Deep Bayesian networks for uncertainty estimation and adversarial resistance of white matter hyperintensity segmentation

White matter hyperintensities (WMH) are frequently observed on structural neuroimaging of elderly populations and are associated with cognitive decline and increased risk of dementia. Many existing WMH segmentation algorithms produce suboptimal results in populations with vascular lesions or brain atrophy, or require parameter tuning and are computationally expensive. Additionally, most algorithms do not generate a confidence estimate of segmentation quality, limiting their interpretation. MRI-based segmentation methods are often sensitive to acquisition protocols, scanners, noise-level, and image contrast, failing to generalize to other populations and out-of-distribution datasets. Given these concerns, we propose a novel Bayesian 3D Convolutional Neural Network (CNN) with a U-Net architecture that automatically segments WMH, provides uncertainty estimates of the segmentation output for quality control and is robust to changes in acquisition protocols. We also provide a second model to differentiate deep and periventricular WMH. 432 subjects were recruited to train the CNNs from four multi-site imaging studies. A separate test set of 158 subjects was used for evaluation, including an unseen multi-site study. We compared our model to two established state-of-the-art techniques (BIANCA and DeepMedic), highlighting its accuracy and efficiency. Our Bayesian 3D U-Net achieved the highest Dice similarity coefficient of 0.89 {+/-} 0.08 and the lowest modified Hausdorff distance of 2.98 {+/-} 4.40 mm. We further validated our models highlighting their robustness on clinical adversarial cases simulating data with low signal-to-noise ratio, low resolution, and different contrast (stemming from MRI sequences with different parameters). Our pipeline and models are available at: https://hypermapp3r.readthedocs.io