# Depth Estimation via Affinity Learned with Convolutional Spatial Propagation Network

arXiv: https://arxiv.org/abs/1808.00150 · HTML: https://mlsanity.com/paper/1808.00150/

## Key facts

- Cited by 110 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2018.

## Built on by (most cited first, 30 of 110)

- [Metric3Dv2: A Versatile Monocular Geometric Foundation Model for Zero-shot Metric Depth and Surface Normal Estimation](https://mlsanity.com/paper/2404.15506/) (2024)
- [Dense Depth Priors for Neural Radiance Fields from Sparse Input Views](https://mlsanity.com/paper/2112.03288/) (2021)
- [PENet: Towards Precise and Efficient Image Guided Depth Completion](https://mlsanity.com/paper/2103.00783/) (2021)
- [CompletionFormer: Depth Completion with Convolutions and Vision Transformers](https://mlsanity.com/paper/2304.13030/) (2023)
- [Pow3R: Empowering Unconstrained 3D Reconstruction with Camera and Scene Priors](https://mlsanity.com/paper/2503.17316/) (2025)
- [Dynamic Spatial Propagation Network for Depth Completion](https://mlsanity.com/paper/2202.09769/) (2022)
- [RGB-D Local Implicit Function for Depth Completion of Transparent Objects](https://mlsanity.com/paper/2104.00622/) (2021)
- [Unsupervised Depth Completion with Calibrated Backprojection Layers](https://mlsanity.com/paper/2108.10531/) (2021)
- [TransCG: A Large-Scale Real-World Dataset for Transparent Object Depth Completion and a Grasping Baseline](https://mlsanity.com/paper/2202.08471/) (2022)
- [VA-DepthNet: A Variational Approach to Single Image Depth Prediction](https://mlsanity.com/paper/2302.06556/) (2023)
- [PanoDiffusion: 360-degree Panorama Outpainting via Diffusion](https://mlsanity.com/paper/2307.03177/) (2023)
- [Marigold-DC: Zero-Shot Monocular Depth Completion with Guided Diffusion](https://mlsanity.com/paper/2412.13389/) (2024)
- [Correlate-and-Excite: Real-Time Stereo Matching via Guided Cost Volume Excitation](https://mlsanity.com/paper/2108.05773/) (2021)
- [Visual Reinforcement Learning with Self-Supervised 3D Representations](https://mlsanity.com/paper/2210.07241/) (2022)
- [Towards Accurate Reconstruction of 3D Scene Shape from A Single Monocular Image](https://mlsanity.com/paper/2208.13241/) (2022)
- [Sparse Auxiliary Networks for Unified Monocular Depth Prediction and Completion](https://mlsanity.com/paper/2103.16690/) (2021)
- [Deep Depth Completion from Extremely Sparse Data: A Survey](https://mlsanity.com/paper/2205.05335/) (2022)
- [Less is More: Consistent Video Depth Estimation with Masked Frames Modeling](https://mlsanity.com/paper/2208.00380/) (2022)
- [Sparsity Agnostic Depth Completion](https://mlsanity.com/paper/2212.00790/) (2022)
- [DELTAR: Depth Estimation from a Light-weight ToF Sensor and RGB Image](https://mlsanity.com/paper/2209.13362/) (2022)
- [Depth Prompting for Sensor-Agnostic Depth Estimation](https://mlsanity.com/paper/2405.11867/) (2024)
- [Depth Completion using Plane-Residual Representation](https://mlsanity.com/paper/2104.07350/) (2021)
- [Monitored Distillation for Positive Congruent Depth Completion](https://mlsanity.com/paper/2203.16034/) (2022)
- [Invisible Stitch: Generating Smooth 3D Scenes with Depth Inpainting](https://mlsanity.com/paper/2404.19758/) (2024)
- [GraphCSPN: Geometry-Aware Depth Completion via Dynamic GCNs](https://mlsanity.com/paper/2210.10758/) (2022)
- [Multi-view Reconstruction via SfM-guided Monocular Depth Estimation](https://mlsanity.com/paper/2503.14483/) (2025)
- [RGB-Depth Fusion GAN for Indoor Depth Completion](https://mlsanity.com/paper/2203.10856/) (2022)
- [Revisiting Depth Completion from a Stereo Matching Perspective for Cross-domain Generalization](https://mlsanity.com/paper/2312.09254/) (2023)
- [DenseLiDAR: A Real-Time Pseudo Dense Depth Guided Depth Completion Network](https://mlsanity.com/paper/2108.12655/) (2021)
- [Improving Monocular Visual Odometry Using Learned Depth](https://mlsanity.com/paper/2204.01268/) (2022)

## Abstract (arXiv)

Depth estimation from a single image is a fundamental problem in computer vision. In this paper, we propose a simple yet effective convolutional spatial propagation network (CSPN) to learn the affinity matrix for depth prediction. Specifically, we adopt an efficient linear propagation model, where the propagation is performed with a manner of recurrent convolutional operation, and the affinity among neighboring pixels is learned through a deep convolutional neural network (CNN). We apply the designed CSPN to two depth estimation tasks given a single image: (1) To refine the depth output from state-of-the-art (SOTA) existing methods; and (2) to convert sparse depth samples to a dense depth map by embedding the depth samples within the propagation procedure. The second task is inspired by the availability of LIDARs that provides sparse but accurate depth measurements. We experimented the proposed CSPN over two popular benchmarks for depth estimation, i.e. NYU v2 and KITTI, where we show that our proposed approach improves in not only quality (e.g., 30% more reduction in depth error), but also speed (e.g., 2 to 5 times faster) than prior SOTA methods.