# CoL3D: Collaborative Learning of Single-view Depth and Camera Intrinsics for Metric 3D Shape Recovery

arXiv: https://arxiv.org/abs/2502.08902 · HTML: https://mlsanity.com/paper/2502.08902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 55 references that are in the map.
- First posted on arXiv 13 Feb 2025.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [ZoeDepth: Zero-shot Transfer by Combining Relative and Metric Depth](https://mlsanity.com/paper/2302.12288/) (2023)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (2018)
- [AdaBins: Depth Estimation using Adaptive Bins](https://mlsanity.com/paper/2011.14141/) (2020)
- [PIFuHD: Multi-Level Pixel-Aligned Implicit Function for High-Resolution 3D Human Digitization](https://mlsanity.com/paper/2004.00452/) (2020)
- [From Big to Small: Multi-Scale Local Planar Guidance for Monocular Depth Estimation](https://mlsanity.com/paper/1907.10326/) (2019)
- [UniDepth: Universal Monocular Metric Depth Estimation](https://mlsanity.com/paper/2403.18913/) (2024)
- [Metric3D: Towards Zero-shot Metric 3D Prediction from A Single Image](https://mlsanity.com/paper/2307.10984/) (2023)
- [Learning to Recover 3D Scene Shape from a Single Image](https://mlsanity.com/paper/2012.09365/) (2020)
- [BinsFormer: Revisiting Adaptive Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2204.00987/) (2022)
- [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)
- [DepthFormer: Exploiting Long-Range Correlation and Local Information for Accurate Monocular Depth Estimation](https://mlsanity.com/paper/2203.14211/) (2022)
- [P3Depth: Monocular Depth Estimation with a Piecewise Planarity Prior](https://mlsanity.com/paper/2204.02091/) (2022)
- [Towards Zero-Shot Scale-Aware Monocular Depth Estimation](https://mlsanity.com/paper/2306.17253/) (2023)
- [LocalBins: Improving Depth Estimation by Learning Local Distributions](https://mlsanity.com/paper/2203.15132/) (2022)
- [CAM-Convs: Camera-Aware Multi-Scale Convolutions for Single-View Depth](https://mlsanity.com/paper/1904.02028/) (2019)
- [Perspective Fields for Single Image Camera Calibration](https://mlsanity.com/paper/2212.03239/) (2022)
- [iDisc: Internal Discretization for Monocular Depth Estimation](https://mlsanity.com/paper/2304.06334/) (2023)
- [Learning Shape Priors for Single-View 3D Completion and Reconstruction](https://mlsanity.com/paper/1809.05068/) (2018)
- [OASIS: A Large-Scale Dataset for Single Image 3D in the Wild](https://mlsanity.com/paper/2007.13215/) (2020)
- [VA-DepthNet: A Variational Approach to Single Image Depth Prediction](https://mlsanity.com/paper/2302.06556/) (2023)
- [IEBins: Iterative Elastic Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2309.14137/) (2023)
- [A Perceptual Measure for Deep Single Image Camera Calibration](https://mlsanity.com/paper/1712.01259/) (2017)

## Abstract (arXiv)

Recovering the metric 3D shape from a single image is particularly relevant for robotics and embodied intelligence applications, where accurate spatial understanding is crucial for navigation and interaction with environments. Usually, the mainstream approaches achieve it through monocular depth estimation. However, without camera intrinsics, the 3D metric shape can not be recovered from depth alone. In this study, we theoretically demonstrate that depth serves as a 3D prior constraint for estimating camera intrinsics and uncover the reciprocal relations between these two elements. Motivated by this, we propose a collaborative learning framework for jointly estimating depth and camera intrinsics, named CoL3D, to learn metric 3D shapes from single images. Specifically, CoL3D adopts a unified network and performs collaborative optimization at three levels: depth, camera intrinsics, and 3D point clouds. For camera intrinsics, we design a canonical incidence field mechanism as a prior that enables the model to learn the residual incident field for enhanced calibration. Additionally, we incorporate a shape similarity measurement loss in the point cloud space, which improves the quality of 3D shapes essential for robotic applications. As a result, when training and testing on a single dataset with in-domain settings, CoL3D delivers outstanding performance in both depth estimation and camera calibration across several indoor and outdoor benchmark datasets, which leads to remarkable 3D shape quality for the perception capabilities of robots.