  Self-supervised paradigms for monocular depth estimation are very appealing
since they do not require ground truth annotations at all. Despite the
astonishing results yielded by such methodologies, learning to reason about the
uncertainty of the estimated depth maps is of paramount importance for
practical applications, yet uncharted in the literature. Purposely, we explore
for the first time how to estimate the uncertainty for this task and how this
affects depth accuracy, proposing a novel peculiar technique specifically
designed for self-supervised approaches. On the standard KITTI dataset, we
exhaustively assess the performance of each method with different
self-supervised paradigms. Such evaluation highlights that our proposal i)
always improves depth accuracy significantly and ii) yields state-of-the-art
results concerning uncertainty estimation when training on sequences and
competitive results uniquely deploying stereo pairs.
