CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2011 vol.33 Issue No.06 - June

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Issue No.06 - June (2011 vol.33)

pp: 1116-1131

Hongsheng Li , Lehigh University, Bethlehem

Tian Shen , Lehigh University, Bethlehem

Xiaolei Huang , Lehigh University, Bethlehem

ABSTRACT

In this paper, we introduce a novel method to solve shape alignment problems. We use gray-scale "images” to represent source shapes, and propose a novel two-component Gaussian Mixture (GM) distance map representation for target shapes. This asymmetric representation is a flexible image-based representation which is able to represent different kinds of shape data, including continuous contours, unstructured sparse point sets, edge maps, and even gray-scale gradient maps. Using this representation, a new energy function based on a novel two-component Gaussian Mixture distance model is proposed. The new energy function was empirically evaluated to be a more robust shape dissimilarity metric that can be computed efficiently. Such high efficiency is essential for global optimization methods. We adopt and modify one of them, the Particle Swarm Optimization (PSO), to effectively estimate the global optimum of the new energy function. Differently from the original PSO, several new strategies were employed to make the optimization more robust and prevent it from converging prematurely. The overall performance of the proposed framework as well as the properties of each algorithmic component were evaluated and compared with those of some state-of-the-art methods. Extensive experiments and comparison performed on generalized 2D and 3D shape data demonstrate the robustness and effectiveness of the method.

INDEX TERMS

Shape alignment, point registration, matching, distance transform, particle swarm optimization.

CITATION

Hongsheng Li, Tian Shen, Xiaolei Huang, "Approximately Global Optimization for Robust Alignment of Generalized Shapes",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.33, no. 6, pp. 1116-1131, June 2011, doi:10.1109/TPAMI.2010.169REFERENCES

- [1] H.G. Barrow, J.M. Tenenbaum, R.C. Bolles, and H.C. Wolf, “Parametric Correspondence and Chamfer Matching: Two Techniques for Image Matching,”
Proc. Int'l Joint Conf. Artificial Intelligence, pp. 1175-1177, 1977.- [2] 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. 509-521, Apr. 2002.- [3] P. Besl and H. 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.- [4] P. Bhowmick, R.K. Pradhan, and B.B. Bhattacharya, “Approximate Matching of Digital Point Sets Using a Novel Angular Tree,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 31, no. 5, pp. 769-782, May 2009.- [5] H. Chui and A. Rangarajan, “A Feature Registration Framework Using Mixture Models,”
Proc. IEEE Workshop Math. Methods in Biomedical Image Analysis, pp. 190-197, 2000.- [6] H. Chui and A. Rangarajan, “A New Point Matching Algorithm for Non-Rigid Registration,”
Computer Vision and Image Understanding, vol. 89, pp. 114-141, 2003.- [7] M. Clerc and J. Kennedy, “The Particle Swarm—Explosion, Stability, and Convergence in a Multidimensional Complex Space,”
IEEE Trans. Evolutionary Computation, vol. 6, no. 1, pp. 58-73, Feb. 2002.- [8] C. Cocosco, V. Kollokian, R. Kwan, and A. Evans, “BrainWeb: Online Interface to a 3D MRI Simulated Brain Database,”
Proc. Int'l Conf. Functional Mapping of the Human Brain, 1997.- [9] A.D.J. Cross and E.R. Hancock, “Graph Matching with a Dual-Step EM Algorithm,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 11, pp. 1236-1253, Nov. 1998.- [10] P.J. de Rezende and D.T. Lee, “Point Matching in d-Dimensions,”
Algorithms, vol. 13, pp. 387-404, 1995.- [11] C. Dorai, J. Weng, and A. Jain, “Optimal Registration of Object Views Using Range Data,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 10, pp. 1131-1138, Oct. 1997.- [12] R. Eberhart and J. Kennedy, “A New Optimizer Using Particle Swarm Theory,”
Proc. Int'l Symp. Micro Machine and Human Science, pp. 39-43, 1995.- [13] H. El Munim and A. Farag, “Shape Representation and Registration Using Vector Distance Functions,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2007.- [14] A. Erafat and A. Itai, “Improvements on Bottleneck Matching and Related Problems Using Geometry,”
Proc. Ann. ACM Symp. Computational Geometry, pp. 301-310, 1996.- [15] 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, pp. 381-395, 1981.- [16] A. Fitzgibbon, “Robust Registration of 2D and 3D Point Sets,”
Image and Vision Computing, vol. 21, pp. 1145-1153, 2003.- [17] G. Godin, M. Rioux, and R. Baribeau, “Three-Dimensional Registration Using Range and Intensity Information,”
Proc. SPIE: Videometrics III, 1994.- [18] 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.- [19] S. Granger and X. Pennec, “Multi-Scale EM-ICP: A Fast and Robust Approach for Surface Registration,”
Proc. European Conf. Computer Vision, pp. 418-432, 2002.- [20] F.S. Hill and S.M. Kelley,
Computer Graphics Using OpenGL. Prentice Hall, 2007.- [21] R. Huang, V. Pavlovic, and D.N. Metaxas, “Embedded Profile Hidden Markov Models for Shape Analysis,”
Proc. IEEE Int'l Conf. Computer Vision, pp. 1-8, 2007.- [22] X. Huang, N. Paragios, and D.N. Metaxas, “Shape Registration in Implicit Spaces Using Information Theory and Free Form Deformations,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 8, pp. 1303-1318, Aug. 2006.- [23] P.J. Huber,
Robust Statistics. Wiley, 1981.- [24] D.P. Huttenlocher, G.A. Klanderman, and W.J. Rucklidge, “Comparing Images Using the Hausdorff Distance,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 9, pp. 850-863, Sept. 1993.- [25] A. Jagannathan and E. Miller, “Unstructured Point Cloud Matching within Graph-Theoretic and Thermodynamic Frameworks,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 1008-1015, 2005.- [26] B. Jian and B. Vemuri, “A Robust Algorithm for Point Set Registration Using Mixture of Gaussians,”
Proc. IEEE Int'l Conf. Computer Vision, vol. 2, pp. 1246-1251, 2005.- [27] V. Lempitsky and Y. Boykov, “Global Optimization for Shape Fitting,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2007.- [28] M.E. Leventon, W.E.L. Grimson, and O. Faugeras, “Statistical Shape Influence in Geodesic Active Contours,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 316-323, 2000.- [29] T. Liu and D. Greiger, “Approximate Tree Matching and Shape Similarity,”
Proc. IEEE Int'l Conf. Computer Vision, pp. 456-462, 1999.- [30] A. Makadia, A. Patterson, and K. Daniilidis, “Fully Automatic Registration of 3D Point Clouds,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 1297-1304, 2006.- [31] S. Manay, D. Cremers, B.W. Hong, A. Yezzi, and S. Soatto, “Integral Invariants for Shape Matching,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1602-1618, Oct. 2006.- [32] T. Masuda, K. Sakaue, and N. Yokoya, “Registration and Integration of Multiple Range Images for 3-D Model Construction,”
Proc. Int'l Conf. Pattern Recognition, vol. 1, pp. 879-883, 1996.- [33] C.R. Maurer, R. Qi, and V. Raghavan, “A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 2, pp. 265-270, Feb. 2003.- [34] N. Paragios, M. Rousson, and V. Ramesh, “Non-Rigid Registration Using Distance Functions,”
Computer Vision and Image Understanding, vol. 89, pp. 142-165, 2003.- [35] A. Rangarajan, H. Chui, E. Mjolsness, S. Pappu, L. Davachi, P. Goldman-Rakic, and J. Duncan, “A Robust Point Matching Algorithm for Autoradiograph Alignment,”
Medical Image Analysis, vol. 4, pp. 379-398, 1997.- [36] S. Rusinkiewicz and M. Levoy, “Efficient Variants of the ICP Algorithm,”
Proc. Int'l Conf. 3D Digital Imaging and Modeling, pp. 145-152, 2001.- [37] R. Sandhu, S. Dambreville, and A. Tannenbaum, “Particle Filtering for Registration of 2D and 3D Point Sets with Stochastic Dynamics,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2008.- [38] F. Schmidt, D. Farin, and D. Cremers, “Fast Matching of Planar Shapes in Sub-Cubic Runtime,”
Proc. IEEE Int'l Conf. Computer Vision, pp. 1-6, 2007.- [39] T. Sebastian, P. Klein, and B. Kimia, “Recognition of Shapes by Editing Shock Graphs,”
Proc. IEEE Int'l Conf. Computer Vision, vol. 1, pp. 755-782, 2001.- [40] D. Sharvit, J. Chan, H. Tek, and B. Kimia, “Symmetry-Based Indexing of Image Databases,”
Proc. IEEE Workshop Content-Based Access of Image and Video Libraries, pp. 56-62, 1998.- [41] Y. Shi and R. Eberhart, “A Modified Particle Swarm Optimizer,”
Proc. IEEE World Congress on Computational Intelligence, pp. 69-73, 1998.- [42] L. Tang and G. Hamarneh, “SMRFI: Shape Matching via Registration of Vector-Valued Feature Images,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2008.- [43] H. Tek and B.B. Kimia, “Symmetry Maps of Free-Form Curve Segments via Wave Propagation,”
Proc. IEEE Int'l Conf. Computer Vision, pp. 362-369, 1999.- [44] Y. Tsin and T. Kanade, “A Correlation-Based Approach to Robust Point Set Registration,”
Proc. European Conf. Computer Vision, vol. 3, pp. 558-569, 2004.- [45] G. Turk and M. Levoy, “Zippered Polygon Meshes from Range Images,”
Proc. ACM SIGGRAPH, pp. 311-318, 1994.- [46] R.C. Veltkamp and M. Hagedoorn, “State-of-the-Art in Shape Matching,”
Principles of Visual Information Retrieval, pp. 87-119, Springer, 1999.- [47] C. Wang, D. Duggins, J. Gowdy, J. Kozar, R. MacLachlan, C. Mertz, A. Suppe, and C. Thorpe, “Navlab SLAMMOT Data Sets,” http://www.cs.cmu.edu/bobwangdata sets.html , 2010.
- [48] F. Wang, B. Vemuri, A. Rangarajan, and S. Eisenschenk, “Simultaneous Nonrigid Registration of Multiple Point Sets and Atlas Construction,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 11, pp. 2011-2022, Nov. 2008.- [49] F. Wang, B. Vemuri, and A. Rangarajan, “Groupwise Point Pattern Registration Using a Novel CDF-Based Jensen-Shannon Divergence,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 1283-1288, 2006.- [50] Y. Wang, X. Huang, C.S. Lee, S. Zhang, Z. Li, D. Samaras, D.N. Metaxas, A. Elgammal, and P. Huang, “High Resolution Acquisition, Learning and Transfer of Dynamic 3-D Facial Expressions,”
Computer Graphics Forum, vol. 23, pp. 677-686, 2004.- [51] P. Xiao, N. Barnes, T. Caetano, and P. Lieby, “An MRF and Gaussian Curvature Based Shape Representation for Shape Matching,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-7, 2007.- [52] X. Xie, W. Zhang, and Z. Yang, “Adaptive Particle Swarm Optimization on Individual Level,”
Proc. Int'l Conf. Signal Processing, vol. 2, pp. 1215-1218, 2002.- [53] H. Zhang and E. Fiume, “Shape Matching of 3D Contours Using Normalized Fourier Descriptors,”
Proc. IEEE Int'l Conf. Shape Modeling and Applications, pp. 261-268, 2002.- [54] Z. Zhang, “Iterative Point Matching for Registration of Free-Form Curves and Surfaces,”
Int'l J. Computer Vision, vol. 13, pp. 119-152, 1994. |