Monocular Depth Estimation via Listwise Ranking using the Plackett-Luce model

In many real-world applications, the relative depth of objects in an image is crucial for scene understanding, e.g., to calculate occlusions in augmented reality scenes. Predicting depth in monocular images has recently been tackled using machine learning methods, mainly 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 \emph{listwise} ranking as a generalization of the pairwise approach. Listwise ranking goes beyond pairwise comparisons between objects and considers rankings of arbitrary length as training information. Our approach is based on the Plackett-Luce model, a probability distribution on rankings, which we combine with a state-of-the-art neural network architecture and a sampling strategy to reduce training complexity. An empirical evaluation on benchmark data in a "zero-shot" setting demonstrates the effectiveness of our proposal compared to existing ranking and regression methods.