Global performance prediction for divergence-based image registration criteria

Divergence measures find application in many areas of statistics, signal processing and machine learning, thus necessitating the need for good estimators of divergence measures. While several estimators of divergence measures have been proposed in literature, the performance of these estimators is not known. We propose a simple kNN density estimation based plug-in estimator for estimation of divergence measures. Based on the properties of kNN density estimates, we derive the bias, variance and mean square error of the estimator in terms of the sample size, the dimension of the samples and the underlying probability distribution. Based on these results, we specify the optimal choice of tuning parameters for minimum mean square error. We also present results on convergence in distribution of the proposed estimator. These results will establish a basis for analyzing the performance of image registration methods that maximize divergence.