# Explicit Differentiable Slicing and Global Deformation for Cardiac Mesh Reconstruction

arXiv: https://arxiv.org/abs/2409.02070 · HTML: https://mlsanity.com/paper/2409.02070/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 73 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Michelangelo: Conditional 3D Shape Generation based on Shape-Image-Text Aligned Latent Representation](https://mlsanity.com/paper/2306.17115/) (2023)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [U-Net and its variants for medical image segmentation: theory and applications](https://mlsanity.com/paper/2011.01118/) (2020)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Evaluation of Algorithms for Multi-Modality Whole Heart Segmentation: An Open-Access Grand Challenge](https://mlsanity.com/paper/1902.07880/) (2019)
- [A Deep-Learning Approach For Direct Whole-Heart Mesh Reconstruction](https://mlsanity.com/paper/2102.07899/) (2021)
- [Abdominal multi-organ segmentation with organ-attention networks and statistical fusion](https://mlsanity.com/paper/1804.08414/) (2018)
- [Multi-class point cloud completion networks for 3D cardiac anatomy reconstruction from cine magnetic resonance images](https://mlsanity.com/paper/2307.08535/) (2023)
- [DeepMesh: Mesh-based Cardiac Motion Tracking using Deep Learning](https://mlsanity.com/paper/2309.14306/) (2023)
- [Automatically Segmenting the Left Atrium from Cardiac Images Using Successive 3D U-Nets and a Contour Loss](https://mlsanity.com/paper/1812.02518/) (2018)
- [LinFlo-Net: A two-stage deep learning method to generate simulation ready meshes of the heart](https://mlsanity.com/paper/2310.20065/) (2023)
- [Anatomy-Aware Cardiac Motion Estimation](https://mlsanity.com/paper/2008.07579/) (2020)
- [CNN-based Cardiac Motion Extraction to Generate Deformable Geometric Left Ventricle Myocardial Models from Cine MRI](https://mlsanity.com/paper/2103.16695/) (2021)
- [Deep Mesh Prior: Unsupervised Mesh Restoration using Graph Convolutional Networks](https://mlsanity.com/paper/2107.02909/) (2021)
- [Intensity-based 3D motion correction for cardiac MR images](https://mlsanity.com/paper/2404.00767/) (2024)

## Built on by (most cited first, 8 of 8)

- [From Pixels to Polygons: A Survey of Deep Learning Approaches for Medical Image-to-Mesh Reconstruction](https://mlsanity.com/paper/2505.03599/) (2025)
- [Two-Stage Generative Model for Intracranial Aneurysm Meshes with Morphological Marker Conditioning](https://mlsanity.com/paper/2505.10407/) (2025)
- [IMC-PINN-FE: A Physics-Informed Neural Network for Patient-Specific Left Ventricular Finite Element Modeling with Image Motion Consistency and Biomechanical Parameter Estimation](https://mlsanity.com/paper/2506.20696/) (2025)
- [Real-Time Pulsatile Flow Prediction for Realistic, Diverse Intracranial Aneurysm Morphologies using a Graph Transformer and Steady-Flow Data Augmentation](https://mlsanity.com/paper/2601.19876/) (2026)
- [Learning to Beat: Phenotype-Guided Latent Flow with Regional Motion Priors for Biventricular Motion Synthesis](https://mlsanity.com/paper/2608.19738/) (2026)
- [MRI-Guided Reslice-Refined Cross-Slice SDF Reconstruction of the Left Ventricle from Cardiac MRI with Sparse Axial Supervision](https://mlsanity.com/paper/2609.08148/) (2026)
- [Anatomy-Aligned Surface Field Learning for Myocardial Reconstruction from Sparse Short-Axis Cine MRI](https://mlsanity.com/paper/2609.29825/) (2026)
- [Local2Mesh: Spatially Localized Contour-to-Mesh for Left Ventricular Reconstruction from Sparse 2D Cardiac MRI](https://mlsanity.com/paper/2610.06052/) (2026)

## Abstract (arXiv)

Mesh reconstruction of the cardiac anatomy from medical images is useful for shape and motion measurements and biophysics simulations to facilitate the assessment of cardiac function and health. However, 3D medical images are often acquired as 2D slices that are sparsely sampled and noisy, and mesh reconstruction on such data is a challenging task. Traditional voxel-based approaches rely on pre- and post-processing that compromises image fidelity, while mesh-level deep learning approaches require mesh annotations that are difficult to get. Therefore, direct cross-domain supervision from 2D images to meshes is a key technique for advancing 3D learning in medical imaging, but it has not been well-developed. While there have been attempts to approximate the optimized meshes' slicing, few existing methods directly use 2D slices to supervise mesh reconstruction in a differentiable manner. Here, we propose a novel explicit differentiable voxelization and slicing (DVS) algorithm that allows gradient backpropagation to a mesh from its slices, facilitating refined mesh optimization directly supervised by the losses defined on 2D images. Further, we propose an innovative framework for extracting patient-specific left ventricle (LV) meshes from medical images by coupling DVS with a graph harmonic deformation (GHD) mesh morphing descriptor of cardiac shape that naturally preserves mesh quality and smoothness during optimization. Experimental results demonstrate that our method achieves state-of-the-art performance in cardiac mesh reconstruction tasks from CT and MRI, with an overall Dice score of 90% on multi-datasets, outperforming existing approaches. The proposed method can further quantify clinically useful parameters such as ejection fraction and global myocardial strains, closely matching the ground truth and surpassing the traditional voxel-based approach in sparse images.