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

2026-03-16

AI Summary

This work addresses the limitation of existing implicit registration methods, which are confined to regions near the zero-level set and struggle to achieve voxel-wise deformation correspondence within placental MRI volumes. To overcome this, the authors propose a novel framework that jointly learns signed distance functions and neural diffeomorphic flows to construct a shared implicit placental template. For the first time in implicit representations, a voxel consistency constraint is introduced. By integrating Jacobian determinant constraints with a biharmonic regularizer, the method guarantees fold-free deformations while preserving global geometric and topological consistency. Experiments on in vivo placental MRI data demonstrate that the approach significantly outperforms surface-based baselines, achieving high-fidelity geometric reconstruction, precise voxel alignment, and enabling anatomically interpretable population-level analysis.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Medical and Biological Imaging
• Intelligent Robots: Localization, Mapping, and Navigation

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• volumetric correspondence
• implicit neural representation
• placenta MRI
• anatomical shape alignment
• group-level analysis

Innovation

• neural diffeomorphic flow
• volumetric consistency
• implicit atlas learning
• signed distance function
• Jacobian-determinant regularization