Subscribe

Issue No.11 - Nov. (2013 vol.19)

pp: 1885-1894

Zhi-Quan Cheng , Nat. Lab. for Parallel & Distrib. Process., Nat. Univ. of Defense Technol., Changsha, China

Yin Chen , Nat. Lab. for Parallel & Distrib. Process., Nat. Univ. of Defense Technol., Changsha, China

R. R. Martin , Sch. of Comput. Sci. & Inf., Cardiff Univ., Cardiff, UK

Yu-Kun Lai , Sch. of Comput. Sci. & Inf., Cardiff Univ., Cardiff, UK

Aiping Wang , Nat. Lab. for Parallel & Distrib. Process., Nat. Univ. of Defense Technol., Changsha, China

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2013.15

ABSTRACT

Feature matching is a challenging problem at the heart of numerous computer graphics and computer vision applications. We present the SuperMatching algorithm for finding correspondences between two sets of features. It does so by considering triples or higher order tuples of points, going beyond the pointwise and pairwise approaches typically used. SuperMatching is formulated using a supersymmetric tensor representing an affinity metric that takes into account feature similarity and geometric constraints between features: Feature matching is cast as a higher order graph matching problem. SuperMatching takes advantage of supersymmetry to devise an efficient sampling strategy to estimate the affinity tensor, as well as to store the estimated tensor compactly. Matching is performed by an efficient higher order power iteration approach that takes advantage of this compact representation. Experiments on both synthetic and real data show that SuperMatching provides more accurate feature matching than other state-of-the-art approaches for a wide range of 2D and 3D features, with competitive computational cost.

INDEX TERMS

Tensile stress, Vectors, Shape, Transmission line matrix methods, Educational institutions, Accuracy, Computational efficiency,supersymmetric tensor, Feature matching, geometric constraints

CITATION

Zhi-Quan Cheng, Yin Chen, R. R. Martin, Yu-Kun Lai, Aiping Wang, "SuperMatching: Feature Matching Using Supersymmetric Geometric Constraints",

*IEEE Transactions on Visualization & Computer Graphics*, vol.19, no. 11, pp. 1885-1894, Nov. 2013, doi:10.1109/TVCG.2013.15REFERENCES

- [1] P.J. Besl and N.D. McKay, "A Method for Registration of 3-D Shapes,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239-256, Feb. 1992.- [2] W. Chang and M. Zwicker, "Global Registration of Dynamic Range Scans for Articulated Model Reconstruction,"
ACM Trans. Graphics, vol. 30, pp. 26:1-26:15, 2011.- [3] A.M. Bronstein, M.M. Bronstein, L.J. Guibas, and M. Ovsjanikov, "Shape Google: Geometric Words and Expressions for Invariant Shape Retrieval,"
ACM Trans. Graphics, vol. 30, pp. 1:1-1:20, 2011.- [4] 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, pp. 26-33, 2005.- [5] T. Windheuser, U. Schlickwei, F.R. Schimdt, and D. Cremers, "Large-Scale Integer Linear Programming for Orientation Preserving 3D Shape Matching,"
Computer Graphics Forum, vol. 30, no. 5, pp. 1471-1480, 2011.- [6] B.J. Brown and S. Rusinkiewicz, "Global Non-Rigid Alignment of 3-D Scans,"
ACM Trans. Graphics, vol. 26, article 21, 2007.- [7] Y. Pekelny and C. Gotsman, "Articulated Object Reconstruction and Markerless Motion Capture from Depth Video,"
Computer Graphics Forum, vol. 27, no. 2, pp. 399-408, 2008.- [8] M. Wand, B. Adams, M. Ovsjanikov, A. Berner, M. Bokeloh, P. Jenke, L. Guibas, H.-P. Seidel, and A. Schilling, "Efficient Reconstruction of Nonrigid Shape and Motion from Real-Time 3D Scanner Data,"
ACM Trans. Graphics, vol. 28, pp. 15:1-15:15, 2009.- [9] D.P. Huttenlocher and S. Ullman, "Recognizing Solid Objects by Alignment with an Image,"
Int'l J. Computer Vision, vol. 5, pp. 195-212, Nov. 1990.- [10] V.G. Kim, Y. Lipman, and T. Funkhouser, "Blended Intrinsic Maps,"
Proc. ACM SIGGRAPH, pp. 79:1-79:12, 2011.- [11] A.E. Johnson and M. Hebert, "Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 433-449, May 1999.- [12] S. Leutenegger, M. Chli, and R. Siegwart, "Brisk: Binary Robust Invariant Scalable Keypoints,"
Proc. Int'l Conf. Computer Vision, 2011.- [13] O. van Kaick, H. Zhang, G. Hamarneh, and D. Cohen-Or, "A Survey on Shape Correspondence,"
Computer Graphics Forum, vol. 30, no. 6, pp. 1681-1707, 2011.- [14] A. Tevs, M. Bokeloh, M. Wand, A. Schilling, and H.-P. Seidel, "Isometric Registration of Ambiguous and Partial Data,"
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1185-1192, 2009.- [15] A. Tevs, A. Berner, M. Wand, I. Ihrke, and H.-P. Seidel, "Intrinsic Shape Matching by Planned Landmark Sampling,"
Computer Graphics Forum, vol. 30, no. 2, pp. 543-552, 2011.- [16] M. Ovsjanikov, Q. Mrigot, F. Mmoli, and L. Guibas, "One Point Isometric Matching with the Heat Kernel,"
Computer Graphics Forum, vol. 29, no. 5, pp. 1555-1564, 2010.- [17] Y. Lipman and T. Funkhouser, "Möbius Voting for Surface Correspondence,"
ACM Trans. Graphics, vol. 28, pp. 72:1-72:12, 2009.- [18] 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.- [19] M. Leordeanu and M. Hebert, "A Spectral Technique for Correspondence Problems Using Pairwise Constraints,"
Proc. Int'l Conf. Computer Vision, pp. 1482-1489, 2005.- [20] Y. Zeng, C. Wang, Y. Wang, X. Gu, D. Samaras, and N. Paragios, "Dense Non-Rigid Surface Registration Using High-Order Graph Matching,"
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 382-389, 2010.- [21] O. Duchenne, F. Bach, I. Kweon, and J. Ponce, "A Tensor-Based Algorithm for High-Order Graph Matching,"
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1980-1987, 2009.- [22] A. Wang, S. Li, and L. Zeng, "Multiple Order Graph Matching,"
Proc. Asian Conf. Computer Vision, pp. 471-482, 2010.- [23] E. Kofidis and P.A. Regalia, "On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors,"
SIAM J. Matrix Analysis and Applications, vol. 23, no. 3, pp. 863-884, 2002.- [24] D.G. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints,"
Int'l J. Computer Vision, vol. 60, pp. 91-110, 2004.- [25] J. Sun, M. Ovsjanikov, and L. Guibas, "A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion,"
Proc. Symp. Geometry Processing, pp. 1383-1392, 2009.- [26] T. Cour, P. Srinivasan, and J. Shi, "Balanced Graph Matching,"
Proc. Advanced in Neural Information Processing System (NIPS), pp. 313-320, 2006.- [27] H. Li, R.W. Sumner, and M. Pauly, "Global Correspondence Optimization for Non-Rigid Registration of Depth Scans,"
Computer Graphics Forum, vol. 27, no. 5, pp. 1421-1430, 2008.- [28] R. Zass and A. Shashua, "Probabilistic Graph and Hypergraph Matching,"
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2008.- [29] O. Duchenne, F. Bach, I.-S. Kweon, and J. Ponce, "A Tensor-Based Algorithm for High-Order Graph Matching,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 33, no. 12, pp. 2383-2395, Dec. 2011.- [30] M. Chertok and Y. Keller, "Efficient High Order Matching,"
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 32, no. 12, pp. 2205-2215, Dec. 2010.- [31] D. Aiger, N.J. Mitra, and D. Cohen-Or, "4-Points Congruent Sets for Robust Pairwise Surface Registration,"
ACM Trans. Graphics, vol. 27, no. 3,article 85, 2008.- [32] T.G. Kolda and B.W. Bader, "Tensor Decompositions and Applications,"
SIAM Rev., vol. 51, no. 3, pp. 455-500, 2009.- [33] F.L. Hitchcock, "The Expression of a Tensor or a Polyadic as a Sum of Products,"
J. Math. and Physics, vol. 6, pp. 64-89, 1927.- [34] L.D. Lathauwer, P. Comon, B.D. Moor, and J. Vandewalle, "Higher-Order Power Method,"
Proc. Symp. Nonlinear Theory and Its Applications (NOLTA), pp. 2709-2712, 1995.- [35] P.A. Regalia and E. Kofidis, "The Higher-Order Power Method Revisited: Convergence Proofs and Effective Initialization,"
Proc. IEEE Int'l Conf. Acoustics, Speech, and Signal Processing, pp. 2709-2712, 2000.- [36] G. Peyré, M. Péchaud, R. Keriven, and L.D. Cohen, "Geodesic Methods in Computer Vision and Graphics,"
Foundations and Trends in Computer Graphics and Vision, vol. 5, pp. 197-397, 2010.- [37] S. Rusinkiewicz and M. Levoy, "Efficient Variants of the ICP Algorithm,"
Proc. Int'l Conf. 3D Digital Imaging and Modeling (3DIM), pp. 145-152, 2001.- [38] N. Gelfand, N.J. Mitra, L.J. Guibas, and H. Pottmann, "Robust Global Registration"
Proc. Symp. Geometry Processing, 2005.- [39] M. Chuang, L. Luo, B.J. Brown, S. Rusinkiewicz, and M.M. Kazhdan, "Estimating the Laplace-Beltrami Operator by Restricting 3D Functions,"
Computer Graphics Forum, vol. 28, no. 5, pp. 1475-1484, 2009.- [40] Kinect, http://www.xbox.com/en-USkinect, 2012.
- [41] N.J. Mitra, L. Guibas, and M. Pauly, "Partial and Approximate Symmetry Detection for 3D Geometry,"
ACM Trans. Graphics, vol. 25, no. 3, pp. 560-568, 2006.- [42] W. Chang and M. Zwicker, "Range Scan Registration Using Reduced Deformable Models,"
Computer Graphics Forum, vol. 28, no. 2, pp. 447-456, 2009.- [43] J. Matas, O. Chum, M. Urban, and T. Pajdla, "Robust Wide-Baseline Stereo from Maximally Stable Extremal Regions,"
Image and Vision Computing, vol. 22, no. 10, pp. 761-767, 2004. |