# Inferring Distributions Over Depth from a Single Image

arXiv: https://arxiv.org/abs/1912.06268 · HTML: https://mlsanity.com/paper/1912.06268/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2019.

## Built on by (most cited first, 8 of 8)

- [Self-Supervised Monocular Depth Estimation with Internal Feature Fusion](https://mlsanity.com/paper/2110.09482/) (2021)
- [Multi-View Depth Estimation by Fusing Single-View Depth Probability with Multi-View Geometry](https://mlsanity.com/paper/2112.08177/) (2021)
- [SLiDE: Self-supervised LiDAR De-snowing through Reconstruction Difficulty](https://mlsanity.com/paper/2208.04043/) (2022)
- [Virtual Occlusions Through Implicit Depth](https://mlsanity.com/paper/2305.07014/) (2023)
- [Real-Time Monocular Human Depth Estimation and Segmentation on Embedded Systems](https://mlsanity.com/paper/2108.10506/) (2021)
- [Bayesian Deep Neural Networks for Supervised Learning of Single-View Depth](https://mlsanity.com/paper/2104.14202/) (2021)
- [Multi-view Monocular Depth and Uncertainty Prediction with Deep SfM in Dynamic Environments](https://mlsanity.com/paper/2201.08633/) (2022)
- [On Monocular Depth Estimation and Uncertainty Quantification using Classification Approaches for Regression](https://mlsanity.com/paper/2202.12369/) (2022)

## Abstract (arXiv)

When building a geometric scene understanding system for autonomous vehicles, it is crucial to know when the system might fail. Most contemporary approaches cast the problem as depth regression, whose output is a depth value for each pixel. Such approaches cannot diagnose when failures might occur. One attractive alternative is a deep Bayesian network, which captures uncertainty in both model parameters and ambiguous sensor measurements. However, estimating uncertainties is often slow and the distributions are often limited to be uni-modal. In this paper, we recast the continuous problem of depth regression as discrete binary classification, whose output is an un-normalized distribution over possible depths for each pixel. Such output allows one to reliably and efficiently capture multi-modal depth distributions in ambiguous cases, such as depth discontinuities and reflective surfaces. Results on standard benchmarks show that our method produces accurate depth predictions and significantly better uncertainty estimations than prior art while running near real-time. Finally, by making use of uncertainties of the predicted distribution, we significantly reduce streak-like artifacts and improves accuracy as well as memory efficiency in 3D map reconstruction.