Efficient Solution to the Epipolar Geometry for Radially Distorted Cameras

Zuzana Kukelova, Jan Heller, Martin Bujnak, Andrew Fitzgibbon, Tomas Pajdla; Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2015, pp. 2309-2317

The estimation of the epipolar geometry of two cameras from image matches is a fundamental problem of computer vision with many applications. While the closely related problem of estimating relative pose of two different uncalibrated cameras with radial distortion is of particular importance, none of the previously published methods is suitable for practical applications. These solutions are either numerically unstable, sensitive to noise, based on a large number of point correspondences, or simply too slow for real-time applications. In this paper, we present a new efficient solution to this problem that uses 10 image correspondences. By manipulating ten input polynomial equations, we derive a degree 10 polynomial equation in one variable. The solutions to this equation are efficiently found using the Sturm sequences method. In the experiments, we show that the proposed solution is stable, noise resistant, and fast, and as such efficiently usable in a practical Structure-from-Motion pipeline.