BridgeUQ: Bayesian Aleatoric Uncertainty Quantification For Time-Series Image Registration via Brownian Bridge Prior

This paper presents \em BridgeUQ, a novel Bayesian framework for aleatoric uncertainty quantification in pretrained deterministic registration models. In contrast to previous approaches that mainly focus on pairwise registration, our work is the first to model posterior uncertainty over spatiotemporal deformation trajectories that captures the intrinsic ambiguity of registration solutions across both space and time. To achieve this, we first introduce a novel hierarchical Gaussian process prior in the temporal deformation space, based on a Brownian bridge formulation with an inverse-Gamma hyper prior on the diffusion variance, to govern stochastic sampling around the predicted registration solution. We then define an energy-based likelihood function derived from the pretrained registration objective to ensure the sampled deformations remain faithful to the observed data. To facilitate efficient inference, we further develop an amortized maximum-a-posterior (MAP) scheme combined with conditional diffusion sampling to approximate this resulting posterior. It is important to note that BridgeUQ is a plug-and-play module that can be seamlessly integrated with arbitrary pretrained registration models without retraining. We validate BridgeUQ on widely used registration networks using comprehensive cardiac and brain magnetic resonance imaging datasets. Experimental results show that our approach is able to produce anatomically meaningful uncertainty estimates for a variety of learning-based registration models. The proposed BridgeUQ provides a practical and principled pathway toward uncertainty-aware and safety-critical medical image registration.