# Monocular Depth Estimation via Listwise Ranking using the Plackett-Luce Model

arXiv: https://arxiv.org/abs/2010.13118 · HTML: https://mlsanity.com/paper/2010.13118/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2020.

## Built on by (most cited first, 12 of 12)

- [VA-DepthNet: A Variational Approach to Single Image Depth Prediction](https://mlsanity.com/paper/2302.06556/) (2023)
- [Single Image Depth Estimation: An Overview](https://mlsanity.com/paper/2104.06456/) (2021)
- [Depth Map Decomposition for Monocular Depth Estimation](https://mlsanity.com/paper/2208.10762/) (2022)
- [Deep Learning-based Depth Estimation Methods from Monocular Image and Videos: A Comprehensive Survey](https://mlsanity.com/paper/2406.19675/) (2024)
- [Single Image Depth Prediction Made Better: A Multivariate Gaussian Take](https://mlsanity.com/paper/2303.18164/) (2023)
- [Single-Stage 3D Geometry-Preserving Depth Estimation Model Training on Dataset Mixtures with Uncalibrated Stereo Data](https://mlsanity.com/paper/2306.02878/) (2023)
- [Enhancing Monocular Height Estimation from Aerial Images with Street-view Images](https://mlsanity.com/paper/2311.02121/) (2023)
- [Versatile Depth Estimator Based on Common Relative Depth Estimation and Camera-Specific Relative-to-Metric Depth Conversion](https://mlsanity.com/paper/2303.10991/) (2023)
- [Enhancing Monocular Height Estimation via Weak Supervision from Imperfect Labels](https://mlsanity.com/paper/2506.02534/) (2025)
- [Single-Eye View: Monocular Real-time Perception Package for Autonomous Driving](https://mlsanity.com/paper/2603.21061/) (2026)
- [Monocular Depth Estimation from a Single Image: Progress and Opportunities](https://mlsanity.com/paper/2609.01172/) (2026)
- [MORE-PLR: multi-output regression employed for partial label ranking](https://mlsanity.com/paper/2609.29386/) (2026)

## Abstract (arXiv)

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.