The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.03 - March (2011 vol.33)
pp: 587-602
Radu Horaud , INRIA Grenoble Rhône-Alpes, Montbonnot Saint-Martin
Florence Forbes , INRIA Grenoble Rhône-Alpes, Montbonnot Saint-Martin
Manuel Yguel , INRIA Grenoble Rhône-Alpes, Montbonnot Saint-Martin
Guillaume Dewaele , INRIA Grenoble Rhône-Alpes, Montbonnot Saint-Martin
Jian Zhang , The University of Hong Kong, Hong Kong
ABSTRACT
This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely, the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyze in detail the associated consequences in terms of estimation of the registration parameters, and propose an optimal method for estimating the rotational and translational parameters based on semidefinite positive relaxation. We extend rigid registration to articulated registration. Robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the Gaussian mixture model at hand. We provide an in-depth analysis of our method and compare it both theoretically and experimentally with other robust methods for point registration.
INDEX TERMS
Point registration, feature matching, articulated object tracking, hand tracking, object pose, robust statistics, outlier detection, expectation maximization, EM, ICP, Gaussian mixture models, convex optimization, SDP relaxation.
CITATION
Radu Horaud, Florence Forbes, Manuel Yguel, Guillaume Dewaele, Jian Zhang, "Rigid and Articulated Point Registration with Expectation Conditional Maximization", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 3, pp. 587-602, March 2011, doi:10.1109/TPAMI.2010.94
REFERENCES
[1] P.J. Besl and N.D. McKay, "A Method for Registration of 3D Shapes," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239-256, Feb. 1992.
[2] Z. Zhang, "Iterative Point Matching for Registration of Free-Form Curves and Surfaces," Int'l J. Computer Vision, vol. 13, pp. 119-152, 1994.
[3] S. Rusinkiewicz and M. Levoy, "Efficient Variants of the ICP Algorithm," Proc. IEEE Third Int'l Conf. 3D Digital Imaging and Modeling, May/June 2001.
[4] A.W. Fitzgibbon, "Robust Registration of 2D and 3D Point Sets," Image and Vision Computing, vol. 21, no. 12, pp. 1145-1153, Dec. 2001.
[5] D. Chetverikov, D. Stepanov, and P. Krsek, "Robust Euclidean Alignment of 3D Point Sets: The Trimmed Iterative Closest Point Algorithm," Image and Vision Computing, vol. 23, no. 3, pp. 299-309, Mar. 2005.
[6] G.C. Sharp, S.W. Lee, and D.K. Wehe, "Maximum-Likelihood Registration of Range Images with Missing Data," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 1, pp. 120-130, Jan. 2008.
[7] D. Demirdjian, "Combining Geometric- and View-Based Approaches for Articulated Pose Estimation," Proc. European Conf. Computer Vision, pp. 183-194, 2004.
[8] L. Munderman, S. Corazza, and T.P. Andriacchi, "Accurately Measuring Human Movement Using Articulated ICP with Soft-Joint Constraints and a Repository of Articulated Models," Proc. IEEE 11th Int'l Conf. Computer Vision, Nov. 2007.
[9] A. Rangarajan, H. Chui, and F.L. Bookstein, "The Softassign Procrustes Matching Algorithm," Proc. Int'l Conf. Information Processing in Medical Imaging, pp. 29-42, 1997.
[10] H. Chui and A. Rangarajan, "A New Point Matching Algorithm for Non-Rigid Registration," Computer Vision and Image Understanding, vol. 89, nos. 2/3, pp. 114-141, Feb. 2003.
[11] Y. Liu, "Automatic 3D Free Form Shape Matching Using the Graduated Assignment Algorithm," Pattern Recognition, vol. 38, pp. 1615-1631, 2005.
[12] Y. Liu, "A Mean Field Annealing Approach to Accurate Free Form Shape Matching," Pattern Recognition, vol. 40, pp. 2418-2436, 2007.
[13] W. Wells,III, "Statistical Approaches to Feature-Based Object Recognition," Int'l J. Computer Vision, vol. 28, nos. 1/2, pp. 63-98, 1997.
[14] 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.
[15] 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.
[16] A. Myronenko, X. Song, and M.A. Carreira-Perpinan, "Non-Rigid Point Set Registration: Coherent Point Drift," Advances in Neural Information Processing Systems, pp. 1009-1016, MIT Press, Dec. 2006.
[17] M. Sofka, G. Yang, and C.V. Stewart, "Simultaneous Covariance Driven Correspondence (CDC) and Transformation Estimation in the Expectation Maximization Framework," Proc. IEEE Conf. Computer Vision and Pattern Recognition, June 2007.
[18] B. Jian and B.C. Vemuri, "A Robust Algorithm for Point Set Registration Using Mixture of Gaussians," Proc. 10th IEEE Int'l Conf. Computer Vision, 2005.
[19] P. Meer, "Robust Techniques for Computer Vision," Emerging Topics in Computer Vision, Prentice Hall, 2004.
[20] R. Sinkhorn, "A Relationship between Arbitrary Positive Matrices and Doubly Stochastic Matrices," Annals of Math. Statistics, vol. 35, pp. 876-879, 1964.
[21] A.P. Dempster, N.M. Laird, and D.B. Rubin, "Maximum Likelihood Estimation from Incomplete Data via the EM Algorithm (with Discussion)," J. Royal Statistical Soc., Series B, vol. 39, pp. 1-38, 1977.
[22] C. Fraley and A.E. Raftery, "Model-Based Clustering, Discriminant Analysis, and Density Estimation," J. Am. Statistical Assoc., vol. 97, pp. 611-631, 2002.
[23] K.S. Arun, T.S. Huang, and S.D. Blostein, "Least-Squares Fitting of Two 3D Point Sets," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 5, pp. 698-700, Sept. 1987.
[24] B. Horn, "Closed-Form Solution of Absolute Orientation Using Orhtonormal Matrices," J. Optical Soc. of Am. A, vol. 5, no. 7, pp. 1127-1135, 1987.
[25] B. Horn, "Closed-Form Solution of Absolute Orientation Using Unit Quaternions," J. Optical Soc. of Am. A, vol. 4, no. 4, pp. 629-642, 1987.
[26] S. Umeyama, "Least-Squares Estimation of Transformation Parameters between Two Point Patterns," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 376-380, Apr. 1991.
[27] J. Williams and M. Bennamoun, "A Multiple View 3D Registration Algorithm with Statistical Error Modeling," IEICE Trans. Information and Systems, vol. E83D, no. 8, pp. 1662-1670, Aug. 2000.
[28] A.I. Yuille, P. Stolorz, and J. Utans, "Statistical Physics, Mixture of Distributions, and the EM Algorithm," Neural Computation, vol. 6, pp. 334-340, 1994.
[29] B. Luo and E. Hancock, "A Unified Framework for Alignment and Correspondence," Computer Vision and Image Understanding, vol. 92, no. 1, pp. 26-55, Oct. 2003.
[30] Y. Tsin and T. Kanade, "A Correlation-Based Approach to Robust Point Set Registration," Proc. Eighth European Conf. Computer Vision, May 2004.
[31] F. Wang, B. Vemuri, A. Rangarajan, I. Schmalfuss, and S. Eisenschenk, "Simultaneous Nonrigid Registration of Multiple Point Sets and Atlas Construction," Proc. Ninth European Conf. Computer Vision, May 2006.
[32] X.-L. Meng and D.B. Rubin, "Maximum Likelihood Estimation via the ECM Algorithm: A General Framework," Biometrika, vol. 80, pp. 267-278, 1993.
[33] C. Lemarechal and F. Oustry, "SDP Relaxations in Combinatorial Optimization from a Lagrangian Viewpoint," Advances in Convex Analysis and Global Optimization, N. Hadjisavvas and P.M. Panos, eds., ch. 6, pp. 119-134, Kluwer Academic Publishers, 2001.
[34] I. Kakadiaris and D. Metaxas, "Model-Based Estimation of 3D Human Motion," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 12, pp. 1453-1459, Dec. 2000.
[35] R. Plaenkers and P. Fua, "Articulated Soft Objects for Multi-View Shape and Motion Capture," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 9, pp. 1182-1187, Sept. 2003.
[36] C. Bregler, J. Malik, and K. Pullen, "Twist Based Acquisition and Tracking of Animal and Human Kinematics," Int'l J. Computer Vision, vol. 56, no. 3, pp. 179-194, Feb./Mar. 2004.
[37] D. Knossow, R. Ronfard, and R. Horaud, "Human Motion Tracking with a Kinematic Parameterization of Extremal Contours," Int'l J. Computer Vision, vol. 79, no. 2, pp. 247-269, Sept. 2008.
[38] R. Horaud, M. Niskanen, G. Dewaele, and E. Boyer, "Human Motion Tracking by Registering an Articulated Surface to 3D Points and Normals," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 31, no. 1, pp. 158-164, Jan. 2009.
[39] S. Pellegrini, K. Schindler, and D. Nardi, "A Generalization of the ICP Algorithm for Articulated Bodies," Proc. British Machine Vision Conf., Sept. 2008.
[40] J.D. Banfield and A.E. Raftery, "Model-Based Gaussian and Non-Gaussian Clustering," Biometrics, vol. 49, no. 3, pp. 803-821, Sept. 2002.
[41] C. Hennig, "Breakdown Points for Maximum Likelihood Estimators of Location-Scale Mixtures," The Annals of Statistics, vol. 32, no. 4, pp. 1313-1340, 2004.
[42] C. Hennig and P. Coretto, "The Noise Component in Model-Based Cluster Analysis," Proc. 31st Ann. Conf. German Classification Soc. on Data Analysis, Machine Learning, and Applications, Mar. 2007.
[43] R.A. Redner and H.F. Walker, "Mixture Densities, Maximum Likelihood and the EM Algorithm," SIAM Rev., vol. 26, no. 2, pp. 195-239, Apr. 1984.
[44] G.J. McLachlan and T. Krishnan, The EM Algorithm and Extensions. Wiley, 1997.
[45] P.J. Rousseeuw, "Least Median of Squares Regression," J. Am. Statistical Assoc., vol. 79, pp. 871-880, 1984.
[46] P.J. Rousseeuw and S. Van Aelst, "Positive-Breakdown Robust Methods in Computer Vision," Computing Science and Statistics, K. Berk and M. Pourahmadi, eds., vol. 31, pp. 451-460, Interface Foundation of North Am., 1999.
[47] C. Bishop, Pattern Recognition and Machine Learning. Springer, 2006.
[48] S. Ingrassia and R. Rocci, "Constrained Monotone EM Algorithms for Finite Mixture of Multivariate Gaussians," Computational Statistics and Data Analysis, vol. 51, pp. 5339-5351, 2007.
[49] R.J. Hathaway, "A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions," Annals of Statistics, vol. 13, pp. 795-800, 1985.
[50] C. Lemarechal and F. Oustry, "Semidefinite Relaxations and Lagrangian Duality with Application to Combinatorial Optimization," Technical Report 3710, INRIA, June 1999.
[51] J.M. McCarthy, Introduction to Theoretical Kinematics. MIT Press, 1990.
[52] M. de la Gorce, N. Paragios, and D. Fleet, "Model-Based Hand Tracking with Texture, Shading and Self-Occlusions," Proc. IEEE Int'l Conf. Computer Vision and Pattern Recognition, June 2008.
[53] H. Hamer, K. Schindler, E. Koller-Meier, and L. Van Gool, "Tracking a Hand Manipulating an Object," Proc. IEEE Int'l Conf. Computer Vision, Oct. 2009.
[54] G. Dewaele, F. Devernay, and R. Horaud, "Hand Motion from 3D Point Trajectories and a Smooth Surface Model," Proc. Eighth European Conf. Computer Vision, pp. 495-507, May 2004.
[55] G. Dewaele, F. Devernay, R. Horaud, and F. Forbes, "The Alignment between 3D Data and Articulated Shapes with Bending Surfaces," Proc. Ninth European Conf. Computer Vision, pp. 578-591, May 2006.
[56] G. Celeux and G. Govaert, "A Classification EM Algorithm for Clustering and Two Stochastic Versions," Computational Statistics and Data Analysis, vol. 14, no. 3, pp. 315-332, 1992.
[57] B. Thiesson, C. Meek, and D. Heckerman, "Accelerating EM for Large Databases," Machine Learning, vol. 45, no. 3, pp. 279-299, 2001.
[58] J. Verbeek, J. Nunnink, and N. Vlassis, "Accelerated EM-Based Clustering of Large Data Sets," Data Mining and Knowledge Discovery, vol. 13, no. 3, pp. 291-307, Nov. 2006.
56 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool