A robust algorithm for point set registration using mixture of Gaussians

This paper proposes a novel and robust approach to the point set registration problem in the presence of large amounts of noise and outliers. Each of the point sets is represented by a mixture of Gaussians and the point set registration is treated as a problem of aligning the two mixtures. We derive a closed-form expression for the L/sub 2/distance between two Gaussian mixtures, which in turn leads to a computationally efficient registration algorithm. This new algorithm has an intuitive interpretation, is simple to implement and exhibits inherent statistical robustness. Experimental results indicate that our algorithm achieves very good performance in terms of both robustness and accuracy.

[1]  Anand Rangarajan,et al.  A new point matching algorithm for non-rigid registration , 2003, Comput. Vis. Image Underst..

[2]  Robust Registration of 2 D and 3 D Point Sets , 2001 .

[3]  Leslie Greengard,et al.  The Fast Gauss Transform , 1991, SIAM J. Sci. Comput..

[4]  Shiri Gordon,et al.  An efficient image similarity measure based on approximations of KL-divergence between two gaussian mixtures , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[5]  Anand Rangarajan,et al.  A new algorithm for non-rigid point matching , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[6]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Andrew W. Fitzgibbon Robust registration of 2D and 3D point sets , 2003, Image Vis. Comput..

[8]  M. C. Jones,et al.  Robust and efficient estimation by minimising a density power divergence , 1998 .

[9]  H. Chui,et al.  A feature registration framework using mixture models , 2000, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis. MMBIA-2000 (Cat. No.PR00737).

[10]  Narendra Ahuja,et al.  Robust Registration and Tracking Using Kernel Density Correlation , 2004, 2004 Conference on Computer Vision and Pattern Recognition Workshop.

[11]  Hongyu Guo,et al.  Non-rigid registration of shapes via diffeomorphic point matching , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).

[12]  Takeo Kanade,et al.  A Correlation-Based Approach to Robust Point Set Registration , 2004, ECCV.

[13]  Anand Rangarajan,et al.  Unsupervised learning of an Atlas from unlabeled point-sets , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  David W. Scott,et al.  Parametric Statistical Modeling by Minimum Integrated Square Error , 2001, Technometrics.

[15]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[16]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[17]  Daniel P. Huttenlocher,et al.  Comparing Images Using the Hausdorff Distance , 1993, IEEE Trans. Pattern Anal. Mach. Intell..