Aligning Fetal Anatomy with Kinematic Tree Log-Euclidean PolyRigid Transforms

Yingcheng Liu; Athena Taymourtash; Yang Liu; Esra Abaci Turk; William M. Wells; Leo Joskowicz; P. Ellen Grant; Polina Golland

cs.CVMar 2, 2026

Aligning Fetal Anatomy with Kinematic Tree Log-Euclidean PolyRigid Transforms

Authors: Yingcheng Liu, Athena Taymourtash, Yang Liu, Esra Abaci Turk, William M. Wells, Leo Joskowicz, P. Ellen Grant, Polina Golland

Organizations: Computer Science and Artificial Intelligence Lab, MIT, Cambridge, USA · California Institute of Technology, Pasadena, USA · Boston Children’s Hospital and Harvard Medical School, Boston, USA · The Hebrew University of Jerusalem, Jerusalem, Israel

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.

Figures & tables

Figure 1: Method overview. KTPolyRigid $\Phi_{T}$ flattens the fetal body into a canonical T-pose. The flow-based mapping $\Phi_{P}$ further standardizes the body shape to the population mean $\bar{V}$ . Averaging the population-level canonical images $J_{s}$ produces a population mean image $\bar{J}$ . Groupwise registration optimizes the body pose $\theta$ to minimize image variance across subjects. Segmentation is achieved by total transformation $\Phi=\Phi_{T}\circ\Phi_{P}$ .

Figure 2: Example canonical image $\tilde{I}_{s}$ of a subject $s$ . Left three panels: Three coronal cross-sections (full and zoomed-in views). Right panel: mid-sagittal cross-section.

Figure 3: Local distortions. Spatial log determinant Jacobian field $\log_{2}\det\left[\partial_{x}\Phi_{T}(x)\right]$ of the deformation $\Phi_{T}$ for subject in Fig. 2 .

Method	% folds ( $\downarrow$ )	$\mathbf{STD\log_{2}\|\det J\|}$ ( $\downarrow$ )	GPU Time (ms, $\downarrow$ )	GPU Mem. (MB, $\downarrow$ )
LBS	$1.88\pm 0.57$	$0.89\pm 0.08$	$0.33\pm 0.03$	$24.27\pm 0.95$
PolyRigid [ 2 ]	$5.37\pm 3.85$	$0.90\pm 0.18$	$93.50\pm 6.13$	$3332\pm 129$
KTPolyRigid (ours)	$1.38\pm 0.40$	$0.74\pm 0.06$	$31.19\pm 2.69$	$1551\pm 66$

Table 1: Deformation field statistics. Mean

\pm

standard deviation are reported. (

\downarrow

) indicates that lower values represent better performance.

Figure 4: Population-level mean image $\bar{J}$ .

Fetal MRI

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

Athena Taymourtash, S. Mazdak Abulnaga, Esra Abaci Turk, P. Ellen Grant+1

MIT Computer Science and Artificial Intelligence Laboratory · Massachusetts General Hospital, Harvard Medical School · Boston Children’s Hospital, Harvard Medical School

Medical Image Analysis Medical Image Registration Deformable Image Registration Implicit Neural Representations

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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.

Abstract

Fetal MRI

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