Underwater Dome-Port Camera Calibration: Modeling of Refraction and Offset through N-Sphere Camera Model

The optical effects that are observed in underwater imagery are more complex than those in-air. This is partially because we enclose most underwater cameras in a watertight enclosure, such as a hemispheric dome window. We then observe optical issues including the distortion effects of the lens, e.g., wide-angle field-of-view (FOV), the refractive effects at the enclosure (water-acrylic and acrylic-air) interfaces, and offset effects of a non-centered camera with respect to the dome. In this paper, we present an N-Sphere (NS) and Shifted N-Sphere (S-NS) camera models, tailored to these cameras and lenses mounted in water-tight dome enclosures. The proposed camera models treat each layer of effects as a ‘sphere’ that a 3D point will project on. Furthermore, the S-NS model includes additional parameters to address the camera offset variability. The versatility of the NS model makes it applicable to various lenses, as validated with fisheye (FOV >120°) and wide-FOV (FOV ≈ 120°). We validated our models with different in-water calibration sequences, lenses, and housing setups, as well as with comparisons with other state-of-the-art camera models. Additionally, we demonstrated the performance of our proposed models in an example stereo-based visual odometry application. The low computational load of the proposed models makes it ideal for integrating in real-time visual navigation and reconstruction frameworks. We provide full math derivations of the proposed models as well as example C++ header files
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for easy incorporation in independent projects.