Closed-Form Jensen-Renyi Divergence for Mixture of Gaussians and Applications to Group-Wise Shape Registration

Authors:
Fei Wang;Tanveer Syeda-Mahmood;Baba C. Vemuri;David Beymer;Anand Rangarajan
Affiliations:
IBM Almaden Research Center, San Jose, USA;IBM Almaden Research Center, San Jose, USA;Department of CISE, University of Florida, Gainesville, USA;IBM Almaden Research Center, San Jose, USA;Department of CISE, University of Florida, Gainesville, USA
Venue:
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
Year:
2009

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Abstract

In this paper, we propose a generalized group-wise non-rigid registration strategy for multiple unlabeled point-sets of unequal cardinality, with no bias toward any of the given point-sets. To quantify the divergence between the probability distributions --- specifically Mixture of Gaussians --- estimated from the given point sets, we use a recently developed information-theoretic measure called Jensen-Renyi (JR) divergence. We evaluate a closed-form JR divergence between multiple probabilistic representations for the general case where the mixture models differ in variance and the number of components. We derive the analytic gradient of the divergence measure with respect to the non-rigid registration parameters, and apply it to numerical optimization of the group-wise registration, leading to a computationally efficient and accurate algorithm. We validate our approach on synthetic data, and evaluate it on 3D cardiac shapes.