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Pairwise-Constrained Implicit Functions for 3D Human Heart Modelling

Hieu Le, Jingyi Xu, Nicolas Talabot, Jiancheng Yang, Pascal Fua

TL;DR

This work tackles the problem of high-fidelity, multi-component 3D heart modeling by introducing pairwise-constrained implicit functions. Each anatomical component is represented by its own SDF, and a sampling-based scheme enforces anatomically accurate contact ratios between neighboring parts, preventing gaps and overlaps in shared walls. The method unifies contact- and distance-based constraints within a single optimization framework and extends naturally to other structures, such as vertebrae, via minimum-distance constraints. Empirical results on cardiac MRI and spine CT data show improved inner-structure accuracy and robust constraint satisfaction compared to single-SDF, UDF-based, and voxel-based baselines. The approach offers a promising path toward high-fidelity, multi-component medical modeling with potential diagnostic and planning applications.

Abstract

Accurate 3D models of the human heart require not only correct outer surfaces but also realistic inner structures, such as the ventricles, atria, and myocardial layers. Approaches relying on implicit surfaces, such as signed distance functions (SDFs), are primarily designed for single watertight surfaces, making them ill-suited for multi-layered anatomical structures. They often produce gaps or overlaps in shared boundaries. Unsigned distance functions (UDFs) can model non-watertight geometries but are harder to optimize, while voxel-based methods are limited in resolution and struggle to produce smooth, anatomically realistic surfaces. We introduce a pairwise-constrained SDF approach that models the heart as a set of interdependent SDFs, each representing a distinct anatomical component. By enforcing proper contact between adjacent SDFs, we ensure that they form anatomically correct shared walls, preserving the internal structure of the heart and preventing overlaps, or unwanted gaps. Our method significantly improves inner structure accuracy over single-SDF, UDF-based, voxel-based, and segmentation-based reconstructions. We further demonstrate its generalizability by applying it to a vertebrae dataset, preventing unwanted contact between structures.

Pairwise-Constrained Implicit Functions for 3D Human Heart Modelling

TL;DR

This work tackles the problem of high-fidelity, multi-component 3D heart modeling by introducing pairwise-constrained implicit functions. Each anatomical component is represented by its own SDF, and a sampling-based scheme enforces anatomically accurate contact ratios between neighboring parts, preventing gaps and overlaps in shared walls. The method unifies contact- and distance-based constraints within a single optimization framework and extends naturally to other structures, such as vertebrae, via minimum-distance constraints. Empirical results on cardiac MRI and spine CT data show improved inner-structure accuracy and robust constraint satisfaction compared to single-SDF, UDF-based, and voxel-based baselines. The approach offers a promising path toward high-fidelity, multi-component medical modeling with potential diagnostic and planning applications.

Abstract

Accurate 3D models of the human heart require not only correct outer surfaces but also realistic inner structures, such as the ventricles, atria, and myocardial layers. Approaches relying on implicit surfaces, such as signed distance functions (SDFs), are primarily designed for single watertight surfaces, making them ill-suited for multi-layered anatomical structures. They often produce gaps or overlaps in shared boundaries. Unsigned distance functions (UDFs) can model non-watertight geometries but are harder to optimize, while voxel-based methods are limited in resolution and struggle to produce smooth, anatomically realistic surfaces. We introduce a pairwise-constrained SDF approach that models the heart as a set of interdependent SDFs, each representing a distinct anatomical component. By enforcing proper contact between adjacent SDFs, we ensure that they form anatomically correct shared walls, preserving the internal structure of the heart and preventing overlaps, or unwanted gaps. Our method significantly improves inner structure accuracy over single-SDF, UDF-based, voxel-based, and segmentation-based reconstructions. We further demonstrate its generalizability by applying it to a vertebrae dataset, preventing unwanted contact between structures.
Paper Structure (14 sections, 7 equations, 2 figures, 4 tables)

This paper contains 14 sections, 7 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Method
  4. Enforcing Correct Shared Surface Areas
  5. Mining Topologically Meaningful Points.
  6. Contact Ratio Loss.
  7. Intersection and data Losses.
  8. Optimization.
  9. Enforcing Minimum Distance Constraints
  10. Experiments
  11. 3D Heart Reconstruction.
  12. 3D Lumbar Spine Segmentation.
  13. Ablation.
  14. Conclusion

Figures (2)

  • Figure 1: The two rows show results from an in-distribution (ID) and an out-of-distribution (OOD) heart sample. We show transparent meshes to highlight contact areas. Red indicates penetration, while green denotes proper shared surfaces.
  • Figure 2: Verterbrae reconstruction. The second row shows zoomed-in crops of the first row. Yellow indicates close but allowable proximity, while green marks undesired contact.