Variational non rigid registration with bregman divergences

Abstract

In this paper, we propose a new energy functional that generalizes the variational method for non-rigid image registration. Our new functional uses the Bregman divergence as a similarity measure. The registration method presented by Fisher and Modersitzki in [5] is an special case in our approach. We show that the variational registration method can be applied to arbitrary Bregman divergences. This result is relevant because these divergences include a large number of useful similarity functions, such as the square of the Euclidean distance, the divergence KL, Logistic loss, the Mahalanobis distance, Itakura-Saito divergence and the Generalized I-divergence. The Euler-Lagrange and the flow equations for the proposed functional were deduced and used to minimize it. Our experiments show that the new functional can determine the deformation field for the images registration obtained from different scans or modalities. The image registration under the Bregman divergences performed better than when using the Euclidean distance as the similarity measure.