Bayesian Atlas Building with Hierarchical Priors for Subject-specific Regularization

Abstract: This paper presents a novel hierarchical Bayesian model for unbiased atlas building with subject-specific regularizations of image registration. We develop an atlas construction process that automatically selects parameters to control the smoothness of diffeomorphic transformation according to individual image data. To achieve this, we introduce a hierarchical prior distribution on regularization parameters that allows multiple penalties on images with various degrees of geometric transformations. We then treat the regularization parameters as latent variables and integrate them out from the model by using the Monte Carlo Expectation Maximization (MCEM) algorithm. Another advantage of our algorithm is that it eliminates the need for manual parameter tuning, which can be tedious and infeasible. We demonstrate the effectiveness of our model on 3D brain MR images. Experimental results show that our model provides a sharper atlas compared to the current atlas building algorithms with single-penalty regularizations. Our code is publicly available at https://github.com/jw4hv/HierarchicalBayesianAtlasBuild.