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

TL;DR

This paper introduces a probabilistic framework combining Deep Signed Distance Functions and MCMC sampling for uncertainty-aware cardiac shape reconstruction, improving reliability and providing uncertainty estimates.

Contribution

It presents a novel Bayesian inference approach in the latent space of DeepSDFs for multi-surface cardiac shape reconstruction with uncertainty quantification.

Findings

Accurate cardiac shape reconstructions achieved.

Well-calibrated uncertainty estimates demonstrated.

Bayesian inference improves clinical reliability.

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.