Group-Wise Point-Set Registration Using a Novel CDF-Based Havrda-Charvát Divergence

Authors:
Ting Chen;Baba C. Vemuri;Anand Rangarajan;Stephan J. Eisenschenk
Affiliations:
Department of CISE, University of Florida, Gainesville, USA 32601;Department of CISE, University of Florida, Gainesville, USA 32601;Department of CISE, University of Florida, Gainesville, USA 32601;Department of Neurology, University of Florida, Gainesville, USA 32601
Venue:
International Journal of Computer Vision
Year:
2010

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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 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.