@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 },
}