Image Registration and Segmentation by Maximizing the Jensen-Rényi Divergence

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Information theoretic measures provide quantitative entropic divergences between two probability distributions or data sets. In this paper, we analyze the theoretical properties of the Jensen-Rényi divergence which is defined between any arbitrary number of probability distributions. Using the theory of majorization, we derive its maximum value, and also some performance upper bounds in terms of the Bayes risk and the asymptotic error of the nearest neighbor classifier. To gain further insight into the robustness and the application of the Jensen-Rényi divergence measure in imaging, we provide substantial numerical experiments to show the power of this entopic measure in image registration and segmentation.