Forward projection multilayer refraction model for underwater camera calibration

Unlike imaging in air, underwater imaging is affected by two distinct properties of water: the absorption and scattering effect of water and the refraction effect of water, resulting in the conventional pinhole model no longer being suitable for underwater imaging. Therefore, without prior calibration in air to calculate the camera intrinsic parameters and distortions for subsequent underwater calibration, an underwater multilayer refraction model based on forward projection method is represented. Along the direction of light propagation, the multilayer refraction model presents a unified scale factor instead of focal length during the perspective projection transformation from the camera coordinate system to the image coordinate system. Simulations regarding the analysis of different medium thicknesses, different medium refractive indices, and different point pixels are performed to explore the influence of the above three parameters on the refraction model. Through the underwater parameter identification and verification, the proposed multilayer refraction model has high measurement accuracy, excellent solution efficiency, stable identification results, more identification parameters, and wide application fields, which are suitable for both single-time refraction and double-time refraction.