Projective LDDMM: Mapping Molecular Digital Pathology with Tissue MRI

Abstract

Reconstructing dense 3D anatomical coordinates from 2D projective measurements has become a central problem in digital pathology for both animal models and human studies. We describe a new family of diffeomorphic mapping technologies called Projective LDDMM which generate diffeomorphic mappings of dense human MRI atlases at tissue scales onto sparse measurements at micron scales associated with histological and more general optical imaging modalities. We solve the problem of dense mapping surjectively onto histological sections by incorporating new technologies for crossing modalities that use non-linear scattering transforms to represent multiple radiomic-like textures at micron scales and incorporating a Gaussian mixture-model frame-work for modelling tears and distortions associated to each section. We highlight the significance of our method through incorporation of neuropathological measures and MRI, as relevant to the development of biomarkers for Alzheimers disease and one instance of the integration of imaging data across the scales of clinical imaging and digital pathology.