title: Group-wise Point-set registration using a novel CDF-based Havrda-Charvát Divergence.
abstract: This paper presents a novel and robust technique for group-wise registration of point sets with unknown correspondence. We begin by defining a Havrda-Charvát (HC) entropy valid for cumulative distribution functions (CDFs) which we dub the HC Cumulative Residual Entropy (HC-CRE). Based on this definition, we propose a new measure called the CDF-HC divergence which is used to quantify the dis-similarity between CDFs estimated from each point-set in the given population of point sets. This CDF-HC divergence generalizes the CDF based Jensen-Shannon (CDF-JS) divergence introduced earlier in the literature, but is much simpler in implementation and computationally more efficient.A closed-form formula for the analytic gradient of the cost function with respect to the non-rigid registration parameters has been derived, which is conducive for efficient quasi-Newton optimization. Our CDF-HC algorithm is especially useful for unbiased point-set atlas construction and can do so without the need to establish correspondences. Mathematical analysis and experimental results indicate that this CDF-HC registration algorithm outperforms the previous group-wise point-set registration algorithms in terms of efficiency, accuracy and robustness.
authors.affiliation: T. Chen, B. C. Vemuri and A. Rangarajan are with Department of CISE, University of Florida, Gainesville, FL 32601. S. J. Eisenschenk is with Department of Neurology, University of Florida.
authors.forename: Ting
authors.initials: T
authors.lastname: Chen
authors.forename: Baba C
authors.initials: BC
authors.lastname: Vemuri
authors.forename: Anand
authors.initials: A
authors.lastname: Rangarajan
authors.forename: Stephan J
authors.initials: SJ
authors.lastname: Eisenschenk