Volumetrically Consistent Implicit Atlas Learning via Neural Diffeomorphic Flow for Placenta MRI

Abstract

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.

Figures (10)

• Figure 1: Method overview. The warping function transforms point samples of shape $i$ to their canonical positions, which are then mapped to SDF values by the implicit template.
• Figure 2: Distribution of discrete Laplacian energy $\|L u\|_2^2$ of vertex displacements across subjects. Lower values correspond to smoother deformation fields.
• Figure 3: Dense pointwise correspondences via the learned implicit template. (a) Two subject instances mapped to the canonical template through the diffeomorphic flow. (b) ACVD‐remeshed surfaces (5 k vertices) with vertex colors propagated from the template. Consistent colors across subjects visually demonstrate stable, smooth correspondences.
• Figure 4: Pose‐invariant flattening and intensity mapping across two maternal positions of the same subject. The placenta in each position is mapped diffeomorphically to the canonical template via $\Phi(\cdot;c_i)$ and $\Phi(\cdot;c_j)$, producing consistent, topology‐preserving flattened intensity maps.
• Figure 5: Volumetric flattening. Given the same tetrahedral placenta mesh (upper left panel), our method produces a coherent, uniformly compressed volumetric flattening. DIT and NDF maintain surface alignment but distort the interior, exhibiting radial compression and anisotropic stretching of tetrahedra toward a mid-surface layer.