# HeartVolMesh: Cardiac Volumetric Mesh Reconstruction via Covariance-Guided Graph Deformation

arXiv: https://arxiv.org/abs/2607.04243 · HTML: https://mlsanity.com/paper/2607.04243/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Voxel2Mesh: 3D Mesh Model Generation from Volumetric Data](https://mlsanity.com/paper/1912.03681/) (2019)
- [A Deep-Learning Approach For Direct Whole-Heart Mesh Reconstruction](https://mlsanity.com/paper/2102.07899/) (2021)
- [Learning Whole Heart Mesh Generation From Patient Images For Computational Simulations](https://mlsanity.com/paper/2203.10517/) (2022)
- [A Generative Shape Compositional Framework to Synthesise Populations of Virtual Chimaeras](https://mlsanity.com/paper/2210.01607/) (2022)
- [From Pixels to Polygons: A Survey of Deep Learning Approaches for Medical Image-to-Mesh Reconstruction](https://mlsanity.com/paper/2505.03599/) (2025)

## Abstract (arXiv)

Accurate patient-specific tetrahedral cardiac meshes are essential for in-silico trials, yet common segmentation-then-modelling pipelines can blur thin-wall anatomy and offer limited cross-case correspondence. We propose HeartVolMesh, which lifts each template vertex to an anisotropic Gaussian kernel and uses a 3D CNN-GNN to predict per-vertex displacements and Cholesky-parameterized covariances from volumetric images. Training is guided by a covariance-aware negative log-likelihood loss with lightweight mesh regularization. For volumetric meshing, we warp a fixed tetrahedral template to the reconstructed surface via staged alignment, non-rigid registration, and deformation propagation, preserving connectivity and correspondence by construction, with resolution controlled by template density. Experiments show consistent gains over deformation-based baselines in surface mesh accuracy and volumetric mesh fidelity.