Modeling the Effects of Windshield Refraction for Camera Calibration

In this paper, we study the effects of windshield refraction for autonomous driving applications. These distortion effects are surprisingly large and can not be explained by traditional camera models. Instead of using a generalized camera approach, we propose a novel approach to jointly optimize a traditional camera model, and a mathematical representation of the windshield’s surface. First, using the laws of geometric optics, the refraction is modeled using a local spherical approximation to the windshield’s geometry. Next, a spline-based model is proposed as a refinement to better adapt to deviations from the ideal shape and manufacturing variations. By jointly optimizing refraction and camera parameters, the projection error can be significantly reduced. The proposed models are validated on real windshield observations and custom setups to compare recordings with and without windshield, with accurate laser scan measurements as 3D ground truth.