The recently introduced Rational Function (RF) model permits a linear solution of epipolar geometry and lens distortion from image correspondences for a very general class of lenses. In this paper we show that the model also permits a very elegant form of the plumbline constraint which allows uncalibrated correction of lens distortion from a single image containing lines known to be straight in the world. We show how this may be expressed as a factorization problem, and discuss its behaviour with noisy data. We also introduce a simple reduced parametrization of the RF model which again models a range of existing lenses. Because the RF model provides a very simple form for the distorted lines, nonlinear minimization can compute the Sampson distance to the distorted lines, allowing fast and accurate estimation of the RF model even from noisy images.

We introduce a new rational function (RF) model for radial lens distortion in wide-angle and catadioptric lenses, which allows the simultaneous linear estimation of motion and lens geometry from two uncalibrated views of a 3D scene. In contrast to existing models which admit such linear estimates, the new model is not specialized to any particular lens geometry, but is sufficiently general to model a variety of extreme distortions. The key step is to define the mapping between image (pixel) coordinates and 3D rays in camera coordinates as a linear combination of nonlinear functions of the image coordinates. Like a "kernel trick", this allows a linear algorithm to estimate nonlinear models, and in particular offers a simple solution to the estimation of nonlinear image distortion. The model also yields an explicit form for the epipolar curves, allowing correspondence search to be efficiently guided by the epipolar geometry. We show results of an implementation of the RF model in estimating the geometry of a real camera lens from uncalibrated footage, and compare the estimate to one obtained using a calibration grid.