarelli, F. Bergamasco, and A. Torsello. A game-theoretic approach to deformable shape matching. In Proc. CVPR, 2012. S. Shalev-Shwartz and Y. Singer. Efficient learning of label ranking by soft projections onto polyhedra. J. Mach. Learn. Res., 7:1567–1599, Dec. 2006. T. Windheuser, U. Schlickewei, F. Schmidt, and D. Cremers. Geometrically consistent elastic matching of 3d shapes: A linear programming solution. In Proc. IEEE Intl. Conf. on Comput. Vis. , pages 2134 –2141, nov. 2011. Y. Zeng, C. Wang, Y. Wang, X. Gu, D. Samaras, and N. Paragios. Dense non-rigid surface registration using high-order graph matching. In Proc. CVPR, pages 382–389, 2010. H. Zou and T. Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B, 67:301–320, 2005. 11 117766