Bayesian Uncertainty Estimation by Hamiltonian Monte Carlo: Applications to Cardiac MRI Segmentation

Deep learning (DL)-based methods have achieved state-of-the-art performance for a wide range of medical image segmentation tasks. Nevertheless, recent studies show that deep neural networks (DNNs) can be miscalibrated and overconfident, leading to "silent failures" that are risky} for clinical applications. Bayesian statistics provide an intuitive approach to DL failure detection, based on posterior probability estimation. However, Bayesian DL, and in particular the posterior estimation, is intractable for large medical image segmentation DNNs. To tackle this challenge, we propose a Bayesian learning framework by Hamiltonian Monte Carlo (HMC), tempered by cold posterior (CP) to accommodate medical data augmentation, named HMC-CP. For HMC computation, we further propose a cyclical annealing strategy, which captures both local and global geometries of the posterior distribution, enabling highly efficient Bayesian DNN training with the same computational budget requirements as training a single DNN. The resulting Bayesian DNN outputs an ensemble segmentation along with the segmentation uncertainty. We evaluate the proposed HMC-CP extensively on cardiac magnetic resonance image (MRI) segmentation, using in-domain steady-state free precession (SSFP) cine images as well as out-of-domain datasets of quantitative $T_1$ and $T_2$ mapping.