Probabilistic Diffeomorphic Registration: Representing Uncertainty
This addresses uncertainty representation in medical image registration, which is crucial for applications like surgical planning, but the approach is incremental as it builds on existing diffeomorphic registration methods.
The paper tackles the problem of representing uncertainty in large deformation diffeomorphic image registration by developing a Bayesian framework that approximates the posterior distribution over deformations using a variational formulation and stochastic differential equations, enabling full uncertainty estimation without Monte Carlo sampling or MAP approximation, as demonstrated on simulated and 3D image data.
This paper presents a novel mathematical framework for representing uncertainty in large deformation diffeomorphic image registration. The Bayesian posterior distribution over the deformations aligning a moving and a fixed image is approximated via a variational formulation. A stochastic differential equation (SDE) modeling the deformations as the evolution of a time-varying velocity field leads to a prior density over deformations in the form of a Gaussian process. This permits estimating the full posterior distribution in order to represent uncertainty, in contrast to methods in which the posterior is approximated via Monte Carlo sampling or maximized in maximum a-posteriori (MAP) estimation. The frame-work is demonstrated in the case of landmark-based image registration, including simulated data and annotated pre and intra-operative 3D images.