Parameter sensitivity analysis in medical image registration algorithms using polynomial chaos expansions

Medical image registration algorithms typically involve numerous user-defined ‘tuning’ parameters, such as regularization weights, smoothing parameters, etc. Their optimal settings depend on the anatomical regions of interest, image modalities, image acquisition settings, the expected severity of deformations, and the clinical requirements. Within a particular application, the optimal settings could even vary across the image pairs to be registered. It is, therefore, crucial to develop methods that provide insight into the effect of each tuning parameter in interaction with the other tuning parameters and allow a user to efficiently identify optimal parameter settings for a given pair of images. An exhaustive search over all possible parameter settings has obvious disadvantages in terms of computational costs and quickly becomes infeasible in practice when the number of tuning parameters increases, due to the curse of dimensionality. In this study, we propose a method based on Polynomial Chaos Expansions (PCE). PCE is a method for sensitivity analysis that approximates the model of interest (in our case the registration of a given pair of images) by a polynomial expansion which can be evaluated very efficiently. PCE renders this approach feasible for a large number of input parameters, by requiring only a modest number of function evaluations for model construction. Once the PCE has been constructed, the sensitivity of the registration results to changes in the parameters can be quantified, and the user can simulate registration results for any combination of input parameters in real-time. The proposed approach is evaluated on 8 pairs of liver CT scans and the results indicate that PCE is a promising method for parameter sensitivity analysis in medical image registration.