Learning Depth from Single Monocular Images Using Deep Convolutional Neural Fields
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Abstract (arXiv)
In this article, we tackle the problem of depth estimation from single monocular images. Compared with depth estimation using multiple images such as stereo depth perception, depth from monocular images is much more challenging. Prior work typically focuses on exploiting geometric priors or additional sources of information, most using hand-crafted features. Recently, there is mounting evidence that features from deep convolutional neural networks (CNN) set new records for various vision applications. On the other hand, considering the continuous characteristic of the depth values, depth estimations can be naturally formulated as a continuous conditional random field (CRF) learning problem. Therefore, here we present a deep convolutional neural field model for estimating depths from single monocular images, aiming to jointly explore the capacity of deep CNN and continuous CRF. In particular, we propose a deep structured learning scheme which learns the unary and pairwise potentials of continuous CRF in a unified deep CNN framework. We then further propose an equally effective model based on fully convolutional networks and a novel superpixel pooling method, which is ~ 10 times faster, to speedup the patch-wise convolutions in the deep model. With this more efficient model, we are able to design deeper networks to pursue better performance. Experiments on both indoor and outdoor scene datasets demonstrate that the proposed method outperforms state-of-the-art depth estimation approaches.
Key facts. Cited by 169 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Feb 2015.
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Citing papers per year: 2021: 46; 2022: 44; 2023: 35; 2024: 25; 2025: 12; 2026: 7.
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- 2022Point-NeRF: Point-based Neural Radiance Fieldscited by 503
- 2024UniDepth: Universal Monocular Metric Depth Estimationcited by 375
- 2022NoPe-NeRF: Optimising Neural Radiance Field with No Pose Priorcited by 235
- 2025UniDepthV2: Universal Monocular Metric Depth Estimation Made Simplercited by 170
- 2022MonoViT: Self-Supervised Monocular Depth Estimation with a Vision Transformercited by 136
- 2022P3Depth: Monocular Depth Estimation with a Piecewise Planarity Priorcited by 106
- 2022Lite-Mono: A Lightweight CNN and Transformer Architecture for Self-Supervised Monocular Depth Estimationcited by 100
- 2021NeuTex: Neural Texture Mapping for Volumetric Neural Renderingcited by 98
- 2021UniFuse: Unidirectional Fusion for 360circ Panorama Depth Estimationcited by 91
- 2023StyleRF: Zero-shot 3D Style Transfer of Neural Radiance Fieldscited by 79
- 2022SurroundDepth: Entangling Surrounding Views for Self-Supervised Multi-Camera Depth Estimationcited by 76
- 2023iDisc: Internal Discretization for Monocular Depth Estimationcited by 71
38 more
- 2021Self-Supervised Monocular Depth and Ego-Motion Estimation in Endoscopy: Appearance Flow to the Rescuecited by 70
- 2021Unsupervised Scale-consistent Depth Learning from Videocited by 69
- 2021Deep Animation Video Interpolation in the Wildcited by 65
- 2023Behind the Scenes: Density Fields for Single View Reconstructioncited by 63
- 2025UniK3D: Universal Camera Monocular 3D Estimationcited by 60
- 2021Fine-grained Semantics-aware Representation Enhancement for Self-supervised Monocular Depth Estimationcited by 55
- 2023VA-DepthNet: A Variational Approach to Single Image Depth Predictioncited by 54
- 2022SC-DepthV3: Robust Self-supervised Monocular Depth Estimation for Dynamic Scenescited by 50
- 2021Virtual Normal: Enforcing Geometric Constraints for Accurate and Robust Depth Predictioncited by 48
- 2023RoboDepth: Robust Out-of-Distribution Depth Estimation under Corruptionscited by 47
- 2021Adaptive Surface Normal Constraint for Depth Estimationcited by 43
- 2022Towards Accurate Reconstruction of 3D Scene Shape from A Single Monocular Imagecited by 42
- 2023NeuralEditor: Editing Neural Radiance Fields via Manipulating Point Cloudscited by 41
- 2023OccNeRF: Advancing 3D Occupancy Prediction in LiDAR-Free Environmentscited by 39
- 2021StructDepth: Leveraging the structural regularities for self-supervised indoor depth estimationcited by 36
- 2022RA-Depth: Resolution Adaptive Self-Supervised Monocular Depth Estimationcited by 36
- 2021SOSD-Net: Joint Semantic Object Segmentation and Depth Estimation from Monocular imagescited by 33
- 2021Learning to Relate Depth and Semantics for Unsupervised Domain Adaptationcited by 32
- 2024Physical 3D Adversarial Attacks against Monocular Depth Estimation in Autonomous Drivingcited by 32
- 2021Deep Learning Based 3D Segmentation: A Surveycited by 30
- 2024Diffusion Models for Monocular Depth Estimation: Overcoming Challenging Conditionscited by 29
- 2023Strivec: Sparse Tri-Vector Radiance Fieldscited by 28
- 2023S4C: Self-Supervised Semantic Scene Completion with Neural Fieldscited by 27
- 2021Defocus Map Estimation and Deblurring from a Single Dual-Pixel Imagecited by 25
- 2021Monocular Depth Estimation through Virtual-world Supervision and Real-world SfM Self-Supervisioncited by 24
- 2024OmniControlNet: Dual-stage Integration for Conditional Image Generationcited by 24
- 2021S2R-DepthNet: Learning a Generalizable Depth-specific Structural Representationcited by 23
- 2021DF-VO: What Should Be Learnt for Visual Odometry?cited by 22
- 2023Digging Into Uncertainty-based Pseudo-label for Robust Stereo Matchingcited by 22
- 2022Depthformer : Multiscale Vision Transformer For Monocular Depth Estimation With Local Global Information Fusioncited by 20
- 2022Towards Scale-Aware, Robust, and Generalizable Unsupervised Monocular Depth Estimation by Integrating IMU Motion Dynamicscited by 20
- 2021Instance and Panoptic Segmentation Using Conditional Convolutionscited by 19
- 2021Fast and Accurate Single-Image Depth Estimation on Mobile Devices, Mobile AI 2021 Challenge: Reportcited by 19
- 2026InfiniDepth: Arbitrary-Resolution and Fine-Grained Depth Estimation with Neural Implicit Fieldscited by 19
- 2023SimCol3D -- 3D Reconstruction during Colonoscopy Challengecited by 18
- 2021Cuboids Revisited: Learning Robust 3D Shape Fitting to Single RGB Imagescited by 17
- 2022Multi-Camera Collaborative Depth Prediction via Consistent Structure Estimationcited by 16
- 2023Enhancing Diffusion Models with 3D Perspective Geometry Constraintscited by 16
50 most cited of 169 All 169 (JSON)
- 2026CrossDepth: Geometry-Constrained Attention for Generalizable Multi-View Surround Depth Estimation4 Sep 2026
- 2026DrivingDepth: Sparse-Prompted Pixel-wise Scale Correction for Driving Depth Estimation30 Jun 2026
- 2026Monocular Depth Estimation via Neural Network with Learnable Algebraic Group and Ring Structures27 Apr 2026
- 2026SHED Light on Segmentation for Dense Prediction30 Jan 2026
- 2026Computational Framework for Estimating Relative Gaussian Blur Kernels between Image Pairs26 Jan 2026
- 2026Defocus Aberration Theory Confirms Gaussian Model in Most Imaging Devices8 Jan 2026
- 2026InfiniDepth: Arbitrary-Resolution and Fine-Grained Depth Estimation with Neural Implicit Fields6 Jan 2026
- 2025Visual Autoregressive Modelling for Monocular Depth Estimation27 Dec 2025
- 2025Estimating Fog Parameters from a Sequence of Stereo Images25 Nov 2025
- 2025CylinderDepth: Cylindrical Spatial Attention for Multi-View Consistent Self-Supervised Surround Depth Estimation20 Nov 2025
- 2025Depth-Supervised Fusion Network for Seamless-Free Image Stitching24 Oct 2025
- 2025Scene Coordinate Reconstruction Priors14 Oct 2025
38 more
- 2025Extending Foundational Monocular Depth Estimators to Fisheye Cameras with Calibration Tokens6 Aug 2025
- 2025Dream-to-Recon: Monocular 3D Reconstruction with Diffusion-Depth Distillation from Single Images4 Aug 2025
- 2025Always Clear Depth: Robust Monocular Depth Estimation under Adverse Weather18 May 2025
- 2025Enhancing Monocular Height Estimation via Sparse LiDAR-Guided Correction11 May 2025
- 2025UniK3D: Universal Camera Monocular 3D Estimation20 Mar 2025
- 2025UniDepthV2: Universal Monocular Metric Depth Estimation Made Simpler27 Feb 2025
- 2025Extended monocular 3D imaging11 Feb 2025
- 2024MetricDepth: Enhancing Monocular Depth Estimation with Deep Metric Learning29 Dec 2024
- 2024MonoPP: Metric-Scaled Self-Supervised Monocular Depth Estimation by Planar-Parallax Geometry in Automotive Applications29 Nov 2024
- 2024Self-supervised Monocular Depth and Pose Estimation for Endoscopy with Latent Priors26 Nov 2024
- 2024ProEdit: Simple Progression is All You Need for High-Quality 3D Scene Editing7 Nov 2024
- 2024A Preliminary Exploration Towards General Image Restoration27 Aug 2024
- 2024Intuitionistic Fuzzy Cognitive Maps for Interpretable Image Classification7 Aug 2024
- 2024Floating No More: Object-Ground Reconstruction from a Single Image26 Jul 2024
- 2024Diffusion Models for Monocular Depth Estimation: Overcoming Challenging Conditions23 Jul 2024
- 2024SCIPaD: Incorporating Spatial Clues into Unsupervised Pose-Depth Joint Learning7 Jul 2024
- 2024Deep Learning-based Depth Estimation Methods from Monocular Image and Videos: A Comprehensive Survey28 Jun 2024
- 2024Deep Learning-Based 3D Instance and Semantic Segmentation: A Review19 Jun 2024
- 2024OmniControlNet: Dual-stage Integration for Conditional Image Generation9 Jun 2024
- 2024Consistency Regularisation for Unsupervised Domain Adaptation in Monocular Depth Estimation27 May 2024
- 2024DCPI-Depth: Explicitly Infusing Dense Correspondence Prior to Unsupervised Monocular Depth Estimation27 May 2024
- 2024FA-Depth: Toward Fast and Accurate Self-supervised Monocular Depth Estimation17 May 2024
- 2024Hologram: Realtime Holographic Overlays via LiDAR Augmented Reconstruction12 May 2024
- 2024Self-supervised Monocular Depth Estimation on Water Scenes via Specular Reflection Prior10 Apr 2024
- 2024UniDepth: Universal Monocular Metric Depth Estimation27 Mar 2024
- 2024Physical 3D Adversarial Attacks against Monocular Depth Estimation in Autonomous Driving26 Mar 2024
- 2024SynFog: A Photo-realistic Synthetic Fog Dataset based on End-to-end Imaging Simulation for Advancing Real-World Defogging in Autonomous Driving25 Mar 2024
- 2024Robust Shape Fitting for 3D Scene Abstraction15 Mar 2024
- 2024Stealing Stable Diffusion Prior for Robust Monocular Depth Estimation8 Mar 2024
- 2024SDGE: Stereo Guided Depth Estimation for 360^circ Camera Sets19 Feb 2024
- 2024Adaptive Surface Normal Constraint for Geometric Estimation from Monocular Images8 Feb 2024
- 2024Monocular Per-Object Distance Estimation with Masked Object Modeling6 Jan 2024
- 2023OccNeRF: Advancing 3D Occupancy Prediction in LiDAR-Free Environments14 Dec 2023
- 2023Learning Naturally Aggregated Appearance for Efficient 3D Editing11 Dec 2023
- 2023Deeper into Self-Supervised Monocular Indoor Depth Estimation3 Dec 2023
- 2023Enhancing Diffusion Models with 3D Perspective Geometry Constraints1 Dec 2023
- 20233D Face Style Transfer with a Hybrid Solution of NeRF and Mesh Rasterization22 Nov 2023
- 2023Central Angle Optimization for 360-degree Holographic 3D Content10 Nov 2023
50 newest of 169 All 169 (JSON)
- 2024Diffusion Models for Monocular Depth Estimation: Overcoming Challenging Conditionscited by 29
- 2023Enhancing Diffusion Models with 3D Perspective Geometry Constraintscited by 16
- 2024ProEdit: Simple Progression is All You Need for High-Quality 3D Scene Editingcited by 12
- 2024Stealing Stable Diffusion Prior for Robust Monocular Depth Estimationcited by 6
- 2025Always Clear Depth: Robust Monocular Depth Estimation under Adverse Weathercited by 4
- 2025Always Clear Depth: Robust Monocular Depth Estimation under Adverse Weather18 May 2025
- 2024ProEdit: Simple Progression is All You Need for High-Quality 3D Scene Editing7 Nov 2024
- 2024Diffusion Models for Monocular Depth Estimation: Overcoming Challenging Conditions23 Jul 2024
- 2024Stealing Stable Diffusion Prior for Robust Monocular Depth Estimation8 Mar 2024
- 2023Enhancing Diffusion Models with 3D Perspective Geometry Constraints1 Dec 2023
- 2022Point-NeRF: Point-based Neural Radiance Fieldscited by 503
- 2024UniDepth: Universal Monocular Metric Depth Estimationcited by 375
- 2022NoPe-NeRF: Optimising Neural Radiance Field with No Pose Priorcited by 235
- 2025UniDepthV2: Universal Monocular Metric Depth Estimation Made Simplercited by 170
- 2022MonoViT: Self-Supervised Monocular Depth Estimation with a Vision Transformercited by 136
- 2022P3Depth: Monocular Depth Estimation with a Piecewise Planarity Priorcited by 106
- 2022Lite-Mono: A Lightweight CNN and Transformer Architecture for Self-Supervised Monocular Depth Estimationcited by 100
- 2021NeuTex: Neural Texture Mapping for Volumetric Neural Renderingcited by 98
- 2021UniFuse: Unidirectional Fusion for 360circ Panorama Depth Estimationcited by 91
- 2023StyleRF: Zero-shot 3D Style Transfer of Neural Radiance Fieldscited by 79
- 2022SurroundDepth: Entangling Surrounding Views for Self-Supervised Multi-Camera Depth Estimationcited by 76
- 2023iDisc: Internal Discretization for Monocular Depth Estimationcited by 71
12 most cited of 164 All 164 (JSON)
- 2026CrossDepth: Geometry-Constrained Attention for Generalizable Multi-View Surround Depth Estimation4 Sep 2026
- 2026DrivingDepth: Sparse-Prompted Pixel-wise Scale Correction for Driving Depth Estimation30 Jun 2026
- 2026Monocular Depth Estimation via Neural Network with Learnable Algebraic Group and Ring Structures27 Apr 2026
- 2026SHED Light on Segmentation for Dense Prediction30 Jan 2026
- 2026Computational Framework for Estimating Relative Gaussian Blur Kernels between Image Pairs26 Jan 2026
- 2026Defocus Aberration Theory Confirms Gaussian Model in Most Imaging Devices8 Jan 2026
- 2026InfiniDepth: Arbitrary-Resolution and Fine-Grained Depth Estimation with Neural Implicit Fields6 Jan 2026
- 2025Visual Autoregressive Modelling for Monocular Depth Estimation27 Dec 2025
- 2025Estimating Fog Parameters from a Sequence of Stereo Images25 Nov 2025
- 2025CylinderDepth: Cylindrical Spatial Attention for Multi-View Consistent Self-Supervised Surround Depth Estimation20 Nov 2025
- 2025Depth-Supervised Fusion Network for Seamless-Free Image Stitching24 Oct 2025
- 2025Scene Coordinate Reconstruction Priors14 Oct 2025
12 newest of 164 All 164 (JSON)