  Deep learning has been successfully applied to the segmentation of 3D
Computed Tomography (CT) scans. Establishing the credibility of these
segmentations requires uncertainty quantification (UQ) to identify
untrustworthy predictions. Recent UQ architectures include Monte Carlo dropout
networks (MCDNs), which approximate deep Gaussian processes, and Bayesian
neural networks (BNNs), which learn the distribution of the weight space. BNNs
are advantageous over MCDNs for UQ but are thought to be computationally
infeasible in high dimension, and neither architecture has produced
interpretable geometric uncertainty maps. We propose a novel 3D Bayesian
convolutional neural network (BCNN), the first deep learning method which
generates statistically credible geometric uncertainty maps and scales for
application to 3D data. We present experimental results on CT scans of graphite
electrodes and laser-welded metals and show that our BCNN outperforms an MCDN
in recent uncertainty metrics. The geometric uncertainty maps generated by our
BCNN capture distributions of sigmoid values that are interpretable as
confidence intervals, critical for applications that rely on deep learning for
high-consequence decisions. Code available at
https://github.com/sandialabs/bcnn.
