# The Double Sphere Camera Model

arXiv: https://arxiv.org/abs/1807.08957 · HTML: https://mlsanity.com/paper/1807.08957/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2018.

## Built on by (most cited first, 30 of 52)

- [Aria Digital Twin: A New Benchmark Dataset for Egocentric 3D Machine Perception](https://mlsanity.com/paper/2306.06362/) (2023)
- [UniK3D: Universal Camera Monocular 3D Estimation](https://mlsanity.com/paper/2503.16591/) (2025)
- [EndoMapper dataset of complete calibrated endoscopy procedures](https://mlsanity.com/paper/2204.14240/) (2022)
- [GeoCalib: Learning Single-image Calibration with Geometric Optimization](https://mlsanity.com/paper/2409.06704/) (2024)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [Surround-view Fisheye Camera Perception for Automated Driving: Overview, Survey and Challenges](https://mlsanity.com/paper/2205.13281/) (2022)
- [Demonstrating Agile Flight from Pixels without State Estimation](https://mlsanity.com/paper/2406.12505/) (2024)
- [360Loc: A Dataset and Benchmark for Omnidirectional Visual Localization with Cross-device Queries](https://mlsanity.com/paper/2311.17389/) (2023)
- [SVDistNet: Self-Supervised Near-Field Distance Estimation on Surround View Fisheye Cameras](https://mlsanity.com/paper/2104.04420/) (2021)
- [Near-field Perception for Low-Speed Vehicle Automation using Surround-view Fisheye Cameras](https://mlsanity.com/paper/2103.17001/) (2021)
- [Learning Quadrotor Control From Visual Features Using Differentiable Simulation](https://mlsanity.com/paper/2410.15979/) (2024)
- [AnyCalib: On-Manifold Learning for Model-Agnostic Single-View Camera Calibration](https://mlsanity.com/paper/2503.12701/) (2025)
- [Self-Supervised Camera Self-Calibration from Video](https://mlsanity.com/paper/2112.03325/) (2021)
- [Contrastive Learning for Enhancing Robust Scene Transfer in Vision-based Agile Flight](https://mlsanity.com/paper/2309.09865/) (2023)
- [BabelCalib: A Universal Approach to Calibrating Central Cameras](https://mlsanity.com/paper/2109.09704/) (2021)
- [F2BEV: Bird's Eye View Generation from Surround-View Fisheye Camera Images for Automated Driving](https://mlsanity.com/paper/2303.03651/) (2023)
- [Continuous-Time Spatiotemporal Calibration of a Rolling Shutter Camera-IMU System](https://mlsanity.com/paper/2108.07200/) (2021)
- [Depth360: Self-supervised Learning for Monocular Depth Estimation using Learnable Camera Distortion Model](https://mlsanity.com/paper/2110.10415/) (2021)
- [A Monocular Event-Camera Motion Capture System](https://mlsanity.com/paper/2502.12113/) (2025)
- [Wid3R: Wide Field-of-View 3D Reconstruction via Camera Model Conditioning](https://mlsanity.com/paper/2602.05321/) (2026)
- [Robust 360-8PA: Redesigning The Normalized 8-point Algorithm for 360-FoV Images](https://mlsanity.com/paper/2104.10900/) (2021)
- [Geometry-Informed Distance Candidate Selection for Adaptive Lightweight Omnidirectional Stereo Vision with Fisheye Images](https://mlsanity.com/paper/2405.05355/) (2024)
- [Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)](https://mlsanity.com/paper/2508.07775/) (2025)
- [Modeling dynamic target deformation in camera calibration](https://mlsanity.com/paper/2110.07322/) (2021)
- [eKalibr: Dynamic Intrinsic Calibration for Event Cameras From First Principles of Events](https://mlsanity.com/paper/2501.05688/) (2025)
- [Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations](https://mlsanity.com/paper/2506.06780/) (2025)
- [Low-Latency Event-Based Velocimetry for Quadrotor Control in a Narrow Pipe](https://mlsanity.com/paper/2507.15444/) (2025)
- [FastViDAR: Real-Time Omnidirectional Depth Estimation via Alternative Hierarchical Attention](https://mlsanity.com/paper/2509.23733/) (2025)
- [CalibAnyView: Beyond Single-View Camera Calibration in the Wild](https://mlsanity.com/paper/2605.14615/) (2026)
- [Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields](https://mlsanity.com/paper/2107.06028/) (2021)

## Abstract (arXiv)

Vision-based motion estimation and 3D reconstruction, which have numerous applications (e.g., autonomous driving, navigation systems for airborne devices and augmented reality) are receiving significant research attention. To increase the accuracy and robustness, several researchers have recently demonstrated the benefit of using large field-of-view cameras for such applications. In this paper, we provide an extensive review of existing models for large field-of-view cameras. For each model we provide projection and unprojection functions and the subspace of points that result in valid projection. Then, we propose the Double Sphere camera model that well fits with large field-of-view lenses, is computationally inexpensive and has a closed-form inverse. We evaluate the model using a calibration dataset with several different lenses and compare the models using the metrics that are relevant for Visual Odometry, i.e., reprojection error, as well as computation time for projection and unprojection functions and their Jacobians. We also provide qualitative results and discuss the performance of all models.