LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics
This work addresses domain uncertainty quantification in hemodynamics for cardiovascular researchers, providing a method to generate realistic 3D shapes and perturbations, though it is incremental as it builds on existing LDDMM-based registration approaches.
The authors tackled the problem of generating realistic 3D biomedical shapes for uncertainty quantification by introducing a conditional stochastic interpolant framework that builds on LDDMM-based registration to learn conditional drifts between geometries. They demonstrated the method's effectiveness by generating aortic shapes from patient data and enabling both data augmentation and controlled random perturbations for quantifying domain uncertainties in cardiovascular simulations.
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.