The Pinax-model for accurate and efficient refraction correction of underwater cameras in flat-pane housings

The calibration and refraction correction process for underwater cameras with flat-pane interfaces is presented that is very easy and convenient to use in real world applications while yielding very accurate results. The correction is derived from an analysis of the axial camera model for underwater cameras, which is among others computationally hard to tackle. It is shown how realistic constraints on the distance of the camera to the window can be exploited, which leads to an approach dubbed Pinax Model as it combines aspects of a virtual pinhole model with the projection function from the axial camera model. It allows the pre-computation of a lookup-table for very fast refraction correction of the flat-pane with high accuracy. The model takes the refraction indices of water into account, especially with respect to salinity, and it is therefore sufficient to calibrate the underwater camera only once in air. It is demonstrated by real world experiments with several underwater cameras in different salt and sweet water conditions that the proposed process outperforms standard methods. Among others, it is shown how the presented method leads to accurate results with single in-air calibration and even with just estimated salinity values.