基于形状注册的随机插值方法，用于心血管模拟中的不确定性量化
LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics
- 用中心线点和内切球半径作为条件变量生成三维血管形状
- 可生成可控幅度的随机形变，支持生物医学数据增强
- 适用于医学图像分割误差引发的模拟不确定性分析
我们提出一种新型条件随机插值框架，用于三维形状的生成建模。该方法基于最近的LDDMM配准技术，学习几何体之间的条件漂移。通过利用所得的拉回与推前算子，将该公式扩展至复杂形状及定义在不同域上的随机变量。我们在心血管模拟中进行了应用，从一组患者初始数据生成主动脉形状。条件变量由一组中心线点及其对应内切球半径构成的隐式几何表示。该方法既支持三维生物医学形状的数据增强，也能为给定形状生成可控幅度的随机扰动，对量化医学图像分割引起的域不确定性在关键生物标志物估计中的影响至关重要。
原文摘要 · Abstract (English)
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.
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