Projective Diffeomorphic Mapping of Molecular Digital Pathology with Tissue MRI

Reconstructing dense 3D anatomical coordinates from 2D projective measurements has become a central problem in digital pathology for both animal models and human studies. Here we describe Projective Large Deformation Diffeomorphic Metric Mapping (LDDMM), a technique which projects diffeomorphic mappings of dense human magnetic resonance imaging (MRI) atlases at tissue scales onto sparse measurements at micrometre scales associated with histological and more general optical imaging modalities. We solve the problem of dense mapping surjectively onto histological sections by incorporating technologies for crossing modalities that use nonlinear scattering transforms to represent multiple radiomic-like textures at micron scales, together with a Gaussian mixture-model framework for modelling tears and distortions associated to each section. We highlight the significance of our method through incorporation of neuropathological measures and MRI, of relevance to the development of biomarkers for Alzheimer's disease and one instance of the integration of imaging data across the scales of clinical imaging and digital pathology.