  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.
