Improving underwater accuracy by empirical weighting of image observations

An underwater imaging system with camera and lens behind a flat port does not behave as a standard pinhole camera with additional parameters. Indeed, whenever the entrance pupil of the lens is not in contact with the flat port, the standard photogrammetric model is not suited anymore and an extended mathematical model that considers the different media would be required. Therefore, when dealing with flat ports, the use of the classic photogrammetric formulation represents a simplification of the image formation phenomenon, clearly causing a degradation in accuracy. Furthermore, flat ports significantly change the characteristics of the enclosed imaging device and negatively affect the image quality, introducing heavy curvilinear distortions and optical aberrations. With the aim of mitigating the effect of systematic errors introduced by a combination of (i) image quality degradation, induced by the flat ports, and (ii) a non-rigorous modelling of refraction, this paper presents a stochastic model for image observations that penalises those that are more affected by aberrations and departure from the pinhole model. Experiments were carried out at sea and in pools showing that the use of the proposed stochastic model is beneficial for the final accuracy with improvements up to 50 %.