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

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Executive Summary

This paper proposes 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, one uses a recently developed information-theoretic measure called Jensen-Renyi (JR) divergence. The paper evaluates 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. The paper derives the analytic gradient of the divergence measure with respect to the non-rigid registration parameters, and applies it to numerical optimization of the group-wise registration, leading to a computationally efficient and accurate algorithm.

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