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