Point-Based Shape Representation Generation with a Correspondence-Preserving Diffusion Model

We propose a diffusion model designed to generate point-based shape representations with correspondences. Traditional statistical shape models have considered point correspondences extensively, but current deep learning methods do not take them into account, focusing on unordered point clouds instead. Current deep generative models for point clouds do not address generating shapes with point correspondences between generated shapes. This work aims to formulate a diffusion model that is capable of generating realistic point-based shape representations, which preserve point correspondences that are present in the training data. Using shape representation data with correspondences derived from Open Access Series of Imaging Studies 3 (OASIS-3), we demonstrate that our correspondence-preserving model effectively generates point-based hippocampal shape representations that are highly realistic compared to existing methods. We further demonstrate the applications of our generative model by downstream tasks, such as conditional generation of healthy and AD subjects and predicting morphological changes of disease progression by counterfactual generation.

Quantifying Hippocampal Shape Asymmetry in Alzheimer's Disease Using Optimal Shape Correspondences

Hippocampal atrophy in Alzheimer's disease (AD) is asymmetric and spatially inhomogeneous. While extensive work has been done on volume and shape analysis of atrophy of the hippocampus in AD, less attention has been given to hippocampal asymmetry specifically. Previous studies of hippocampal asymmetry are limited to global volume or shape measures, which don't localize shape asymmetry at the point level. In this paper, we propose to quantify localized shape asymmetry by optimizing point correspondences between left and right hippocampi within a subject, while simultaneously favoring a compact statistical shape model of the entire sample. To account for related variables that have impact on AD and healthy subject differences, we build linear models with other confounding factors. Our results on the OASIS3 dataset demonstrate that compared to using volumetric information, shape asymmetry reveals fine-grained, localized differences that indicate the hippocampal regions of most significant shape asymmetry in AD patients.