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

TL;DR

This paper presents a novel implicit neural model that ensures volumetric consistency and diffeomorphic deformations for placenta MRI registration, enabling accurate, topologically consistent group analysis.

Contribution

It introduces a volumetrically consistent implicit model combining SDF reconstruction with neural diffeomorphic flow for placenta MRI registration, improving interior deformation modeling.

Findings

Enhanced geometric fidelity over surface-based methods

Achieved topologically consistent flattening of placentas

Enabled voxel-wise intensity mapping in a canonical space

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.