  This paper presents a variational framework for dense diffeomorphic
atlas-mapping onto high-throughput histology stacks at the 20 um meso-scale.
The observed sections are modelled as Gaussian random fields conditioned on a
sequence of unknown section by section rigid motions and unknown diffeomorphic
transformation of a three-dimensional atlas. To regularize over the
high-dimensionality of our parameter space (which is a product space of the
rigid motion dimensions and the diffeomorphism dimensions), the histology
stacks are modelled as arising from a first order Sobolev space smoothness
prior. We show that the joint maximum a-posteriori, penalized-likelihood
estimator of our high dimensional parameter space emerges as a joint
optimization interleaving rigid motion estimation for histology restacking and
large deformation diffeomorphic metric mapping to atlas coordinates. We show
that joint optimization in this parameter space solves the classical curvature
non-identifiability of the histology stacking problem. The algorithms are
demonstrated on a collection of whole-brain histological image stacks from the
Mouse Brain Architecture Project.
