Intensity-based image registration using Earth Mover's Distance

Abstract

We introduce two image alignment measures using Earth Mover's Distance (EMD) as a metric on the space of joint intensity distributions. Our first approach consists of computing EMD between a joint distribution and the product of its marginals. This yields a measure of statistical dependence comparable to Mutual Information, a criterion widely used for multimodal image registration. When a-priori knowledge is available, we also propose to compute EMD between the observed distribution and a joint distribution estimated from pairs of pre-aligned images. EMD is a cross-bin dissimilarity function and generally offers a generalization ability which is superior to previously proposed metrics, such as Kullback-Leibler divergence. Computing EMD amounts to solving an optimal mass transport problem whose solution can be very efficiently obtained using an algorithm recently proposed by Ling and Okada.¹⁰ We performed a preliminary experimental evaluation of this approach with real and simulated MR images. Our results show that EMD-based measures can be efficiently applied to rigid registration tasks.