Unsupervised learning for graph matching

Graph matching is an important problem in computer vision. It is used in 2D and 3D object matching and recognition. Despite its importance, there is little literature on learning the parameters that control the graph matching problem, even though learning is important for improving the matching rate, as shown by this and other work. In this paper we show for the first time how to perform parameter learning in an unsupervised fashion, that is when no correct correspondences between graphs are given during training. We show empirically that unsupervised learning is comparable in efficiency and quality with the supervised one, while avoiding the tedious manual labeling of ground truth correspondences. We also verify experimentally that this learning method can improve the performance of several state-of-the art graph matching algorithms.

[1]  Vladimir Kolmogorov,et al.  Feature Correspondence Via Graph Matching: Models and Global Optimization , 2008, ECCV.

[2]  Tsuhan Chen,et al.  Unsupervised Identification of Multiple Objects of Interest from Multiple Images: dISCOVER , 2007, ACCV.

[3]  Christos Faloutsos,et al.  Unsupervised modeling and recognition of object categories with combination of visual contents and geometric similarity links , 2008, MIR '08.

[4]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[5]  Hans-Peter Seidel,et al.  Performance capture from sparse multi-view video , 2008, SIGGRAPH 2008.

[6]  M. Zaslavskiy,et al.  A Path Following Algorithm for the Graph Matching Problem , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Mubarak Shah,et al.  Learning 4D action feature models for arbitrary view action recognition , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[8]  Jianbo Shi,et al.  Solving Markov Random Fields with Spectral Relaxation , 2007, AISTATS.

[9]  Martial Hebert,et al.  Beyond Local Appearance: Category Recognition from Pairwise Interactions of Simple Features , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[10]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

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

[12]  Jitendra Malik,et al.  Shape matching and object recognition using low distortion correspondences , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[13]  J. Besag On the Statistical Analysis of Dirty Pictures , 1986 .

[14]  Tsuhan Chen,et al.  Unsupervised Learning of Hierarchical Semantics of Objects (hSOs) , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

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

[16]  Jitendra Malik,et al.  Shape matching and object recognition using shape contexts , 2010, 2010 3rd International Conference on Computer Science and Information Technology.

[17]  Francis R. Bach,et al.  A Path Following Algorithm for Graph Matching , 2008, ICISP.

[18]  Edwin R. Hancock,et al.  Alignment using Spectral Clusters , 2002, BMVC.

[19]  Alexei A. Efros,et al.  Discovering Texture Regularity as a Higher-Order Correspondence Problem , 2006, ECCV.

[20]  L. Pottier,et al.  Optimization of positive generalized polynomials under constraints. , 1998 .

[21]  Martial Hebert,et al.  Efficient MAP approximation for dense energy functions , 2006, ICML.

[22]  Yosi Keller,et al.  Spectral Symmetry Analysis , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Ben Taskar,et al.  Max-Margin Markov Networks , 2003, NIPS.

[24]  Christos Faloutsos,et al.  Unsupervised modeling of object categories using link analysis techniques , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[25]  M. Leordeanu,et al.  Unsupervised learning of object features from video sequences , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[26]  Derek Hoiem,et al.  Learning CRFs Using Graph Cuts , 2008, ECCV.

[27]  Sanjiv Kumar,et al.  Models for learning spatial interactions in natural images , 2004 .

[28]  Xiaofeng Ren,et al.  Learning and Matching Line Aspects for Articulated Objects , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[29]  Jiebo Luo,et al.  Recognizing realistic actions from videos , 2009, CVPR.

[30]  Philip H. S. Torr,et al.  Solving Markov Random Fields using Semi Definite Programming , 2003, AISTATS.

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

[32]  Wolfgang Straßer,et al.  On-the-fly scene acquisition with a handy multi-sensor system , 2008, Int. J. Intell. Syst. Technol. Appl..

[33]  William Brendel,et al.  Segmentation as Maximum-Weight Independent Set , 2010, NIPS.

[34]  Martial Hebert,et al.  Smoothing-based Optimization , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[35]  Martial Hebert,et al.  An Integer Projected Fixed Point Method for Graph Matching and MAP Inference , 2009, NIPS.

[36]  Jianbo Shi,et al.  Learning spectral graph segmentation , 2005, AISTATS.

[37]  Pradeep Ravikumar,et al.  Quadratic programming relaxations for metric labeling and Markov random field MAP estimation , 2006, ICML.

[38]  Arcot Sowmya,et al.  Tensor Power Method for Efficient MAP Inference in Higher-order MRFs , 2010, 2010 20th International Conference on Pattern Recognition.

[39]  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.

[40]  Alexander J. Smola,et al.  Learning Graph Matching , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[42]  Michael I. Jordan,et al.  Learning Spectral Clustering , 2003, NIPS.

[43]  Christoph Schnörr,et al.  Probabilistic Subgraph Matching Based on Convex Relaxation , 2005, EMMCVPR.