Bayesian atlas estimation from high angular resolution diffusion imaging (HARDI)

Abstract

We present a Bayesian probabilistic model to estimate the atlas of the brain white matter characterized by orientation distribution functions (ODFs) derived from HARDI. We employ the framework of large deformation diffeomorphic metric mapping and assume that the HARDI atlas is generated from a known hyperatlas through a flow of diffeomorphisms. We represent the shape prior of the HARDI atlas and the diffeomorphic transformation of individual observations relative to the atlas using centered Gaussian random fields (GRF). We then assume that the observed ODFs are generated by an exponential map of random tangent vectors at the deformed atlas ODF and model the likelihood of the ODFs using a GRF of their tangent vectors in the ODF Riemannian manifold. We solve for the maximum a posteriori using the Expectation-Maximization (EM) algorithm. We illustrate the HARDI atlas constructed based on a cohort of 40 normal adults and empirically demonstrate the convergence of this EM atlas generation algorithm and effects of the hyperatlas on the estimated HARDI atlas. © 2013 Springer-Verlag.