A minimal solution to the autocalibration of radial distortion

Zuzana Kukelova (CMP Prague, Czech Republic)

Epipolar geometry and relative camera pose computation are examples of tasks which can be formulated as minimal problems, i.e. they can be 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 suggest improvements of current techniques for solving systems of polynomial equations suitable for some vision problems. We introduce two tricks. The first trick helps to reduce the number of variables and degrees of the equations. The second trick can be used to replace computationally complex construction of Gr?obner basis by a simpler procedure. We demonstrate benefits of our technique by providing 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. We provide an efficient and robust solver of this problem. The quality of the solver is demonstrated on synthetic and real data.