Copula based divergence measures and their use in image registration

This paper explores a new measure, based on the copula density functions, for image registration, especially for the multimodal image registration. The measure relies on determining the mutual information between images taken at different times from different viewpoints or by different sensors. The process aims to find the optimal spatial correspondence that offers maximal dependence between the grey levels of the images when they are correctly aligned. Misalignment results in a decrease in the measure. To this effect, this paper focuses on improving the estimation of mutual information. It is shown that copulas form an integral definition of mutual information, and lead to robust estimation tools. The paper includes new results on generalised divergence measures, including the Kullback-Liebler divergence, Kolomgorov, Tsallis, I_α, and Renyi measures amongst others. These are expressed in terms of copula density functions. Results are presented on the registration of two classes of images, using the Clayton Copula to estimate the divergence between the images, and their performance evaluated.