The Community for Technology Leaders
RSS Icon
Issue No.09 - September (2009 vol.31)
pp: 1616-1629
Anuj Srivastava , Florida State University, Tallahassee
Ian H. Jermyn , INRIA (Ariana), France
We study the problem of identifying shape classes in point clouds. These clouds contain sampled points along contours and are corrupted by clutter and observation noise. Taking an analysis-by-synthesis approach, we simulate high-probability configurations of sampled contours using models learned from training data to evaluate the given test data. To facilitate simulations, we develop statistical models for sources of (nuisance) variability: 1) shape variations within classes, 2) variability in sampling continuous curves, 3) pose and scale variability, 4) observation noise, and 5) points introduced by clutter. The variability in sampling closed curves into finite points is represented by positive diffeomorphisms of a unit circle. We derive probability models on these functions using their square-root forms and the Fisher-Rao metric. Using a Monte Carlo approach, we simulate configurations from a joint prior on the shape-sample space and compare them to the data using a likelihood function. Average likelihoods of simulated configurations lead to estimates of posterior probabilities of different classes and, hence, Bayesian classification.
Shape classification, clutter model, Fisher-Rao metric, planar shape model, diffeomorphism.
Anuj Srivastava, Ian H. Jermyn, "Looking for Shapes in Two-Dimensional Cluttered Point Clouds", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.31, no. 9, pp. 1616-1629, September 2009, doi:10.1109/TPAMI.2008.223
[1] T.F. Cootes, C.J. Taylor, D.H. Cooper, and J. Graham, “Active Shape Models: Their Training and Application,” Computer Vision and Image Understanding, vol. 61, no. 1, pp. 38-59, 1995.
[2] T.F. Cootes, G. Edwards, and C.J. Taylor, “Active Appearance Models,” Proc. Fifth European Conf. Computer Vision, H.Burkhardt and B. Neumann, eds., pp. 484-498, 1998.
[3] E. Klassen, A. Srivastava, W. Mio, and S. Joshi, “Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 3, pp. 372-383, Mar. 2004.
[4] P.W. Michor and D. Mumford, “Riemannian Geometries on Spaces of Plane Curves,” J. European Math. Soc., vol. 8, pp. 1-48, 2006.
[5] A. Srivastava, M.I. Miller, and U. Grenander, “Bayesian Automated Target Recognition,” Handbook of Image and Video Processing, pp. 869-881, Academic Press, 2000.
[6] T.B. Sebastian, P.N. Klein, and B.B. Kimia, “On Aligning Curves,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 1, pp. 116-125, Jan. 2003.
[7] M.A. Fischler and R.C. Bolles, “Random Samples Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography,” Comm. ACM, vol. 24, pp. 381-395, 1981.
[8] R. Schnabel, R. Wahl, and R. Klein, “Efficient RANSAC for Point-Cloud Shape Detection,” Computer Graphics Forum, vol. 26, no. 2, pp. 214-226, 2007.
[9] F. Memoli and G. Sapiro, “A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data,” Foundations and Computational Math., vol. 5, no. 3, pp. 313-347, 2005.
[10] J. Glaunes, A. Trouvé, and L. Younes, “Diffeomorphic Matching of Distributions: A New Approach for Unlabelled Point-Sets and Sub-Manifolds Matching,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 712-718, 2004.
[11] A. Peter and A. Rangarajan, “A New Closed-Form Information Metric for Shape Analysis,” Proc. Ninth Int'l Conf. Medical Image Computing and Computer-Assisted Intervention, 2006.
[12] P. Felzenszwalb and J. Schwartz, “Hierarchical Matching of Deformable Shapes,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007.
[13] N.N. Čencov, Statistical Decision Rules and Optimal Inferences Translations of Mathematical Monographs 53. AMS, 1982.
[14] S.J. Maybank, “Detection of Image Structures Using the Fisher Information and the Rao Metric,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 12, pp. 1579-1589, Dec. 2004.
[15] A. Bhattacharya, “On a Measure of Divergence between Two Statistical Populations Defined by Their Probability Distributions,” Bull. Calcutta Math. Soc., vol. 35, pp. 99-109, 1943.
[16] S. Amari, Differential Geometric Methods in Statistics Lecture Notes in Statistics 28. Springer, 1985.
[17] S. Lang, Fundamentals of Differential Geometry. Springer, 1999.
[18] A. Srivastava, S. Joshi, W. Mio, and X. Liu, “Statistical Shape Analysis: Clustering, Learning and Testing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 4, pp. 590-602, Apr. 2005.
[19] W. Mio, A. Srivastava, and S. Joshi, “On Shape of Plane Elastic Curves,” Int'l J. Computer Vision, vol. 73, no. 3, pp. 307-324, 2007.
[20] S.H. Joshi, E. Klassen, A. Srivastava, and I.H. Jermyn, “A Novel Representation for Efficient Computation of Geodesics between $n$ -Dimensional Curves,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007.
[21] S.H. Joshi, E. Klassen, A. Srivastava, and I.H. Jermyn, “Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves,” Proc. Sixth Int'l Conf. Energy Minimization Methods in Computer Vision and Pattern Recognition, A. Yuille et al., eds., pp. 387-398, 2007.
[22] M. Leventon, W.E.L. Grimson, and O. Faugeras, “Statistical Shape Influence in Geodesic Active Contours,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 316-323, 2000.
[23] M. Rochery, I.H. Jermyn, and J. Zerubia, “Phase Field Models and Higher-Order Active Contours,” Proc. 10th IEEE Int'l Conf. Computer Vision, 2005.
[24] G. Charpiat, O. Faugeras, and R. Keriven, “Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics,” J. Foundations of Computational Math., vol. 5, no. 1, pp. 1-58, 2005.
20 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool