Distributable Consistent Multi-Graph Matching

In this paper we propose an optimization-based framework to multiple graph matching. The framework takes as input maps computed between pairs of graphs, and outputs maps that 1) are consistent among all pairs of graphs, and 2) preserve edge connectivity between pairs of graphs. The central idea of our approach is to divide the input graph into overlapping sub-graphs and enforce consistency among sub-graphs. This leads to a distributed formulation, which is scalable to large-scale datasets. We also present an equivalence condition between this decoupled scheme and the original scheme. Experiments on both synthetic and real-world datasets show that our framework is competent against state-of-the-art global optimization-based techniques.

[1]  Hongyuan Zha,et al.  Multi-Graph Matching via Affinity Optimization with Graduated Consistency Regularization , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Trevor J. Hastie,et al.  Matrix completion and low-rank SVD via fast alternating least squares , 2014, J. Mach. Learn. Res..

[3]  Ping Zhu,et al.  A study of graph spectra for comparing graphs and trees , 2008, Pattern Recognit..

[4]  Afra Zomorodian,et al.  Computing Persistent Homology , 2005, Discret. Comput. Geom..

[5]  Leonidas J. Guibas,et al.  An Optimization Approach to Improving Collections of Shape Maps , 2011, Comput. Graph. Forum.

[6]  Leonidas J. Guibas,et al.  Consistent Shape Maps via Semidefinite Programming , 2013, SGP '13.

[7]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[8]  Vikas Singh,et al.  Permutation Diffusion Maps (PDM) with Application to the Image Association Problem in Computer Vision , 2014, NIPS.

[9]  DaiYuchao,et al.  A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization , 2014 .

[10]  Yosi Keller,et al.  A Probabilistic Approach to Spectral Graph Matching , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Xiaowei Zhou,et al.  Multi-image Matching via Fast Alternating Minimization , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[12]  Stephen DiVerdi,et al.  Exploring collections of 3D models using fuzzy correspondences , 2012, ACM Trans. Graph..

[13]  Leonidas J. Guibas,et al.  Graph Matching with Anchor Nodes: A Learning Approach , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[14]  Jun Wang,et al.  Consistency-Driven Alternating Optimization for Multigraph Matching: A Unified Approach , 2015, IEEE Transactions on Image Processing.

[15]  Pablo A. Parrilo,et al.  Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization , 2007, SIAM Rev..

[16]  Vikas Singh,et al.  Solving the multi-way matching problem by permutation synchronization , 2013, NIPS.

[17]  Daniel Cremers,et al.  Consistent Partial Matching of Shape Collections via Sparse Modeling , 2017, Comput. Graph. Forum.

[18]  Hongyuan Zha,et al.  A Matrix Decomposition Perspective to Multiple Graph Matching , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[19]  Marc Pollefeys,et al.  Disambiguating visual relations using loop constraints , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[20]  Marco Gori,et al.  Exact and approximate graph matching using random walks , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[22]  Andrea Vedaldi,et al.  Vlfeat: an open and portable library of computer vision algorithms , 2010, ACM Multimedia.

[23]  Xiaowei Zhou,et al.  Distributed Consistent Data Association , 2016, ArXiv.

[24]  R. Ho Algebraic Topology , 2022 .

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

[26]  Leonidas J. Guibas,et al.  Near-Optimal Joint Object Matching via Convex Relaxation , 2014, ICML.

[27]  Edwin R. Hancock,et al.  Graph matching using the interference of continuous-time quantum walks , 2009, Pattern Recognit..

[28]  Cordelia Schmid,et al.  A Comparison of Affine Region Detectors , 2005, International Journal of Computer Vision.

[29]  Henning Biermann,et al.  Recovering non-rigid 3D shape from image streams , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[30]  Jianbo Shi,et al.  Balanced Graph Matching , 2006, NIPS.

[31]  Xinlei Chen,et al.  Enriching Visual Knowledge Bases via Object Discovery and Segmentation , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[32]  Amnon Shashua,et al.  Probabilistic graph and hypergraph matching , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[33]  Leonidas J. Guibas,et al.  Stable and Informative Spectral Signatures for Graph Matching , 2013, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[34]  Alexandre Bernardino,et al.  Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition , 2013, 2013 IEEE International Conference on Computer Vision.

[35]  Hongdong Li,et al.  A simple prior-free method for non-rigid structure-from-motion factorization , 2012, CVPR.