Local image registration uncertainty estimation using polynomial chaos expansions

Most image registration methods involve multiple user-defined tuning parameters, such as regularization weights and smoothing parameters. Changing these tuning parameters leads to differences in the local deformation estimates that result from the registration algorithm. Uncertainty in the optimal value of the tuning parameters thus leads to uncertainty in the local deformation estimates. In this work, we propose a method to quantify this uncertainty using an efficient surrogate modeling approach based on polynomial chaos expansion. Given a specified distribution on each input tuning parameter, this approach requires only a few image registration runs to characterize the distribution of output deformation estimates at each voxel. In experiments on liver CT images, we evaluate the accuracy of the uncertainty estimate by comparing with a brute force Monte Carlo estimate. The results show that there is a negligible difference between estimates of Monte-Carlo simulation and the proposed method. The proposed method thus provides a good indication of the uncertainty in local deformation estimates due to uncertainty in the optimal setting of tuning parameters.