# Gradient-based Uncertainty for Monocular Depth Estimation

arXiv: https://arxiv.org/abs/2208.02005 · HTML: https://mlsanity.com/paper/2208.02005/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 3 Aug 2022.

## Builds on (most cited first, 27 of 27)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Unsupervised Monocular Depth Estimation with Left-Right Consistency](https://mlsanity.com/paper/1609.03677/) (2016)
- [Unsupervised Learning of Depth and Ego-Motion from Video](https://mlsanity.com/paper/1704.07813/) (2017)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [AdaBins: Depth Estimation using Adaptive Bins](https://mlsanity.com/paper/2011.14141/) (2020)
- [Deeper Depth Prediction with Fully Convolutional Residual Networks](https://mlsanity.com/paper/1606.00373/) (2016)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [Sparsity Invariant CNNs](https://mlsanity.com/paper/1708.06500/) (2017)
- [Unsupervised Scale-consistent Depth and Ego-motion Learning from Monocular Video](https://mlsanity.com/paper/1908.10553/) (2019)
- [D3VO: Deep Depth, Deep Pose and Deep Uncertainty for Monocular Visual Odometry](https://mlsanity.com/paper/2003.01060/) (2020)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Deep Virtual Stereo Odometry: Leveraging Deep Depth Prediction for Monocular Direct Sparse Odometry](https://mlsanity.com/paper/1807.02570/) (2018)
- [Self-Supervised Monocular Depth Estimation with Internal Feature Fusion](https://mlsanity.com/paper/2110.09482/) (2021)
- [Learning monocular depth estimation infusing traditional stereo knowledge](https://mlsanity.com/paper/1904.04144/) (2019)
- [Gradients as a Measure of Uncertainty in Neural Networks](https://mlsanity.com/paper/2008.08030/) (2020)
- [Classification Uncertainty of Deep Neural Networks Based on Gradient Information](https://mlsanity.com/paper/1805.08440/) (2018)
- [Training-Free Uncertainty Estimation for Dense Regression: Sensitivity as a Surrogate](https://mlsanity.com/paper/1910.04858/) (2019)
- [ProbFlow: Joint Optical Flow and Uncertainty Estimation](https://mlsanity.com/paper/1708.06509/) (2017)
- [CamLessMonoDepth: Monocular Depth Estimation with Unknown Camera Parameters](https://mlsanity.com/paper/2110.14347/) (2021)
- [SUB-Depth: Self-distillation and Uncertainty Boosting Self-supervised Monocular Depth Estimation](https://mlsanity.com/paper/2111.09692/) (2021)
- [NVS-MonoDepth: Improving Monocular Depth Prediction with Novel View Synthesis](https://mlsanity.com/paper/2112.12577/) (2021)
- [Region Deformer Networks for Unsupervised Depth Estimation from Unconstrained Monocular Videos](https://mlsanity.com/paper/1902.09907/) (2019)

## Built on by (most cited first, 26 of 26)

- [NeRF On-the-go: Exploiting Uncertainty for Distractor-free NeRFs in the Wild](https://mlsanity.com/paper/2405.18715/) (2024)
- [Stereo Anywhere: Robust Zero-Shot Deep Stereo Matching Even Where Either Stereo or Mono Fail](https://mlsanity.com/paper/2412.04472/) (2024)
- [Diffusion Models for Monocular Depth Estimation: Overcoming Challenging Conditions](https://mlsanity.com/paper/2407.16698/) (2024)
- [POCO: 3D Pose and Shape Estimation with Confidence](https://mlsanity.com/paper/2308.12965/) (2023)
- [Diffusion Model Guided Sampling with Pixel-Wise Aleatoric Uncertainty Estimation](https://mlsanity.com/paper/2412.00205/) (2024)
- [Toward Real-world BEV Perception: Depth Uncertainty Estimation via Gaussian Splatting](https://mlsanity.com/paper/2504.01957/) (2025)
- [RankED: Addressing Imbalance and Uncertainty in Edge Detection Using Ranking-based Losses](https://mlsanity.com/paper/2403.01795/) (2024)
- [ZigZag: Universal Sampling-free Uncertainty Estimation Through Two-Step Inference](https://mlsanity.com/paper/2211.11435/) (2022)
- [Single Image Depth Prediction Made Better: A Multivariate Gaussian Take](https://mlsanity.com/paper/2303.18164/) (2023)
- [Pixel-wise Gradient Uncertainty for Convolutional Neural Networks applied to Out-of-Distribution Segmentation](https://mlsanity.com/paper/2303.06920/) (2023)
- [Human as Points: Explicit Point-based 3D Human Reconstruction from Single-view RGB Images](https://mlsanity.com/paper/2311.02892/) (2023)
- [ProbVLM: Probabilistic Adapter for Frozen Vision-Language Models](https://mlsanity.com/paper/2307.00398/) (2023)
- [Out-of-Distribution Detection for Monocular Depth Estimation](https://mlsanity.com/paper/2308.06072/) (2023)
- [Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression](https://mlsanity.com/paper/2308.09065/) (2023)
- [Revisiting Gradient-based Uncertainty for Monocular Depth Estimation](https://mlsanity.com/paper/2502.05964/) (2025)
- [Robust Self-Supervised Extrinsic Self-Calibration](https://mlsanity.com/paper/2308.02153/) (2023)
- [Uni-SLAM: Uncertainty-Aware Neural Implicit SLAM for Real-Time Dense Indoor Scene Reconstruction](https://mlsanity.com/paper/2412.00242/) (2024)
- [ADU-Depth: Attention-based Distillation with Uncertainty Modeling for Depth Estimation](https://mlsanity.com/paper/2309.14744/) (2023)
- [A Critical Synthesis of Uncertainty Quantification and Foundation Models in Monocular Depth Estimation](https://mlsanity.com/paper/2501.08188/) (2025)
- [Measuring and Modeling Uncertainty Degree for Monocular Depth Estimation](https://mlsanity.com/paper/2307.09929/) (2023)
- [FocDepthFormer: Transformer with latent LSTM for Depth Estimation from Focal Stack](https://mlsanity.com/paper/2310.11178/) (2023)
- [Consistency Regularisation for Unsupervised Domain Adaptation in Monocular Depth Estimation](https://mlsanity.com/paper/2405.17704/) (2024)
- [Probabilistic Modeling of Disparity Uncertainty for Robust and Efficient Stereo Matching](https://mlsanity.com/paper/2412.18703/) (2024)
- [Adaptive Dual Uncertainty Optimization: Boosting Monocular 3D Object Detection under Test-Time Shifts](https://mlsanity.com/paper/2508.20488/) (2025)
- [Robust Uncertainty Estimation under Distribution Shift via Difference Reconstruction](https://mlsanity.com/paper/2601.19341/) (2026)
- [A Calibration Audit of Confidence in Feed-Forward 3D Reconstruction Models](https://mlsanity.com/paper/2608.29705/) (2026)

## Abstract (arXiv)

In monocular depth estimation, disturbances in the image context, like moving objects or reflecting materials, can easily lead to erroneous predictions. For that reason, uncertainty estimates for each pixel are necessary, in particular for safety-critical applications such as automated driving. We propose a post hoc uncertainty estimation approach for an already trained and thus fixed depth estimation model, represented by a deep neural network. The uncertainty is estimated with the gradients which are extracted with an auxiliary loss function. To avoid relying on ground-truth information for the loss definition, we present an auxiliary loss function based on the correspondence of the depth prediction for an image and its horizontally flipped counterpart. Our approach achieves state-of-the-art uncertainty estimation results on the KITTI and NYU Depth V2 benchmarks without the need to retrain the neural network. Models and code are publicly available at https://github.com/jhornauer/GrUMoDepth.