RBF-Based Camera Model Based on a Ray Constraint to Compensate for Refraction Error

A camera equipped with a transparent shield can be modeled using the pinhole camera model and residual error vectors defined by the difference between the estimated ray from the pinhole camera model and the actual three-dimensional (3D) point. To calculate the residual error vectors, we employ sparse calibration data consisting of 3D points and their corresponding 2D points on the image. However, the observation noise and sparsity of the 3D calibration points pose challenges in determining the residual error vectors. To address this, we first fit Gaussian Process Regression (GPR) operating robustly against data noise to the observed residual error vectors from the sparse calibration data to obtain dense residual error vectors. Subsequently, to improve performance in unobserved areas due to data sparsity, we use an additional constraint; the 3D points on the estimated ray should be projected to one 2D image point, called the ray constraint. Finally, we optimize the radial basis function (RBF)-based regression model to reduce the residual error vector differences with GPR at the predetermined dense set of 3D points while reflecting the ray constraint. The proposed RBF-based camera model reduces the error of the estimated rays by 6% on average and the reprojection error by 26% on average.