# Refractive Geometry for Underwater Domes

arXiv: https://arxiv.org/abs/2108.06575 · HTML: https://mlsanity.com/paper/2108.06575/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 46 references that are in the map.
- First posted on arXiv 14 Aug 2021.

## Builds on (most cited first, 1 of 1)

- [Calibration Wizard: A Guidance System for Camera Calibration Based on Modelling Geometric and Corner Uncertainty](https://mlsanity.com/paper/1811.03264/) (2018)

## Built on by (most cited first, 6 of 6)

- [Refractive COLMAP: Refractive Structure-from-Motion Revisited](https://mlsanity.com/paper/2403.08640/) (2024)
- [Semihierarchical Reconstruction and Weak-area Revisiting for Robotic Visual Seafloor Mapping](https://mlsanity.com/paper/2308.06147/) (2023)
- [Design, Implementation and Evaluation of an External Pose-Tracking System for Underwater Cameras](https://mlsanity.com/paper/2305.04226/) (2023)
- [Relative Illumination Fields: Learning Medium and Light Independent Underwater Scenes](https://mlsanity.com/paper/2504.10024/) (2025)
- [Marine Bubble Flow Quantification Using Wide-Baseline Stereo Photogrammetry](https://mlsanity.com/paper/2112.07414/) (2021)
- [A Calibration Tool for Refractive Underwater Vision](https://mlsanity.com/paper/2405.18018/) (2024)

## Abstract (arXiv)

Underwater cameras are typically placed behind glass windows to protect them from the water. Spherical glass, a dome port, is well suited for high water pressures at great depth, allows for a large field of view, and avoids refraction if a pinhole camera is positioned exactly at the sphere's center. Adjusting a real lens perfectly to the dome center is a challenging task, both in terms of how to actually guide the centering process (e.g. visual servoing) and how to measure the alignment quality, but also, how to mechanically perform the alignment. Consequently, such systems are prone to being decentered by some offset, leading to challenging refraction patterns at the sphere that invalidate the pinhole camera model. We show that the overall camera system becomes an axial camera, even for thick domes as used for deep sea exploration and provide a non-iterative way to compute the center of refraction without requiring knowledge of exact air, glass or water properties. We also analyze the refractive geometry at the sphere, looking at effects such as forward- vs. backward decentering, iso-refraction curves and obtain a 6th-degree polynomial equation for forward projection of 3D points in thin domes. We then propose a pure underwater calibration procedure to estimate the decentering from multiple images. This estimate can either be used during adjustment to guide the mechanical position of the lens, or can be considered in photogrammetric underwater applications.