# Uncertainty Quantification for Cardiac Shape Reconstruction with Deep Signed Distance Functions via MCMC methods

arXiv: https://arxiv.org/abs/2605.07987 · HTML: https://mlsanity.com/paper/2605.07987/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 19 of 19)

- [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)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [DeepSSM: A Deep Learning Framework for Statistical Shape Modeling from Raw Images](https://mlsanity.com/paper/1810.00111/) (2018)
- [Uncertain-DeepSSM: From Images to Probabilistic Shape Models](https://mlsanity.com/paper/2007.06516/) (2020)
- [UncertaINR: Uncertainty Quantification of End-to-End Implicit Neural Representations for Computed Tomography](https://mlsanity.com/paper/2202.10847/) (2022)
- [A personalized time-resolved 3D mesh generative model for unveiling normal heart dynamics](https://mlsanity.com/paper/2409.13825/) (2024)
- [From Images to Probabilistic Anatomical Shapes: A Deep Variational Bottleneck Approach](https://mlsanity.com/paper/2205.06862/) (2022)
- [SDF4CHD: Generative Modeling of Cardiac Anatomies with Congenital Heart Defects](https://mlsanity.com/paper/2311.00332/) (2023)
- [4D Myocardium Reconstruction with Decoupled Motion and Shape Model](https://mlsanity.com/paper/2308.14083/) (2023)
- [Stochastic Poisson Surface Reconstruction](https://mlsanity.com/paper/2206.15236/) (2022)
- [Fully Bayesian VIB-DeepSSM](https://mlsanity.com/paper/2305.05797/) (2023)
- [Shape of my heart: Cardiac models through learned signed distance functions](https://mlsanity.com/paper/2308.16568/) (2023)
- [Neural Stochastic Screened Poisson Reconstruction](https://mlsanity.com/paper/2309.11993/) (2023)
- [Spatio-temporal neural distance fields for conditional generative modeling of the heart](https://mlsanity.com/paper/2407.10663/) (2024)
- [A Survey of Medical Point Cloud Shape Learning: Registration, Reconstruction and Variation](https://mlsanity.com/paper/2508.03057/) (2025)

## Abstract (arXiv)

Atlas-based approaches allow high-quality, patient-specific shape reconstructions of cardiac anatomy from sparse and/or noisy data such as point clouds. However, these methods are mainly prior-driven, so the impact of uncertainty can be large, limiting their clinical reliability. We propose a probabilistic framework for uncertainty-aware cardiac shape reconstruction that combines Deep Signed Distance Functions (DeepSDFs) with Markov Chain Monte Carlo (MCMC) sampling. Cardiac geometries are modeled implicitly as zero-level sets of a neural network conditioned on learned latent codes, enabling multi-surface reconstruction of the left and right ventricles. By interpreting the reconstruction loss as a log-likelihood, we perform Bayesian inference in the latent space to obtain both maximum a posteriori (MAP) and posterior-sampled reconstructions. Experiments on a public cardiac dataset show that our approach produces accurate reconstructions and well-calibrated uncertainty estimates.