Uncertainty Quantification for Cardiac Shape Reconstruction with Deep Signed Distance Functions via MCMC methods
This work addresses the need for uncertainty quantification in cardiac shape reconstruction, which is critical for clinical reliability, but the approach is incremental as it applies existing Bayesian inference methods to a known problem.
The paper proposes a probabilistic framework for cardiac shape reconstruction that combines DeepSDF with MCMC sampling to provide both accurate reconstructions and well-calibrated uncertainty estimates from sparse point clouds.
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.