An Efficient Model for a Camera Behind a Parallel Refractive Slab

We present a new and efficient solution for the forward world to image projection of a pinhole camera with distortions placed behind a planar refractive slab. Firstly, we introduce a novel way to compute the projection by reducing the problem to finding a real quantity called a slab shift. We characterize a physically meaningful slab shift as the unique solution of a fixed point equation on the one hand and as a specific uniquely defined root of a quartic polynomial in the unknown slab shift on the other. In the latter case we obtain a closed-form formula, which provides the unique physically meaningful projection. Secondly, we develop an approximation of the projection through the slab that reaches single-precision floating point accuracy for practically relevant problem instances with considerably lower computational costs compared to the exact solution. We demonstrate the accuracy and the efficiency of our method with realistic synthetic experiments. We demonstrate with real experiments that our method enables efficient camera calibration behind the windshield for automotive industry applications.