Bayesian Uncertainty Estimation by Hamiltonian Monte Carlo: Applications
  to Cardiac MRI Segmentation
Yidong Zhao Joao Tourais Iain Pierce Christian Nitsche Thomas A. Treibel Sebastian Weingärtner Artur M. Schweidtmann Qian Tao
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.