A multilevel Markov Chain Monte Carlo approach for uncertainty quantification in deformable registration

Image guided diagnostics and therapy comprise decisions concerning treatment and intervention based on registered image data of patients in many clinical settings. Therefore, knowledge about the reliability of the registration result is crucial. In this paper, we tackle this issue by estimating the registration uncertainty based on Bayesian analysis, i.e. examining the posterior distribution of parameters describing the underlying transformations. The intractability of posterior distributions allows only an approximation, usually realized by Monte Carlo sampling methods. Conventional Markov Chain Monte Carlo (MCMC) algorithms require a large number of posterior samples to ensure robust estimates, which inflicts a high computational burden. The contribution of this work is the embedding of the MCMC approach into a cost reducing multilevel framework. Multilevel MCMC fits into the multi-resolution framework usually applied for image registration. In this work we evaluate the performance of our method using a B-spline transformation framework, i.e. the B-spline coefficients are the parameters to estimate. We demonstrate its correctness by comparison with a ground-truth of the posterior distribution, evaluate the efficiency through examination of the cost reduction and show the reliability as uncertainty estimator on brain MRI images.