论文标题
随机汉密尔顿系统的扩散桥和形状的演变
Diffusion bridges for stochastic Hamiltonian systems and shape evolutions
论文作者
论文摘要
在形状分析和计算解剖结构中研究了随机发展的几何系统，用于建模人体器官形状的随机发展。形状之间的大地路径的概念对于形状分析至关重要，并且在随机环境中具有扩散桥的自然概括。这种桥梁的模拟是解决形状分析中的推理和注册问题的关键。我们演示了如何将最新的扩散桥模拟方法应用于最近引入随机形状变形模型，从而实质上扩展了此类模型的适用性。我们通过从观察到的形状配置中估算模板形状的同时学习模型参数来体现这些方法。
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a natural generalisation as diffusion bridges in a stochastic setting. Simulation of such bridges is key to solve inference and registration problems in shape analysis. We demonstrate how to apply state-of-the-art diffusion bridge simulation methods to recently introduced stochastic shape deformation models thereby substantially expanding the applicability of such models. We exemplify these methods by estimating template shapes from observed shape configurations while simultaneously learning model parameters.
