Aligning Fetal Anatomy with Kinematic Tree Log-Euclidean PolyRigid Transforms

TL;DR

This paper introduces a novel differentiable volumetric model for fetal anatomy that ensures anatomical consistency and reduces artifacts, improving registration and segmentation in medical imaging.

Contribution

It proposes the KTPolyRigid transform based on Lie algebra to enhance volumetric modeling of articulated bodies, addressing limitations of existing surface-based methods.

Findings

Fewer folding artifacts in deformation fields.

Improved groupwise image registration.

Enhanced fetal organ segmentation.

Abstract

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.