# Structure from Motion on a Sphere

arXiv: https://arxiv.org/abs/1604.00409 · HTML: https://mlsanity.com/paper/1604.00409/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2016.

## Built on by (most cited first, 4 of 4)

- [Camera Calibration using a Collimator System](https://mlsanity.com/paper/2409.20034/) (2024)
- [LighthouseGS: Indoor Structure-aware 3D Gaussian Splatting for Panorama-Style Mobile Captures](https://mlsanity.com/paper/2507.06109/) (2025)
- [DFR: Depth from Rotation by Uncalibrated Image Rectification with Latitudinal Motion Assumption](https://mlsanity.com/paper/2307.05129/) (2023)
- [Flexible Camera Calibration using a Collimator System](https://mlsanity.com/paper/2512.16113/) (2025)

## Abstract (arXiv)

We describe a special case of structure from motion where the camera rotates on a sphere. The camera's optical axis lies perpendicular to the sphere's surface. In this case, the camera's pose is minimally represented by three rotation parameters. From analysis of the epipolar geometry we derive a novel and efficient solution for the essential matrix relating two images, requiring only three point correspondences in the minimal case. We apply this solver in a structure-from-motion pipeline that aggregates pairwise relations by rotation averaging followed by bundle adjustment with an inverse depth parameterization. Our methods enable scene modeling with an outward-facing camera and object scanning with an inward-facing camera.