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Issue No.07 - July (2011 vol.33)
pp: 1339-1355
Stella X. Yu , Boston College, Chestnut Hill
Hao Jiang , Boston College, Chestnut Hill
ABSTRACT
Matching visual patterns that appear scaled, rotated, and deformed with respect to each other is a challenging problem. We propose a linear formulation that simultaneously matches feature points and estimates global geometrical transformation in a constrained linear space. The linear scheme enables search space reduction based on the lower convex hull property so that the problem size is largely decoupled from the original hard combinatorial problem. Our method therefore can be used to solve large scale problems that involve a very large number of candidate feature points. Without using prepruning in the search, this method is more robust in dealing with weak features and clutter. We apply the proposed method to action detection and image matching. Our results on a variety of images and videos demonstrate that our method is accurate, efficient, and robust.
INDEX TERMS
Scale and rotation invariant matching, deformable matching, linear programming, action detection, shape matching, object matching.
CITATION
Stella X. Yu, Hao Jiang, "Linear Scale and Rotation Invariant Matching", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 7, pp. 1339-1355, July 2011, doi:10.1109/TPAMI.2010.212
REFERENCES
[1] J.M. Gonzlez-Linares, N. Guil, and E.L. Zapata, "An Efficient 2D Deformable Objects Detection and Location Algorithm," Pattern Recognition, vol. 36, no. 11, pp. 2543-2556, 2003.
[2] C. Schmid and R. Mohr, "Local Grayvalue Invariants for Image Retrieval," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 5, pp. 530-535, May 1997.
[3] D.G. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int'l J. Computer Vision, vol. 60, no. 2, pp. 91-110, 2004.
[4] P.F. Felzenszwalb and D.P. Huttenlocher, "Pictorial Structures for Object Recognition," Int'l J. Computer Vision, vol. 61, no. 1, pp. 55-79, 2005.
[5] S. Roy and I.J. Cox, "A Maximum-Flow Formulation of the N-Camera Stereo Correspondence Problem," Proc. Int'l Conf. Computer Vision, 1998.
[6] W.E.L. Grimson, "The Combinatorics of Object Recognition in Cluttered Environment Using Constrained Search," A.I. Memo No. 1019, Feb. 1988.
[7] J. Besag, "On the Statistical Analysis of Dirty Pictures," J. Royal Statistical Soc., vol. B-48, no. 3, pp. 259-302, 1986.
[8] V. Kolmogorov and R. Zabih, "What Energy Functions Can Be Minimized via Graph Cuts?" Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 2, pp. 147-159, Feb. 2004.
[9] V. Kolmogorov and R. Zabih, "Computing Visual Correspondence with Occlusions Using Graph Guts," Proc. IEEE Int'l Conf. Computer Vision, 2001.
[10] Y. Weiss and W.T. Freeman, "On the Optimality of Solutions of the Max-Product Belief Propagation Algorithm in Arbitrary Graphs," IEEE Trans. Information Theory, vol. 47, no. 2, p. 736, Feb. 2001.
[11] J. Sun, N.N. Zheng, and H.Y. Shum, "Stereo Matching Using Belief Propagation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 7, pp. 787-800, July 2003.
[12] E. Sudderth, M. Mandel, W. Freeman, and A. Willsky, "Distributed Occlusion Reasoning for Tracking with Nonparametric Belief Propagation," Proc. Conf. Neural Information Processing Systems, 2004.
[13] D. Ramanan and C. Sminchisescu, "Training Deformable Models for Localization," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2006.
[14] A. Quattoni, M. Collins, and T. Darrell, "Conditional Random Fields for Object Recognition," Proc. Conf. Neural Information Processing Systems, 2004.
[15] H. Chui and A. Rangarajan, "A New Algorithm for Non-Rigid Point Matching," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2000.
[16] Z. Tu and A. Yuille, "Shape Matching and Recognition-Using Generative Models and Informative Features," Proc. European Conf. Computer Vision, 2004.
[17] P.F. Felzenszwalb and D.P. Huttenlocher, "Efficient Belief Propagation for Early Vision," Int'l J. Computer Vision, vol. 70, no. 1, pp. 41-54, 2006.
[18] A.C. Berg, T.L. Berg, and J. Malik, "Shape Matching and Object Recognition Using Low Distortion Correspondence," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2005.
[19] H. Jiang, M.S. Drew, and Z.N. Li, "Matching by Linear Programming and Successive Convexification," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 959-975, June 2007.
[20] 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.
[21] V. Chvátal, Linear Programming. W.H. Freeman and Co. 1983.
[22] B. Glocker, N. Komodakis, G. Tziritas, N. Navab, and N. Paragios, "Dense Image Registration through MRFs and Efficient Linear Programming" Medical Image Analysis, 2008.
[23] C.J. Taylor and A. Bhusnurmath, "Solving Image Registration Problems Using Interior Point Methods," Proc. European Conf. Computer Vision, 2008.
[24] N. Komodakis and G. Tziritas, "Approximate Labeling via Graph-Cuts Based on Linear Programming," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 8, pp. 1436-1453, Aug. 2007.
[25] C. Chekuri, S. Khanna, J. Naor, and L. Zosin, "Approximation Algorithms for the Metric Labeling Problem via a New Linear Programming Formulation," Proc. 12th Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 109-118, 2001.
[26] A. Shekhovtsov, I. Kovtun, and V. Hlavac, "Efficient MRF Deformation Model for Non-Rigid Image Matching," Computer Vision and Image Understanding Archive, vol. 112, no. 1, pp. 91-99, Oct. 2008.
[27] D. Sharvit, J. Chan, H. Tek, and B.B. Kimia, "Symmetry-Based Indexing of Image Databases," J. Visual Comm. and Image Representation, vol. 9, no. 4, pp. 366-380, 1998.
[28] M. Blank, L. Gorelick, E. Shechtman, M. Irani, and R. Basri, "Actions as Space-Time Shapes," Proc. IEEE Int'l Conf. Computer Vision, 2005.
[29] D. Kenwright and G. Mallinson, "A 3-D Streamline Tracking Algorithm Using Dual Stream Functions," Proc. Conf. Visualization, pp. 62-68, 1992.
[30] H. Jiang and D.R. Martin, "Finding Actions Using Shape Flows," Proc. European Conf. Computer Vision, 2008.
[31] H. Jiang and S.X. Yu, "Linear Solution to Scale and Rotation Invariant Object Matching," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2009.
[32] J. Maciel and J.P. Costeira, "A Global Solution to Sparse Correspondence Problems," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 2, pp. 187-199, Feb. 2003.
[33] O. Duchenne, F. Bach, I. Kweon, and J. Ponce, "Tensor-Based Algorithm for High-Order Graph Matching," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2009.
[34] P.H.S. Torr and D.W. Murray, "The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix," Int'l J. Computer Vision, vol. 24, no.3, pp. 271-300, 1997.
[35] M.A. Fischler and R.C. Bolles, "Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography," Comm. ACM, vol. 24, no. 5, pp. 381-395. 1981.
[36] R.O. Duda and P.E. Hart, "Use of the Hough Transform to Detect Lines and Curves in Pictures," Comm. ACM, vol. 15, no. 1, pp. 11-15, 1972.
[37] P.H.S. Torr, "Solving Markov Random Fields Using Semi Definite Programming," Proc. Ninth Int'l Workshop Artificial Intelligence and Statistics, 2003.
[38] C. Schellewald and C. Schnrr, "Probabilistic Subgraph Matching Based on Convex Relaxation," Proc. Int'l Workshop Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 171-186, 2005.
[39] L. Torresani, V. Kolmogorov, and C. Rother, "Feature Correspondence via Graph Matching: Models and Global Optimization Export," Proc. European Conf. Computer Vision, 2008.
[40] N. Komodakis and N. Paragios, "Beyond Loose LP-Relaxations: Optimizing MRFs by Repairing Cycles," Proc. European Conf. Computer Vision, 2008.
[41] J. Duchi, D. Tarlow, G. Elidan, and D. Koller, "Using Combinatorial Optimization within Max-Product Belief Propagation," Proc. Conf. Neural Information Processing Systems, 2006.
[42] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge Univ. Press.
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