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

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.

Dealing with shadows: Capturing intrinsic scene appearance for image-based outdoor localisation

“…Formally, we compute the Jensen-Renyi (JR) divergence [15] between the set of images for a single place represented as intensity histograms. The JR divergence evaluates the cumulative dissimilarity between two point sets (histograms in our case).…”

Novel multimodality segmentation using level sets and Jensen‐Rényi divergence

“…The JRD is a convenient objective function in that it can also be applied to the task of registration as investigated by a number of reports. 38,39,48 This may facilitate future work involving the simultaneous segmentation and registration of multimodality images using this metric in order to reduce computation time and improve accuracy of both processes. Such an algorithm would have great application towards IGART where previous plan contours provide a good approximation for initialization.…”

“…Some studies have observed that the JRD is more robust to image noise than mutual information when applied to registration as long as the weighting parameters are chosen appropriately. 38,39 Mutual information is a common objective function for registration tasks, and while it is not commonly used for segmentation, it is based on entropy terms which a number of authors have investigated for use in segmentation. [40][41][42][43] The use of entropy based on intensity value histograms (in particular using nonparametric density estimates) is an effective objective for statistically based segmentation.…”

Robust point set registration using EM-ICP with information-theoretically optimal outlier handling

“…After construction of the probability density functions, registration reduces to the computation of transformation parameters minimizing the distance between these density functions. Thereto, several information-theoretic measures are used such as KullbackLeibler (KL) divergence [14], Kernel Correlation [11], the L2-norm [7,10], Jensen-Shannon Divergence [13] or Jensen-Renyi Divergence [12]. Due to their independence to point correspondences, some of these methods are inherently robust against outliers.…”