# Depth from a Single Image by Harmonizing Overcomplete Local Network Predictions

arXiv: https://arxiv.org/abs/1605.07081 · HTML: https://mlsanity.com/paper/1605.07081/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2016.

## Built on by (most cited first, 16 of 16)

- [P3Depth: Monocular Depth Estimation with a Piecewise Planarity Prior](https://mlsanity.com/paper/2204.02091/) (2022)
- [Unsupervised Scale-consistent Depth Learning from Video](https://mlsanity.com/paper/2105.11610/) (2021)
- [SC-DepthV3: Robust Self-supervised Monocular Depth Estimation for Dynamic Scenes](https://mlsanity.com/paper/2211.03660/) (2022)
- [Virtual Normal: Enforcing Geometric Constraints for Accurate and Robust Depth Prediction](https://mlsanity.com/paper/2103.04216/) (2021)
- [Adaptive Surface Normal Constraint for Depth Estimation](https://mlsanity.com/paper/2103.15483/) (2021)
- [MonoIndoor: Towards Good Practice of Self-Supervised Monocular Depth Estimation for Indoor Environments](https://mlsanity.com/paper/2107.12429/) (2021)
- [Adaptive Surface Normal Constraint for Geometric Estimation from Monocular Images](https://mlsanity.com/paper/2402.05869/) (2024)
- [MonoIndoor++:Towards Better Practice of Self-Supervised Monocular Depth Estimation for Indoor Environments](https://mlsanity.com/paper/2207.08951/) (2022)
- [EdgeConv with Attention Module for Monocular Depth Estimation](https://mlsanity.com/paper/2106.08615/) (2021)
- [Vision-Based Environmental Perception for Autonomous Driving](https://mlsanity.com/paper/2212.11453/) (2022)
- [Deeper into Self-Supervised Monocular Indoor Depth Estimation](https://mlsanity.com/paper/2312.01283/) (2023)
- [Pyramid Frequency Network with Spatial Attention Residual Refinement Module for Monocular Depth Estimation](https://mlsanity.com/paper/2204.02386/) (2022)
- [U-HRNet: Delving into Improving Semantic Representation of High Resolution Network for Dense Prediction](https://mlsanity.com/paper/2210.07140/) (2022)
- [MSFNet:Multi-scale features network for monocular depth estimation](https://mlsanity.com/paper/2107.06445/) (2021)
- [Recursive Least-Squares Estimator-Aided Online Learning for Visual Tracking](https://mlsanity.com/paper/2112.14016/) (2021)
- [THIRDEYE: Cue-Aware Monocular Depth Estimation via Brain-Inspired Multi-Stage Fusion](https://mlsanity.com/paper/2506.20877/) (2025)

## Abstract (arXiv)

A single color image can contain many cues informative towards different aspects of local geometric structure. We approach the problem of monocular depth estimation by using a neural network to produce a mid-level representation that summarizes these cues. This network is trained to characterize local scene geometry by predicting, at every image location, depth derivatives of different orders, orientations and scales. However, instead of a single estimate for each derivative, the network outputs probability distributions that allow it to express confidence about some coefficients, and ambiguity about others. Scene depth is then estimated by harmonizing this overcomplete set of network predictions, using a globalization procedure that finds a single consistent depth map that best matches all the local derivative distributions. We demonstrate the efficacy of this approach through evaluation on the NYU v2 depth data set.