  We propose a new approach for the problem of relative depth estimation from a
single image. Instead of directly regressing over depth scores, we formulate
the problem as estimation of a probability distribution over depth and aim to
learn the parameters of the distributions which maximize the likelihood of the
given data. To train our model, we propose a new ranking loss, Distributional
Loss, which tries to increase the probability of farther pixel's depth being
greater than the closer pixel's depth. Our proposed approach allows our model
to output confidence in its estimation in the form of standard deviation of the
distribution. We achieve state of the art results against a number of baselines
while providing confidence in our estimations. Our analysis show that estimated
confidence is actually a good indicator of accuracy. We investigate the usage
of confidence information in a downstream task of metric depth estimation, to
increase its performance.
