  When building a geometric scene understanding system for autonomous vehicles,
it is crucial to know when the system might fail. Most contemporary approaches
cast the problem as depth regression, whose output is a depth value for each
pixel. Such approaches cannot diagnose when failures might occur. One
attractive alternative is a deep Bayesian network, which captures uncertainty
in both model parameters and ambiguous sensor measurements. However, estimating
uncertainties is often slow and the distributions are often limited to be
uni-modal. In this paper, we recast the continuous problem of depth regression
as discrete binary classification, whose output is an un-normalized
distribution over possible depths for each pixel. Such output allows one to
reliably and efficiently capture multi-modal depth distributions in ambiguous
cases, such as depth discontinuities and reflective surfaces. Results on
standard benchmarks show that our method produces accurate depth predictions
and significantly better uncertainty estimations than prior art while running
near real-time. Finally, by making use of uncertainties of the predicted
distribution, we significantly reduce streak-like artifacts and improves
accuracy as well as memory efficiency in 3D map reconstruction.
