Fast Nonparametric Mutual-information-based Registration and Uncertainty Estimation

摘要

In this paper we propose a probabilistic model for multimodal non-linear registration that directly incorporates the mutual information (MI) metric into a demons-like optimization scheme. In contrast to uni-modal registration, where the demons algorithm uses repeated spatial filtering to obtain very fast solutions, Mi-based registration currently relies on general-purpose optimization schemes that are much slower. The central idea of this work is to reformulate an often-used histogram interpolation technique in MI implementations as an explicit spatial interpolation step within a generative model. By exploiting the specific structure of this model, we obtain a dedicated and fast expectation-maximization optimizer with demons-like properties. This also leads to an easy-to-implement Gibbs sampler to infer registration uncertainty in high-dimensional deformation models, involving very little additional code and no external tuning. Preliminary experiments on multi-modal brain MRI images show that the proposed optimizer can be both faster and more accurate than the free-form deformation method implemented in Elastix. We also demonstrate the sampler's ability to produce direct uncertainty estimates of Mi-based registrations - to the best of our knowledge the first method in the literature to do so.