Establishing dense volumetric correspondences across anatomical shapes is essential for group-level analysis but remains challenging for implicit neural representations. Most existing implicit registration methods rely on supervision near the zero-level set and thus capture only surface correspondences, leaving interior deformations under-constrained. We introduce a volumetrically consistent implicit model that couples reconstruction of signed distance functions (SDFs) with neural diffeomorphic flow to learn a shared canonical template of the placenta. Volumetric regularization, including Jacobian-determinant and biharmonic penalties, suppresses local folding and promotes globally coherent deformations. In the motivating application to placenta MRI, our formulation jointly reconstructs individual placentas, aligns them to a population-derived implicit template, and enables voxel-wise intensity mapping in a unified canonical space. Experiments on in-vivo placenta MRI scans demonstrate improved geometric fidelity and volumetric alignment over surface-based implicit baseline methods, yielding anatomically interpretable and topologically consistent flattening suitable for group analysis.

翻译：在解剖形状间建立密集的体积对应关系对于群体水平分析至关重要，但对于隐式神经表示而言仍然具有挑战性。大多数现有的隐式配准方法依赖于零水平集附近的监督，因此仅捕获表面对应关系，导致内部变形约束不足。我们提出了一种体积一致性的隐式模型，该模型将符号距离函数（SDFs）的重建与神经微分同胚流耦合，以学习一个共享的胎盘规范模板。体积正则化，包括雅可比行列式和双调和惩罚项，抑制了局部折叠并促进了全局一致的变形。在胎盘MRI这一应用场景中，我们的方法联合重建了个体胎盘，将它们对齐到一个群体衍生的隐式模板，并在统一的规范空间中实现了体素级的强度映射。在活体胎盘MRI扫描上的实验表明，相较于基于表面的隐式基线方法，我们的方法在几何保真度和体积对齐方面均有提升，产生了适用于群体分析的、解剖学上可解释且拓扑一致的扁平化结果。