# Shape of my heart: Cardiac models through learned signed distance functions

arXiv: https://arxiv.org/abs/2308.16568 · HTML: https://mlsanity.com/paper/2308.16568/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 58 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations](https://mlsanity.com/paper/2008.01639/) (2020)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [Deep Level Sets: Implicit Surface Representations for 3D Shape Inference](https://mlsanity.com/paper/1901.06802/) (2019)
- [A Deep-Learning Approach For Direct Whole-Heart Mesh Reconstruction](https://mlsanity.com/paper/2102.07899/) (2021)
- [Cardiac Segmentation with Strong Anatomical Guarantees](https://mlsanity.com/paper/2006.08825/) (2020)
- [Cardiac Segmentation on Late Gadolinium Enhancement MRI: A Benchmark Study from Multi-Sequence Cardiac MR Segmentation Challenge](https://mlsanity.com/paper/2006.12434/) (2020)
- [Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling](https://mlsanity.com/paper/2207.14663/) (2022)
- [Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps](https://mlsanity.com/paper/2201.12362/) (2022)
- [Joint Motion Correction and Super Resolution for Cardiac Segmentation via Latent Optimisation](https://mlsanity.com/paper/2107.03887/) (2021)
- [Gaussian Process Landmarking on Manifolds](https://mlsanity.com/paper/1802.03479/) (2018)
- [A bi-atrial statistical shape model for large-scale in silico studies of human atria: model development and application to ECG simulations](https://mlsanity.com/paper/2102.10838/) (2021)
- [Space-time shape uncertainties in the forward and inverse problem of electrocardiography](https://mlsanity.com/paper/2010.16104/) (2020)

## Built on by (most cited first, 10 of 10)

- [Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiology](https://mlsanity.com/paper/2408.09818/) (2024)
- [A Diffusion Model for Simulation Ready Coronary Anatomy with Morpho-skeletal Control](https://mlsanity.com/paper/2407.15631/) (2024)
- [A Survey of Medical Point Cloud Shape Learning: Registration, Reconstruction and Variation](https://mlsanity.com/paper/2508.03057/) (2025)
- [From 2D to 3D, Deep Learning-based Shape Reconstruction in Magnetic Resonance Imaging: A Review](https://mlsanity.com/paper/2510.01296/) (2025)
- [Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation](https://mlsanity.com/paper/2602.20306/) (2026)
- [MorphiNet: A Graph Subdivision Network for Adaptive Bi-ventricle Surface Reconstruction](https://mlsanity.com/paper/2412.10985/) (2024)
- [PrIntMesh: Precise Intersection Surfaces for 3D Organ Mesh Reconstruction](https://mlsanity.com/paper/2511.16186/) (2025)
- [Learning geometry-dependent lead-field operators for forward ECG modeling](https://mlsanity.com/paper/2602.22367/) (2026)
- [Non-Invasive Reconstruction of Cardiac Activation Dynamics Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.03832/) (2026)
- [Uncertainty Quantification for Cardiac Shape Reconstruction with Deep Signed Distance Functions via MCMC methods](https://mlsanity.com/paper/2605.07987/) (2026)

## Abstract (arXiv)

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM).