A Correlation-Based Approach to Robust Point Set Registration

Correlation is a very effective way to align intensity images. We extend the correlation technique to point set registration using a method we call kernel correlation. Kernel correlation is an affinity measure, and it is also a function of the point set entropy. We define the point set registration problem as finding the maximum kernel correlation configuration of the the two point sets to be registered. The new registration method has intuitive interpretations, simple to implement algorithm and easy to prove convergence property. Our method shows favorable performance when compared with the iterative closest point (ICP) and EM-ICP methods.

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

[2]  Anand Rangarajan,et al.  The Softassign Procrustes Matching Algorithm , 1997, IPMI.

[3]  Haifeng Chen,et al.  Robust Computer Vision through Kernel Density Estimation , 2002, ECCV.

[4]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[5]  E. Parzen On Estimation of a Probability Density Function and Mode , 1962 .

[6]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

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

[8]  H. C. Longuet-Higgins,et al.  An algorithm for associating the features of two images , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[9]  Xavier Pennec,et al.  Multi-scale EM-ICP: A Fast and Robust Approach for Surface Registration , 2002, ECCV.

[10]  Andrew W. Fitzgibbon,et al.  Robust Registration of 2D and 3D Point Sets , 2003, BMVC.

[11]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[12]  D. Ruppert The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .

[13]  Zhengyou Zhang,et al.  Iterative point matching for registration of free-form curves and surfaces , 1994, International Journal of Computer Vision.

[14]  Mads Nielsen,et al.  Computer Vision — ECCV 2002 , 2002, Lecture Notes in Computer Science.

[15]  Richard Szeliski,et al.  Recovering the Position and Orientation of Free-Form Objects from Image Contours Using 3D Distance Maps , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

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

[17]  J. Príncipe,et al.  Information-Theoretic Learning Using Renyi's Quadratic Entropy , 1999 .

[18]  T. Kanade,et al.  Kernel correlation as an affinity measure in point-sampled vision problems , 2003 .

[19]  H. L. Le Roy,et al.  Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Vol. IV , 1969 .

[20]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[21]  Gunilla Borgefors,et al.  Hierarchical Chamfer Matching: A Parametric Edge Matching Algorithm , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

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

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

[24]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.