A variational approach to non-rigid image registration with Bregman divergences and multiple features. (May 2018) - Ferreira, Daniela Portes Leal; Ribeiro, Eraldo; Zorzo Barcelos, Celia A.
Highlights: We propose to use Bregman divergences as similarity functions of the variational functional in image registration. Our formulation is a meta-algorithm that can be applied using any Bregman divergence associated to different features. Our new similarity measure generalizes the variational method, which of multiple image can combine image characteristics. Bregman divergences allows us to combine both local spatial and statistical information into the similarity measure. Abstract: Variational methods register images by minimizing functionals that balance measures of smoothness and image similarity. However, the specificity of image-similarity measures can limit the application of variational methods. To address this issue, we propose a new energy functional that generalizes the classical variational method for nonrigid image registration. Our generalization uses Bregman divergences as the similarity measure of the registration functional. These divergences include a number of important similarity measures, such as the Squared Loss distance, the KL divergence, the Logistic Loss, the Mahalanobis distance, the Itakura–Saito divergence, and the I-divergence. We derive the Euler Lagrange and gradient-flow equations associated with the new functional. By using Bregman divergences, our registration method can combine various types of image characterization as well as spatial and statistical information. Our experiments show that the use of Bregman divergences improves registration quality.