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Refractive Epipolar Geometry for Underwater Stereo Matching

A fundamental component of stereo vision is that of epipolar geometry. It tells us that the corresponding point of a pixel in one image is restricted to a line in another image. This constraint reduces both the complexity of finding stereo correspondences and also the chance of making incorrect matches. When a refractive surface is introduced, which is in underwater imaging, this constraint no longer holds. Instead, the corresponding point of a pixel in one image is now restricted to a curve, not a line. In this paper we investigate the impact of a planar refractive interface has on underwater imaging and stereo matching. We address the issue of 3D point projection in a refractive medium, including cases where the refractive interface is not parallel with the camera's imaging plane. A novel method for calibrating the parameters of a planar refractive interface in the local image space is proposed. We show how to compute the refractive epipolar curve for a pixel, which allows us to generate a matching cost volume that compensates for the effects of refraction. Our experimental results show that our new approach can significantly improve the results of underwater stereo matching over previous approaches.