Diffeomorphic Registration With Intensity Transformation and Missing Data: Application to 3D Digital Pathology of Alzheimer's Disease

Abstract

This paper examines the problem of diffeomorphic image registration in the presence of differing image intensity profiles and sparsely sampled, missing, or damaged tissue. Our motivation comes from the problem of aligning 3D brain MRI with 100-micron isotropic resolution to histology sections at 1 × 1 × 1,000-micron resolution with multiple varying stains. We pose registration as a penalized Bayesian estimation, exploiting statistical models of image formation where the target images are modeled as sparse and noisy observations of the atlas. In this injective setting, there is no assumption of symmetry between atlas and target. Cross-modality image matching is achieved by jointly estimating polynomial transformations of the atlas intensity. Missing data is accommodated via a multiple atlas selection procedure where several atlas images may be of homogeneous intensity and correspond to “background” or “artifact.” The two concepts are combined within an Expectation-Maximization algorithm, where atlas selection posteriors and deformation parameters are updated iteratively and polynomial coefficients are computed in closed form. We validate our method with simulated images, examples from neuropathology, and a standard benchmarking dataset. Finally, we apply it to reconstructing digital pathology and MRI in standard atlas coordinates. By using a standard convolutional neural network to detect tau tangles in histology slices, this registration method enabled us to quantify the 3D density distribution of tauopathy throughout the medial temporal lobe of an Alzheimer's disease postmortem specimen.