Bayesian Characterization of Uncertainty in Multi-modal Image Registration

Abstract

Understanding and quantifying the uncertainty involved when registering images is an important problem in medical imaging, where clinical decisions are made based on the registered solution. This is especially important in non-rigid registration where the higher degrees of freedom may provide unwarranted confidence in the results, through over-fitting. The Bayesian approach, which defines uncertainty as the posterior distribution on deformations, requires a generative model of the image formation process where the fixed image is modeled as a deformed version of the moving image plus a noise term. As per this model, the likelihood term is equivalent to the sum-of-squared differences image matching metric and is therefore valid only for same-mode image registration. In this paper, we propose a general formalism to quantify Bayesian uncertainty in the registration of multi-modal images through an extended probability model that introduces and then marginalizes out a stochastic transfer function between moving and fixed image intensities.