LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics

TL;DR

This paper presents a new stochastic interpolant framework based on LDDMM for generating and perturbing 3D shapes, aiding in quantifying domain uncertainties in cardiovascular modeling.

Contribution

It extends LDDMM registration to complex shapes and random variables, enabling data augmentation and controlled shape perturbations for biomedical applications.

Findings

Generated realistic aortic shape variations from patient data.

Facilitated uncertainty quantification in cardiovascular biomarker estimation.

Extended LDDMM methods to non-Cartesian, domain-specific geometries.

Abstract

We introduce a novel conditional stochastic interpolant framework for generative modeling of three-dimensional shapes. The method builds on a recent LDDMM-based registration approach to learn the conditional drift between geometries. By leveraging the resulting pull-back and push-forward operators, we extend this formulation beyond standard Cartesian grids to complex shapes and random variables defined on distinct domains. We present an application in the context of cardiovascular simulations, where aortic shapes are generated from an initial cohort of patients. The conditioning variable is a latent geometric representation defined by a set of centerline points and the radii of the corresponding inscribed spheres. This methodology facilitates both data augmentation for three-dimensional biomedical shapes, and the generation of random perturbations of controlled magnitude for a given shape. These capabilities are essential for quantifying the impact of domain uncertainties arising from medical image segmentation on the estimation of relevant biomarkers.