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Issue No.02 - Feb. (2013 vol.35)
pp: 259-271
L. Torresani , Dept. of Comput. Sci., Dartmouth Coll., Hanover, NH, USA
V. Kolmogorov , Inst. of Sci. & Technol., IST Austria, Klosterneuburg, Austria
C. Rother , Microsoft Res. Cambridge, Cambridge, UK
ABSTRACT
In this paper, we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from images of different instances of the same object category. We formulate this matching task as an energy minimization problem by defining an elaborate objective function of the appearance and the spatial arrangement of the features. Optimization of this energy is an instance of graph matching, which is in general an NP-hard problem. We describe a novel graph matching optimization technique, which we refer to as dual decomposition (DD), and demonstrate on a variety of examples that this method outperforms existing graph matching algorithms. In the majority of our examples, DD is able to find the global minimum within a minute. The ability to globally optimize the objective allows us to accurately learn the parameters of our matching model from training examples. We show on several matching tasks that our learned model yields results superior to those of state-of-the-art methods.
INDEX TERMS
Vectors, Optimization, Labeling, Computational modeling, Indexes, Feature extraction, Minimization,dual decomposition, Graph matching, feature correspondence
CITATION
L. Torresani, V. Kolmogorov, C. Rother, "A Dual Decomposition Approach to Feature Correspondence", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.35, no. 2, pp. 259-271, Feb. 2013, doi:10.1109/TPAMI.2012.105
REFERENCES
[1] http://pub.ist.ac.at/~vnk/softwareGraphMatching-v1.0.src.tar. gz , 2011.
[2] R. Ahuja, T. Magnanti, and J. Orlin, Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993.
[3] P.N. Belhumeur, "A Binocular Stereo Algorithm for Reconstructing Sloping, Creased, and Broken Surfaces in the Presence of Half-Occlusion," Proc. Fourth IEEE Int'l Conf. Computer Vision, May 1993.
[4] S. Belongie, J. Malik, and J. Puzicha, "Shape Matching and Object Recognition Using Shape Contexts," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp. 509-522, Apr. 2002.
[5] A. Berg, T. Berg, and J. Malik, "Shape Matching and Object Recognition Using Low Distortion Correspondence," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2005.
[6] D. Bertsekas, Nonlinear Programming. Athena Scientific, 1999.
[7] E. Boros and P. Hammer, "Pseudo-Boolean Optimization," Discrete Applied Math., vol. 123, nos. 1-3, pp. 155-225, 2002.
[8] E. Boros, P.L. Hammer, and X. Sun, "Network Flows and Minimization of Quadratic Pseudo-Boolean Functions," Technical Report RRR 17-1991, RUTCOR, May 1991.
[9] E. Boros, P.L. Hammer, and G. Tavares, "Preprocessing of Unconstrained Quadratic Binary Optimization," Technical Report RRR 10-2006, RUTCOR, Apr. 2006.
[10] A. Cabot and R. Francis, "Solving Certain Nonconvex Quadratic Minimization Problems by Ranking the Extreme Points," Operations Research, vol. 18, no. 1, pp. 82-86, 1970.
[11] T.S. Caetano, L. Cheng, Q.V. Le, and A.J. Smola, "Learning Graph Matching," Proc. 11th IEEE Int'l Conf. Computer Vision, 2007.
[12] P. Chardaire and A. Sutter, "A Decomposition Method for Quadratic Zero-One Programming," Management Science, vol. 41, no. 4, pp. 704-712, 1995.
[13] D. Conte, P. Foggia, C. Sansone, and M. Vento, "Thirty Years of Graph Matching in Pattern Recognition," Int'l J. Pattern Recognition and Artificial Intelligence, vol. 18, no. 3, pp. 265-298, 2004.
[14] T. Cour, P. Srinivasan, and J. Shi, "Balanced Graph Matching," Proc. Neural Information Processing Systems, 2007.
[15] G. Csurka, C. Bray, C. Dance, and L. Fan, "Visual Categorization with Bags of Keypoints," Proc. Workshop Statistical Learning in Computer Vision, 2004.
[16] G. Dorko and C. Schmid, "Selection of Scale-Invariant Parts for Object Class Recognition," Proc. Ninth IEEE Int'l Conf. Computer Vision, 2003.
[17] J. Duchi, D. Tarlow, G. Elidan, and D. Koller, "Using Combinatorial Optimization within Max-Product Belief Propagation," Proc. Neural Information Processing Systems, 2007.
[18] G. Elidan, I. McGraw, and D. Koller, "Residual Belief Propagation: Informed Scheduling for Asynchronous Message Passing," Proc. 22nd Conf. Uncertainty in AI, 2006.
[19] S. Gold and A. Rangarajan, "A Graduated Assignment Algorithm for Graph Matching," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 4, pp. 377-388, Apr. 1996.
[20] K. Grauman and T. Darrell, "The Pyramid Match Kernel: Discriminative Classification with Sets of Image Features," Proc. 10th IEEE Int'l Conf. Computer Vision, 2005.
[21] P.L. Hammer, P. Hansen, and B. Simeone, "Roof Duality, Complementation and Persistency in Quadratic 0-1 Optimization," Math. Programming, vol. 28, pp. 121-155, 1984.
[22] V. Kolmogorov, "Convergent Tree-Reweighted Message Passing for Energy Minimization," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1568-1583, Oct. 2006.
[23] V. Kolmogorov and C. Rother, "Minimizing Non-Submodular Functions with Graph Cuts—A Review," IEEE Trans. Pattern Analysis and Machine Intelligence,, vol. 29, no. 7, pp. 1274-1279, July 2007.
[24] V. Kolmogorov and R. Zabih, "Computing Visual Correspondence with Occlusions Using Graph Cuts," Proc. Eighth IEEE Int'l Conf. Computer Vision, 2001.
[25] N. Komodakis, N. Paragios, and G. Tziritas, "MRF Optimization via Dual Decomposition: Message-Passing Revisited," Proc. 11th IEEE Int'l Conf. Computer Vision, 2007.
[26] Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, "Gradient-Based Learning Applied to Document Recognition," Proc. IEEE, vol. 86, no. 11, pp. 2278-2324, Nov. 1998.
[27] V. Lempitsky, C. Rother, and A. Blake, "LogCut—Efficient Graph Cut Optimization for Markov Random Fields," Proc. 11th IEEE Int'l Conf. Computer Vision, 2007.
[28] M. Leordeanu and M. Hebert, "A Spectral Technique for Correspondence Problems Using Pairwise Constraints," Proc. 10th IEEE Int'l Conf. Computer Vision, 2005.
[29] M. Leordeanu, M. Hebert, and R. Sukthankar, "An Integer Projected Fixed Point Method for Graph Matching and Map Inference," Advances in Neural Information Processing Systems 22, pp. 1114-1122, 2009.
[30] C. Lim and H.D. Sherali, "Convergence and Computational Analyses for Some Variable Target Value and Subgradient Deflection Methods," Computational Optimization and Applications, vol. 34, no. 3, pp. 409-428, 2006.
[31] C.K. Liu, A. Hertzmann, and Z. Popović, "Learning Physics-Based Motion Style with Nonlinear Inverse Optimization," ACM Trans. Graphics, vol. 24, no. 3, pp. 1071-1081, 2005.
[32] J. Maciel and J. Costeira, "A Global Solution to Sparse Correspondence Problems," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 2, pp. 187-199, Feb. 2002.
[33] D. Metaxas, E. Koh, and N. Badler, "Multi-Level Shape Representation Using Global Deformations and Locally Adaptive Finite Elements," Int'l J. Computer Vision, vol. 25, no. 1, pp. 49-61, 1997.
[34] C. Rother, V. Kolmogorov, V. Lempitsky, and M. Szummer, "Optimizing Binary MRFs via Extended Roof Duality," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007.
[35] C. Schellewald and C. Schnörr, "Probabilistic Subgraph Matching Based on Convex Relaxation," Proc. Fifth Int'l Conf. Energy Minimization Methods in Computer Vision and Pattern Recognition, 2005.
[36] M.I. Schlesinger and V.V. Giginyak, "Solution to Structural Recognition (MAX,+)-Problems by Their Equivalent Transformations. Part 1," Control Systems and Computers, vol. 1, pp. 3-15, 2007.
[37] M.I. Schlesinger and V.V. Giginyak, "Solution to Structural Recognition (MAX,+)-Problems by Their Equivalent Transformations. Part 2," Control Systems and Computers, vol. 2, pp. 3-18, 2007.
[38] S. Sclaroff and A. Pentland, "Modal Matching for Correspondence and Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 6, pp. 545-561, June 1995.
[39] N.Z. Shor, Minimization Methods for Nondifferentiable Functions. Springer-Verlag, 1985.
[40] J. Sivic, B. Russell, A. Efros, and A. Zisserman, "Discovering Object Categories in Image Collections," Proc. IEEE Int'l Conf. Computer Vision, 2005.
[41] G. Storvik and G. Dahl, "Lagrangian-Based Methods for Finding MAP," IEEE Trans. Image Processing, vol. 9, no. 3, pp. 469-479, Mar. 2000.
[42] P.H.S. Torr, "Geometric Motion Segmentation and Model Selection," Philosophical Trans. Royal Soc., vol. 356, pp. 1321-1340, 1998.
[43] P.H.S. Torr, "Solving Markov Random Fields Using Semi Definite Programming," Proc. Artificial Intelligence and Simulation Conf., 2003.
[44] M. Wainwright, T. Jaakkola, and A. Willsky, "MAP Estimation via Agreement on Trees: Message-Passing and Linear-Programming Approaches," IEEE Trans. Information Theory, vol. 51, no. 11, pp. 3697-3717, Nov. 2005.
[45] C. Wallraven, B. Caputo, and A. Graf, "Recognition with Local Features: The Kernel Recipe," Proc. Ninth IEEE Int'l Conf. Computer Vision, 2003.
[46] T. Werner, "A Linear Programming Approach to Max-Sum Problem: A Review," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 7, pp. 1165-1179, July 2007.
[47] J. Willamowski, D. Arregui, G. Csurka, C. Dance, and L. Fan, "Categorizing Nine Visual Classes Using Local Appearance Descriptors," Proc. ICPR Workshop Learning for Adaptable Visual Systems, 2004.
[48] J. Yarkony, C.C. Fowlkes, and A.T. Ihler, "Covering Trees and Lower-Bounds on Quadratic Assignment," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010.
[49] J. Zhang, M. Marszalek, S. Lazebnik, and C. Schmid, "Local Features and Kernels for Classifcation of Texture and Object Categories: An In-Depth Study," Technical Report RR-5737, INRIA Rhone-Alpes, Nov. 2005.
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