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.

翻译：基于深度学习的方法已在广泛的医学图像分割任务中取得了最先进的性能。然而，近期研究表明深度神经网络可能存在校准错误和过度自信的问题，从而导致临床应用中存在风险的“静默失败”。贝叶斯统计学为深度学习失败检测提供了一种基于后验概率估计的直观方法。然而，贝叶斯深度学习，特别是后验估计，对于大型医学图像分割深度神经网络而言是难以处理的。为应对这一挑战，我们提出了一种通过哈密顿蒙特卡洛实现的贝叶斯学习框架，并采用冷后验进行调节以适应医学数据增强，该方法命名为HMC-CP。针对HMC计算，我们进一步提出了循环退火策略，该策略能够捕捉后验分布的局部与全局几何特征，从而在与训练单个深度神经网络相同的计算预算要求下实现高效的贝叶斯深度神经网络训练。所得贝叶斯深度神经网络可输出集成分割结果及分割不确定性。我们在心脏磁共振图像分割任务上对提出的HMC-CP方法进行了全面评估，所使用的数据包括域内稳态自由进动电影图像以及域外定量$T_1$和$T_2$ mapping数据集。