Uncertainty Quantification for Cardiac Shape Reconstruction with Deep Signed Distance Functions via MCMC methods
Jan Verhülsdonk, Thomas Grandits, Francisco Sahli Costabal, Thomas Beiert, Simone Pezzuto + 1 more
TLDR
This paper introduces a probabilistic framework for uncertainty-aware cardiac shape reconstruction using DeepSDFs and MCMC, providing accurate results.
Key contributions
- Proposes a probabilistic framework for uncertainty-aware cardiac shape reconstruction.
- Combines Deep Signed Distance Functions (DeepSDFs) with MCMC for Bayesian inference.
- Models cardiac geometries implicitly via neural networks for multi-surface reconstruction.
- Achieves accurate reconstructions and well-calibrated uncertainty estimates on cardiac data.
Why it matters
Existing cardiac shape reconstruction methods often lack uncertainty quantification, limiting their clinical reliability. This paper introduces a probabilistic framework that provides well-calibrated uncertainty estimates, making cardiac shape models more trustworthy for medical applications. This advancement is crucial for improving diagnostic accuracy and treatment planning.
Original 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.
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