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

2026-05-08

AI Summary

This work addresses the high uncertainty and limited clinical reliability of traditional atlas-based cardiac reconstruction methods under sparse or noisy data conditions, which stem from their reliance on strong anatomical priors. The authors propose a novel probabilistic framework that, for the first time, integrates Deep Signed Distance Functions (DeepSDF) with Markov Chain Monte Carlo (MCMC) sampling to perform Bayesian inference in the latent space of implicit neural representations. This approach enables high-fidelity reconstruction of multi-chamber cardiac geometries alongside well-calibrated uncertainty quantification. The method supports joint reconstruction of multiple endocardial and epicardial surfaces of both the left and right ventricles and demonstrates robust performance on public cardiac datasets, validating both its reconstruction accuracy and the reliability of its uncertainty estimates.

Abstract

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.

Problem

• Uncertainty Quantification
• Cardiac Shape Reconstruction
• Deep Signed Distance Functions
• MCMC
• Atlas-based Methods

Innovation

• Deep Signed Distance Functions
• Uncertainty Quantification
• Markov Chain Monte Carlo
• Bayesian Inference
• Cardiac Shape Reconstruction