  Nonlinear registration of 2D histological sections with corresponding slices
of MRI data is a critical step of 3D histology reconstruction. This task is
difficult due to the large differences in image contrast and resolution, as
well as the complex nonrigid distortions produced when sectioning the sample
and mounting it on the glass slide. It has been shown in brain MRI registration
that better spatial alignment across modalities can be obtained by synthesizing
one modality from the other and then using intra-modality registration metrics,
rather than by using mutual information (MI) as metric. However, such an
approach typically requires a database of aligned images from the two
modalities, which is very difficult to obtain for histology/MRI.
  Here, we overcome this limitation with a probabilistic method that
simultaneously solves for registration and synthesis directly on the target
images, without any training data. In our model, the MRI slice is assumed to be
a contrast-warped, spatially deformed version of the histological section. We
use approximate Bayesian inference to iteratively refine the probabilistic
estimate of the synthesis and the registration, while accounting for each
other's uncertainty. Moreover, manually placed landmarks can be seamlessly
integrated in the framework for increased performance.
  Experiments on a synthetic dataset show that, compared with MI, the proposed
method makes it possible to use a much more flexible deformation model in the
registration to improve its accuracy, without compromising robustness.
Moreover, our framework also exploits information in manually placed landmarks
more efficiently than MI, since landmarks inform both synthesis and
registration - as opposed to registration alone. Finally, we show qualitative
results on the public Allen atlas, in which the proposed method provides a
clear improvement over MI based registration.
