Dense shape correspondences using spectral high-order graph matching

This paper addresses the problem of establishing point correspondences between two object instances using spectral high-order graph matching. Therefore, 3D objects are intrinsically represented by weighted high-order adjacency tensors. These are, depending on the weighting scheme, invariant for structure-preserving, equi-areal, conformal or volume-preserving object deformations. Higher-order spectral decomposition transforms the NP-hard assignment problem into a linear assignment problem by canonical embedding. This allows to extract dense correspondence information with reasonable computational complexity, making the method faster than any other previously published method imposing higher-order constraints to shape matching. Robustness against missing data and resampling is measured and compared with a baseline spectral graph matching method.

[1]  Minsu Cho,et al.  Reweighted Random Walks for Graph Matching , 2010, ECCV.

[2]  F. L. Hitchcock.  The Expression of a Tensor or a Polyadic as a Sum of Products , 1927 .

[3]  Leonidas J. Guibas,et al.  SHREC 2010: robust correspondence benchmark , 2010 .

[4]  Nikos Paragios,et al.  Dense non-rigid surface registration using high-order graph matching , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[5]  R. Kimmel,et al.  Matching shapes by eigendecomposition of the Laplace-Beltrami operator , 2010 .

[6]  H. C. Longuet-Higgins,et al.  An algorithm for associating the features of two images , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[7]  Radu Horaud,et al.  Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[8]  Hao Zhang,et al.  Non-Rigid Spectral Correspondence of Triangle Meshes , 2007, Int. J. Shape Model..

[9]  J. Munkres.  ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[10]  Michael Brady,et al.  Feature-based correspondence: an eigenvector approach , 1992, Image Vis. Comput..

[11]  Edwin R. Hancock,et al.  Spectral correspondence for point pattern matching , 2003, Pattern Recognit..

[12]  Radu Horaud,et al.  Shape matching based on diffusion embedding and on mutual isometric consistency , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Workshops.

[13]  Endika Bengoetxea,et al.  Inexact Graph Matching Using Estimation of Distribution Algorithms , 2002 .

[14]  Steven Gold,et al.  A Graduated Assignment Algorithm for Graph Matching , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Alexander M. Bronstein,et al.  Numerical Geometry of Non-Rigid Shapes , 2009, Monographs in Computer Science.

[17]  Tamara G. Kolda,et al.  MATLAB Tensor Toolbox , 2006 .

[18]  Ghassan Hamarneh,et al.  A Survey on Shape Correspondence , 2011, Comput. Graph. Forum.

[19]  Shinji Umeyama,et al.  An Eigendecomposition Approach to Weighted Graph Matching Problems , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Tamara G. Kolda,et al.  Efficient MATLAB Computations with Sparse and Factored Tensors , 2007, SIAM J. Sci. Comput..

[21]  Jean Ponce,et al.  A tensor-based algorithm for high-order graph matching , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[22]  Radu Horaud,et al.  Rigid and Articulated Point Registration with Expectation Conditional Maximization , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Laurent D. Cohen,et al.  Heuristically Driven Front Propagation for Fast Geodesic Extraction , 2008 .

[24]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Martial Hebert,et al.  A spectral technique for correspondence problems using pairwise constraints , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[26]  Sebastian Thrun,et al.  SCAPE: shape completion and animation of people , 2005, SIGGRAPH 2005.