  In many real-world applications, the relative depth of objects in an image is
crucial for scene understanding. Recent approaches mainly tackle the problem of
depth prediction in monocular images by treating the problem as a regression
task. Yet, being interested in an order relation in the first place, ranking
methods suggest themselves as a natural alternative to regression, and indeed,
ranking approaches leveraging pairwise comparisons as training information
("object A is closer to the camera than B") have shown promising performance on
this problem. In this paper, we elaborate on the use of so-called listwise
ranking as a generalization of the pairwise approach. Our method is based on
the Plackett-Luce (PL) model, a probability distribution on rankings, which we
combine with a state-of-the-art neural network architecture and a simple
sampling strategy to reduce training complexity. Moreover, taking advantage of
the representation of PL as a random utility model, the proposed predictor
offers a natural way to recover (shift-invariant) metric depth information from
ranking-only data provided at training time. An empirical evaluation on several
benchmark datasets in a "zero-shot" setting demonstrates the effectiveness of
our approach compared to existing ranking and regression methods.
