@InProceedings{Kukelova-Pajdla-CVPR-2007-InProceedings, IS = { zkontrolovano 15 Dec 2007 }, UPDATE = { 2007-12-11 }, author = {Kukelova, Zuzana and Pajdla, Tomas}, title = {A minimal solution to the autocalibration of radial distortion}, year = {2007}, pages = {7}, booktitle = {Proceedings of the Computer Vision and Pattern Recognition conference (CVPR)}, publisher = {IEEE Computer Society Press}, address = {Los Alamitos, USA}, isbn = {1-4244-1180-7 }, book_pages = {2816}, month = {June}, day = {19-21}, venue = { Minneapolis, Minnesota , USA}, organization ={IEEE Computer Society}, annote = { 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 this 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 computing complete Gr\"{o}bner basis, which provides an efficient and robust solver. The quality of the solver is demonstrated on synthetic and real data. }, keywords = {Gr\"{o}bner basis, minimal problems, radial distortion}, authorship = {50-50}, project = {FP6-IST-027787 DIRAC, MSM6840770038}, psurl = { [PDF] }, www = { Zuzana Kukelova , Tomas Pajdla }, prestige = { important }, note = { CD-ROM }, }