Automated analysis of articulated bodies is crucial in medical imaging. Existing surface-based models often ignore internal volumetric structures and rely on deformation methods that lack anatomical consistency guarantees. To address this problem, we introduce a differentiable volumetric body model based on the Skinned Multi-Person Linear (SMPL) formulation, driven by a new Kinematic Tree-based Log-Euclidean PolyRigid (KTPolyRigid) transform. KTPolyRigid resolves Lie algebra ambiguities associated with large, non-local articulated motions, and encourages smooth, bijective volumetric mappings. Evaluated on 53 fetal MRI volumes, KTPolyRigid yields deformation fields with significantly fewer folding artifacts. Furthermore, our framework enables robust groupwise image registration and a label-efficient, template-based segmentation of fetal organs. It provides a robust foundation for standardized volumetric analysis of articulated bodies in medical imaging.

翻译：在医学影像中，关节化躯体的自动分析至关重要。现有的基于表面的模型通常忽略内部体积结构，并依赖于缺乏解剖一致性保证的变形方法。为解决此问题，我们引入了一种基于蒙皮多人线性（SMPL）公式的可微分体积躯体模型，该模型由一种新的基于运动树的对数欧几里得多刚体（KTPolyRigid）变换驱动。KTPolyRigid解决了与大规模、非局部关节运动相关的李代数歧义，并促进了平滑、双射的体积映射。在53个胎儿MRI体积数据上的评估表明，KTPolyRigid产生的变形场具有显著更少的折叠伪影。此外，我们的框架实现了鲁棒的群体图像配准以及一种标签高效、基于模板的胎儿器官分割方法。它为医学影像中关节化躯体的标准化体积分析提供了一个鲁棒的基础。