The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.08 - August (2011 vol.33)
pp: 1633-1645
Bing Jian , Siemens Healthcare, Malvern
Baba C. Vemuri , University of Florida, Gainesville
ABSTRACT
In this paper, we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers. The key idea of this registration framework is to represent the input point sets using Gaussian mixture models. Then, the problem of point set registration is reformulated as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized. We show that the popular iterative closest point (ICP) method [1] and several existing point set registration methods [2], [3], [4], [5], [6], [7] in the field are closely related and can be reinterpreted meaningfully in our general framework. Our instantiation of this general framework is based on the the L2 distance between two Gaussian mixtures, which has the closed-form expression and in turn leads to a computationally efficient registration algorithm. The resulting registration algorithm exhibits inherent statistical robustness, has an intuitive interpretation, and is simple to implement. We also provide theoretical and experimental comparisons with other robust methods for point set registration.
INDEX TERMS
Point set registration, nonrigid registration, Gaussian mixtures, robust matching.
CITATION
Bing Jian, Baba C. Vemuri, "Robust Point Set Registration Using Gaussian Mixture Models", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 8, pp. 1633-1645, August 2011, doi:10.1109/TPAMI.2010.223
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] H. Chui and A. Rangarajan, "A New Algorithm for Non-Rigid Point Matching," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 44-51, 2000.
[3] H. Chui and A. Rangarajan, "A Feature Registration Framework Using Mixture Models," Proc. IEEE Workshop on Math. Methods in Biomedical Image Analysis, pp. 190-197, 2000.
[4] Y. Tsin and T. Kanade, "A Correlation-Based Approach to Robust Point Set Registration," Proc. European Conf. Computer Vision, pp. 558-569, 2004.
[5] B. Jian and B.C. Vemuri, "A Robust Algorithm for Point Set Registration Using Mixture of Gaussians," Proc. IEEE Int'l Conf. Computer Vision, pp. 1246-1251, 2005.
[6] A. Myronenko, X.B. Song, and M.Á. Carreira-Perpiñán, "Non-Rigid Point Set Registration: Coherent Point Drift," Advances in Neural Information Processing Systems, pp. 1009-1016, MIT Press, 2006.
[7] A. Myronenko and X.B. Song, "Point-Set Registration: Coherent Point Drift," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 32, no. 12, pp. 2262-2275, Dec. 2010.
[8] P.B. van Wamelen, Z. Li, and S.S. Iyengar, "A Fast Expected Time Algorithm for the 2D Point Pattern Matching Problem," Pattern Recognition, vol. 37, no. 8, pp. 1699-1711, 2004.
[9] 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.
[10] B. Luo and E.R. Hancock, "A Unified Framework for Alignment and Correspondence," Computer Vision and Image Understanding, vol. 92, pp. 26-55, 2003.
[11] M. Carcassoni and E.R. Hancock, "Spectral Correspondence for Point Pattern Matching," Pattern Recognition, vol. 36, no. 1, pp. 193-204, 2003.
[12] T.S. Caetano, T. Caelli, D. Schuurmans, and D.A. Barone, "Graphical Models and Point Pattern Matching," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1646-1663, Oct. 2006.
[13] 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.
[14] Y. Zheng and D.S. Doermann, "Robust Point Matching for Nonrigid Shapes by Preserving Local Neighborhood Structures," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 4, pp. 643-649, Apr. 2006.
[15] 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.
[16] Z. Zhang, "Iterative Point Matching for Registration of Free-Form Curves and Surfaces," Int'l J. Computer Vision, vol. 13, no. 2, pp. 119-152, 1994.
[17] 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.
[18] C.V. Stewart, C.-L. Tsai, and B. Roysam, "The Dual Bootstrap Iterative Closest Point Algorithm with Application to Retinal Image Registration," IEEE Trans. Medical Imaging, vol. 22, no. 11, pp. 1379-1394, Nov. 2003.
[19] 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, pp. 299-309, 2005.
[20] A.P. Dempster, N.M. Laird, and D.B. Rubin, "Maximum Likelihood from Incomplete Data via the EM Algorithm," J. Royal Statistical Soc. B, vol. 39, no. 1, pp. 1-38, 1977.
[21] M. Sofka, G. Yang, and C.V. Stewart, "Simultaneous Covariance Driven Correspondence (CDC) and Transformation Estimation in the Expectation Maximization," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007.
[22] R.P. Horaud, F. Forbes, M. Yguel, G. Dewaele, and J. Zhang, "Rigid and Articulated Point Registration with Expectation Conditional Maximization," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. PP, no. 99, p. 1, Apr. 2010.
[23] A.W. Fitzgibbon, "Robust Registration of 2D and 3D Point Sets," Image and Vision Computing, vol. 21, nos. 13/14, pp. 1145-1153, 2003.
[24] J. Glaunes, A. Trouvé, and L. Younes, "Diffeomorphic Matching of Distributions: A New Approach for Unlabelled Point-Sets and Sub-Manifolds Matching," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 712-718, 2004.
[25] K. Kanatani, "Uncertainty Modeling and Model Selection for Geometric Inference," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 10, pp. 1307-1319, Oct. 2004.
[26] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization. John Wiley & Sons, 1992.
[27] M. Wand and M. Jones, Kernel Smoothing. Chapman & Hall, 1995.
[28] J. Shi and C. Tomasi, "Good Features to Track," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 593-600, 1994.
[29] D.D. Morris and T. Kanade, "A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models," Proc. Int'l Conf. Computer Vision, pp. 696-702, 1998.
[30] Y. Kanazawa and K. Kanatani, "Do We Really Have to Consider Covariance Matrices for Image Features?" Proc. IEEE Int'l Conf. Computer Vision, pp. 301-306, 2001.
[31] D. Comaniciu, V. Ramesh, and P. Meer, "Kernel-Based Object Tracking," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 5, pp. 564-575, May 2003.
[32] D. Comaniciu, "An Algorithm for Data-Driven Bandwidth Selection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 2, pp. 281-288, Feb. 2003.
[33] D.W. Scott and W.F. Szewczyk, "From Kernels to Mixtures," Technometrics, vol. 43, no. 3, pp. 323-335, 2001.
[34] D. Scott, "Parametric Statistical Modeling by Minimum Integrated Square Error," Technometrics, vol. 43, no. 3, pp. 274-285, 2001.
[35] A. Basu, I.R. Harris, N.L. Hjort, and M.C. Jones, "Robust and Efficient Estimation by Minimising a Density Power Divergence," Biometrika, vol. 85, no. 3, pp. 549-559, 1998.
[36] L.M. Bregman, "The Relaxation Method of Finding the Common Points of Convex Sets and Its Application to the Solution of Problems in Convex Programming," USSR Computational Math. and Math. Physics, vol. 7, pp. 200-217, 1967.
[37] F. Hampel, E. Ronchetti, P. Rousseeuw, and W. Stahel, Robust Statistics: The Approach Based on Influence Functions. Wiley, 1986.
[38] C.V. Stewart, "Robust Parameter Estimation in Computer Vision," SIAM Rev., vol. 41, no. 3, pp. 513-537, 1999.
[39] J. Liu, B.C. Vemuri, and J.L. Marroquín, "Local Frequency Representations for Robust Multimodal Image Registration," IEEE Trans. Medical Imaging, vol. 21, no. 5, pp. 462-469, May 2002.
[40] L. Yang, P. Meer, and D.J. Foran, "Unsupervised Segmentation Based on Robust Estimation and Color Active Contour Models," IEEE Trans. Information Technology in Biomedicine, vol. 9, no. 3, pp. 475-486, Sept. 2005.
[41] M. Mihoko and S. Eguchi, "Robust Blind Source Separation by Beta Divergence," Neural Computation, vol. 14, no. 8, pp. 1859-1886, 2002.
[42] J. Goldberger, S. Gordon, and H. Greenspan, "An Efficient Image Similarity Measure Based on Approximations of KL-Divergence between Two Gaussian Mixtures," Proc. IEEE Int'l Conf. Computer Vision, pp. 487-493, 2003.
[43] R. Jenssen, D. Erdogmus, J.C. Príncipe, and T. Eltoft, "The Laplacian PDF Distance: A Cost Function for Clustering in a Kernel Feature Space," Advances in Neural Information Processing Systems, MIT Press, 2004.
[44] R. Sandhu, S. Dambreville, and A. Tannenbaum, "Point Set Registration via Particle Filtering and Stochastic Dynamics," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 32, no. 8, pp. 1459-1473, Aug. 2010.
[45] M.C. Jones, N.L. Hjort, I.R. Harris, and A. Basu, "A Comparison of Related Density-Based Minimum Divergence Estimators," Biometrika, vol. 88, no. 3, pp. 865-873, 2001.
[46] M.P. Windham, "Robustifying Model Fitting," J. Royal Statistical Soc. B, vol. 57, pp. 599-609, 1995.
[47] L. Greengard and J. Strain, "The Fast Gauss Transform," SIAM J. Scientific Computing, vol. 12, no. 1, pp. 79-94, 1991.
[48] C. Yang, R. Duraiswami, N.A. Gumerov, and L.S. Davis, "Improved Fast Gauss Transform and Efficient Kernel Density Estimation," Proc. IEEE Int'l Conf. Computer Vision, pp. 464-471, 2003.
[49] F.L. Bookstein, "Principal Warps: Thin-Plate Splines and the Decomposition of Deformations," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 6, pp. 567-585, June 1989.
[50] G. Wahba, Spline Models for Observational Data. SIAM, 1990.
[51] K. Rohr, Landmark-Based Image Analysis: Using Geometric and Intensity Models. Kluwer Academic Publishers, 2001.
[52] A.L. Yuille and N.M. Grzywacz, "A Mathematical Analysis of the Motion Coherence Theory," Int'l J. Computer Vision, vol. 3, no. 2, pp. 155-175, 1989.
[53] C. Zhu, R.H. Byrd, P. Lu, and J. Nocedal, "Algorithm 778: L-BFGS-B: Fortran Subroutines for Large-Scale Bound-Constrained Optimization," ACM Trans. Math. Software, vol. 23, no. 4, pp. 550-560, 1997.
[54] C. Harris and M. Stephens, "A Combined Corner and Edge Detector," Proc. Fourth Alvey Vision Conf., pp. 147-152, 1988.
[55] 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. 6, pp. 381-395, 1981.
[56] R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision. Cambridge Univ. Press, 2003.
[57] J. Starck and A. Hilton, "Correspondence Labelling for Wide-Timeframe Free-Form Surface Matching," Proc. IEEE Int'l Conf. Computer Vision, 2007.
[58] F. Wang, T. Syeda-Mahmood, B.C. Vemuri, D. Beymer, and A. Rangarajan, "Closed-Form Jensen-Renyi Divergence for Mixture of Gaussians and Applications to Group-Wise Shape Registration," Proc. Int'l Conf. Medical Image Computing and Computer Assisted Intervention, pp. 648-655, 2009.
[59] F. Wang, B.C. Vemuri, A. Rangarajan, and S.J. 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.
[60] T. Chen, B.C. Vemuri, A. Rangarajan, and S.J. Eisenschenk, "Group-Wise Point-Set Registration Using a Novel CDF-Based Havrda-Charvát Divergence," Int'l J. Computer Vision, vol. 86, no. 1, pp. 111-124, 2010.
17 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool