Theory of multi-level refractive geometry

When capturing images of a submerged object using a conventional digital camera in the air, the light ray no longer travels along a straight line due to refraction occurring at the interface between different media, making the traditional multi-view geometry based on a perspective camera model invalid. By analysing the imaging formulation of a submerged object and taking into account refraction effects, a novel theory of multi-level refractive geometry for refractive camera calibration and for submerged scene depth perception is proposed. The effectiveness and efficiency of the proposed theory are verified by experiments on synthetic datasets under various imaging configurations. The proposed theory is believed to be the first that allows recovering both the pose of the camera and the depth of a submerged object simultaneously, without using any calibration object or a priori camera pose.