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In this paper, we present a novel refractive calibration method for an underwater stereo camera system where both cameras are looking through multiple parallel flat refractive interfaces. At the heart of our method is an important finding that the thickness of the interface can be estimated from a set of pixel correspondences in the stereo images when the refractive axis is given. To our best knowledge, such a finding has not been studied or reported. Moreover, by exploring the search space for the refractive axis and using reprojection error as a measure, both the refractive axis and the thickness of the interface can be recovered simultaneously. Our method does not require any calibration target such as a checkerboard pattern which may be difficult to manipulate when the cameras are deployed deep undersea. The implementation of our method is simple. In particular, it only requires solving a set of linear equations of the form $Ax = b$ and applies sparse bundle adjustment to refine the initial estimated results. Extensive experiments have been carried out which include simulations with and without outliers to verify the correctness of our method as well as to test its robustness to noise and outliers. The results of real experiments are also provided. The accuracy of our results is comparable to that of a state-of-the-art method that requires known 3D geometry of a scene.
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