The uncertainty in registration of medical images may contain important information in cases where clinical decisions are based on registered data. Posing the registration problem in a Bayesian framework allows characterization of the posterior distribution of the deformation parameters which represents the uncertainty of the registration. Uncertainty estimation approaches are complicated by the need to specify the values of hyper-parameters (HPs) of the underlying registration model, e.g. the regularization weight (tissue stiffness) and image noise variance, which have a significant effect on the shape of the posterior distribution. However, it is difficult to assign these HPs physical meaningful values and they are often specified on an ad-hoc basis. In a Bayesian framework, the marginalization of HPs under a suitable prior distribution is a principled alternative to manually tuning the HP values. This paper presents a fast method for marginalizing the HPs of an elastic registration model using local Laplace approximations. We show the feasibility and the advantage of this method in terms of robustness and convergence speed compared to alternative approaches on a clinical image data-set.
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