# Deep Convolutional Neural Fields for Depth Estimation from a Single Image

arXiv: https://arxiv.org/abs/1411.6387 · HTML: https://mlsanity.com/paper/1411.6387/

## Key facts

- Cited by 106 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2014.

## Built on by (most cited first, 30 of 106)

- [NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimation](https://mlsanity.com/paper/2203.01502/) (2022)
- [Transformer-Based Attention Networks for Continuous Pixel-Wise Prediction](https://mlsanity.com/paper/2103.12091/) (2021)
- [A Study of Face Obfuscation in ImageNet](https://mlsanity.com/paper/2103.06191/) (2021)
- [Transfer Learning from Synthetic to Real LiDAR Point Cloud for Semantic Segmentation](https://mlsanity.com/paper/2107.05399/) (2021)
- [Channel-Wise Attention-Based Network for Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/2112.13047/) (2021)
- [ShapeCrafter: A Recursive Text-Conditioned 3D Shape Generation Model](https://mlsanity.com/paper/2207.09446/) (2022)
- [All in Tokens: Unifying Output Space of Visual Tasks via Soft Token](https://mlsanity.com/paper/2301.02229/) (2023)
- [Virtual Normal: Enforcing Geometric Constraints for Accurate and Robust Depth Prediction](https://mlsanity.com/paper/2103.04216/) (2021)
- [Multi-View Depth Estimation by Fusing Single-View Depth Probability with Multi-View Geometry](https://mlsanity.com/paper/2112.08177/) (2021)
- [Toward Practical Monocular Indoor Depth Estimation](https://mlsanity.com/paper/2112.02306/) (2021)
- [MonoIndoor: Towards Good Practice of Self-Supervised Monocular Depth Estimation for Indoor Environments](https://mlsanity.com/paper/2107.12429/) (2021)
- [HCRF-Flow: Scene Flow from Point Clouds with Continuous High-order CRFs and Position-aware Flow Embedding](https://mlsanity.com/paper/2105.07751/) (2021)
- [RA-Depth: Resolution Adaptive Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/2207.11984/) (2022)
- [HairStep: Transfer Synthetic to Real Using Strand and Depth Maps for Single-View 3D Hair Modeling](https://mlsanity.com/paper/2303.02700/) (2023)
- [Single Image Depth Estimation: An Overview](https://mlsanity.com/paper/2104.06456/) (2021)
- [BiFuse++: Self-supervised and Efficient Bi-projection Fusion for 360 Depth Estimation](https://mlsanity.com/paper/2209.02952/) (2022)
- [BEVNeXt: Reviving Dense BEV Frameworks for 3D Object Detection](https://mlsanity.com/paper/2312.01696/) (2023)
- [SOSD-Net: Joint Semantic Object Segmentation and Depth Estimation from Monocular images](https://mlsanity.com/paper/2101.07422/) (2021)
- [IronDepth: Iterative Refinement of Single-View Depth using Surface Normal and its Uncertainty](https://mlsanity.com/paper/2210.03676/) (2022)
- [When the Sun Goes Down: Repairing Photometric Losses for All-Day Depth Estimation](https://mlsanity.com/paper/2206.13850/) (2022)
- [InfiniDepth: Arbitrary-Resolution and Fine-Grained Depth Estimation with Neural Implicit Fields](https://mlsanity.com/paper/2601.03252/) (2026)
- [DF-VO: What Should Be Learnt for Visual Odometry?](https://mlsanity.com/paper/2103.00933/) (2021)
- [Fast and Accurate Single-Image Depth Estimation on Mobile Devices, Mobile AI 2021 Challenge: Report](https://mlsanity.com/paper/2105.08630/) (2021)
- [Outdoor inverse rendering from a single image using multiview self-supervision](https://mlsanity.com/paper/2102.06591/) (2021)
- [Beyond Monocular Deraining: Parallel Stereo Deraining Network Via Semantic Prior](https://mlsanity.com/paper/2105.03830/) (2021)
- [Robust Depth Completion with Uncertainty-Driven Loss Functions](https://mlsanity.com/paper/2112.07895/) (2021)
- [GLPanoDepth: Global-to-Local Panoramic Depth Estimation](https://mlsanity.com/paper/2202.02796/) (2022)
- [360 Depth Estimation in the Wild -- The Depth360 Dataset and the SegFuse Network](https://mlsanity.com/paper/2202.08010/) (2022)
- [Deep Learning-based Depth Estimation Methods from Monocular Image and Videos: A Comprehensive Survey](https://mlsanity.com/paper/2406.19675/) (2024)
- [ScaleDepth: Decomposing Metric Depth Estimation into Scale Prediction and Relative Depth Estimation](https://mlsanity.com/paper/2407.08187/) (2024)

## Abstract (arXiv)

We consider the problem of depth estimation from a single monocular image in this work. It is a challenging task as no reliable depth cues are available, e.g., stereo correspondences, motions, etc. Previous efforts have been focusing on exploiting geometric priors or additional sources of information, with all using hand-crafted features. Recently, there is mounting evidence that features from deep convolutional neural networks (CNN) are setting new records for various vision applications. On the other hand, considering the continuous characteristic of the depth values, depth estimations can be naturally formulated into a continuous conditional random field (CRF) learning problem. Therefore, we in this paper present a deep convolutional neural field model for estimating depths from a single image, aiming to jointly explore the capacity of deep CNN and continuous CRF. Specifically, we propose a deep structured learning scheme which learns the unary and pairwise potentials of continuous CRF in a unified deep CNN framework. The proposed method can be used for depth estimations of general scenes with no geometric priors nor any extra information injected. In our case, the integral of the partition function can be analytically calculated, thus we can exactly solve the log-likelihood optimization. Moreover, solving the MAP problem for predicting depths of a new image is highly efficient as closed-form solutions exist. We experimentally demonstrate that the proposed method outperforms state-of-the-art depth estimation methods on both indoor and outdoor scene datasets.