Universal underwater camera calibration method based on a forward multilayer refractive model

Multiple refractions between different media lead to camera refractive distortions, thereby making it difficult to ensure underwater measurement accuracy. Consequently, precise modeling and calibration of underwater multilayer imaging systems is essential to address these distortions. In this paper, employing a perspective projection scale factor along the light propagation direction, a universal forward multilayer refractive model is presented. On this basis, the refractive model incorporates a general rotation matrix, which not only enriches application diversity but also enhances solution precision. Allowing for direct underwater camera calibration without prior calibration in air, the model simplifies the calibration process and enhances its suitability for practical applications. Through underwater calibration experiments, the refractive model enhances solution efficiency, improves identification precision and distributes evenly and mediately in terms of reprojection error. In addition, it increases the number of identifiable parameters, demonstrating its robustness and superiority in complex parameter identification scenarios. Finally, underwater measurement experiments indicate that the absolute accuracy calibrated and measured by the refractive model is better than 0.25 mm. Overall, combining all the benefits of forward and backward compensation methods, the forward refractive model offers versatility in handling multiple refractions without limited refractive layers.