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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

TL;DR

A differentiable volumetric body model based on the Skinned Multi-Person Linear formulation, driven by a new Kinematic Tree-based Log-Euclidean PolyRigid (KTPolyRigid) transform, that provides a robust foundation for standardized volumetric analysis of articulated bodies in medical imaging.

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.

Aligning Fetal Anatomy with Kinematic Tree Log-Euclidean PolyRigid Transforms

TL;DR

A differentiable volumetric body model based on the Skinned Multi-Person Linear formulation, driven by a new Kinematic Tree-based Log-Euclidean PolyRigid (KTPolyRigid) transform, that provides a robust foundation for standardized volumetric analysis of articulated bodies in medical imaging.

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.
Paper Structure (16 sections, 5 equations, 4 figures, 1 table)

This paper contains 16 sections, 5 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. SMPL Model.
  4. From Images to a Canonical Shape Model.
  5. Kinematic Tree Log-Euclidean PolyRigid Transform $\Phi_T$.
  6. Flow-Based Diffeomorphic Mapping $\Phi_P$.
  7. Groupwise Registration and Template-Based Segmentation.
  8. Experimental Results
  9. Data.
  10. Baseline Methods.
  11. Canonical Image $\tilde{I}_s$ Visualization.
  12. Deformation Field $\Phi_T$ Evaluation.
  13. Groupwise Image Registration.
  14. Fetal Lung Segmentation.
  15. Conclusion
  16. ...and 1 more sections

Figures (4)

  • 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. \ref{['fig:exp-1']}.
  • Figure 4: Population-level mean image $\bar{J}$.