  Deep Learning (DL) holds great promise in reshaping the healthcare industry
owing to its precision, efficiency, and objectivity. However, the brittleness
of DL models to noisy and out-of-distribution inputs is ailing their deployment
in the clinic. Most models produce point estimates without further information
about model uncertainty or confidence. This paper introduces a new Bayesian DL
framework for uncertainty quantification in segmentation neural networks:
SUPER-Net: trustworthy medical image Segmentation with Uncertainty Propagation
in Encoder-decodeR Networks. SUPER-Net analytically propagates, using Taylor
series approximations, the first two moments (mean and covariance) of the
posterior distribution of the model parameters across the nonlinear layers. In
particular, SUPER-Net simultaneously learns the mean and covariance without
expensive post-hoc Monte Carlo sampling or model ensembling. The output
consists of two simultaneous maps: the segmented image and its pixelwise
uncertainty map, which corresponds to the covariance matrix of the predictive
distribution. We conduct an extensive evaluation of SUPER-Net on medical image
segmentation of Magnetic Resonances Imaging and Computed Tomography scans under
various noisy and adversarial conditions. Our experiments on multiple benchmark
datasets demonstrate that SUPER-Net is more robust to noise and adversarial
attacks than state-of-the-art segmentation models. Moreover, the uncertainty
map of the proposed SUPER-Net associates low confidence (or equivalently high
uncertainty) to patches in the test input images that are corrupted with noise,
artifacts, or adversarial attacks. Perhaps more importantly, the model exhibits
the ability of self-assessment of its segmentation decisions, notably when
making erroneous predictions due to noise or adversarial examples.
