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.

翻译：我们提出了一种新颖的条件随机插值器框架，用于三维形状的生成式建模。该方法基于近期基于LDDMM的配准方法，学习几何体之间的条件漂移。通过利用由此产生的拉回和推前算子，我们将此公式从标准笛卡尔网格扩展到复杂形状及定义在不同域上的随机变量。我们展示了该方法在心血管模拟中的应用，其中主动脉形状基于初始患者队列生成。条件变量为由一组中心线点及其对应的内切球半径定义的潜在几何表示。该框架既促进了三维生物医学形状的数据扩充，也支持对给定形状生成可控幅度的随机扰动。这些能力对于量化医学图像分割引起的领域不确定性对相关生物标志物估计的影响至关重要。