Closed-Form Jensen-Renyi Divergence for Mixture of Gaussians and Applications to Group-Wise Shape Registration
By Fei Wang, Tanveer Fathima Syeda-Mahmood, Baba C. Vemuri, D. Beymer, Anand Rangarajan. 2009
60 citations recorded by the source corpus.
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.
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- Sergey Levine
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Citations in the corpus
- Learning Theory for Distribution Regression (2014, background): “Typical examples with explicit formulas include Gaussians, finite mixtures of Gaussians, and distributions from the exponential family (with known log-normalizer function and zero carrier measure, see Kondor and Jebara, 2003; Jebara et al., 2004; Wang et al., 2009; Nielsen and Nock, 2012).”
- Learning Awareness Models (2018, background): “A more complete derivation is shown in Appendix A, which extends the result of Wang et al. (2009) to the case when the mixture components have different variances.”
- Proposal : Scalable , Active and Flexible Learning on Distributions (2015, unknown): “For mixtures specifically of Gaussians, F. Wang et al. (2009) obtain the quadratic ( 2 ) entropy, which allows the computation of Jensen-Rényi divergences for α = 2.”