Novel divergence measure based on Cauchy-Schwarz for multimodal medical image registration

Information theoretic similarity measures, especially mutual information, have been widely and successfully employed in multimodal image registration. Apart from these metrics, however, there are other measures which could be considered for image registration. A new similarity metrics was introduced for this task. The connections between Shannon mutual information, Kullback-Leibler divergence and Shannon inequality were analyzed. From these connections and Cauchy-Schwarz inequality, a novel generalized divergence was proposed. According to the new divergence function, a novel similarity measure based on Cauchy-Schwarz inequality for multi-modal image registration was put forward. Unlike Kullback-Leibler divergence, the new measures have some fundamental and appealing mathematical properties such as convexity, symmetry and do not require the condition of absolute continuity to be satisfied by the probability distribution involved. The performance of mutual information and normalized mutual information with the new similarity measures were compared. These measures are applied to rigid registration of clinical MR/PET images. An accurate gold standard transformation is avail able for the images. The results of tests indicated these new similarity functions have even better performance, compared with Shannon information theoretic measures.