A minimal solution to the autocalibration of radial distortion

Epipolar geometry and relative camera pose computation are examples of tasks which can be formulated as minimal problems and solved from a minimal number of image points. Finding the solution leads to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this paper we provide a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the problem from nine correspondences only, we enforce the determinant of the fundamental matrix be zero. This leads to a system of eight quadratic and one cubic equation in nine variables. We simplify the system by eliminating six of these variables. Then, we solve the system by finding eigenvectors of an action matrix of a suitably chosen polynomial. We show how to construct the action matrix without ...

• Type: Conference
• Year: 2007
• Where: CVPR
• Authors: Tomás Pajdla, Zuzana Kukelova
• Keywords: Action Matrix, Computer Vision, CVPR 2007, Epipolar Geometry, Fundamental Matrix, Relative Camera Pose, Robust Solver