Estimating the fundamental matrix under pure translation and radial distortion

Four algorithms for estimating the fundamental matrix and radial distortion for the case that the images are related by a pure camera translation are proposed. This restricted class of motions is important in robotics and industrial applications. It is assumed that the radial distortions can be modeled by the division model. First, a linear 3-point minimal solver is derived, which is essential to drive a RANSAC algorithm. The minimal solver is then extended to an overdetermined linear solver, which is essential to compute starting values for the third algorithm, a Gold Standard solver that returns the maximum likelihood estimate fundamental matrix and radial distortion. The three algorithms are combined into a RANSAC algorithm that determines the fundamental matrix and radial distortion automatically. An experimental evaluation determines the characteristics of the algorithms and shows the high accuracy, precision, and robustness that can be achieved. Furthermore, the evaluation shows that using algorithms that determine the fundamental matrix and radial distortion for general camera motions are not a viable alternative for the case of pure camera translations because they are significantly slower and less robust than the algorithms proposed here.