IS = { zkontrolovano 15 Dec 2007 },
  UPDATE  = { 2007-12-11 },
  author =      {Kukelova, Zuzana and Pajdla, Tomas},
  title =       {Solving polynomial equations for minimal problems in computer vision},
  year =        {2007},
  pages =       {8},
  booktitle =   {CVWW 2007: Proceedings of the 12th Computer Vision Winter Workshop},
  editor =      {Michael Grabner and Helmut Grabner},
  publisher =   {Verlag der Technischen Universit{\"a}t Graz},
  address =     {Graz, Austria},
  isbn =        {978-3-902465-60-3},
  book_pages =  {146},
  month =       {February},
  day =         {6-8},
  venue =       {St. Lambrecht, Austria},
  organization ={Institute for Computer Graphics and Vision, 
                 Graz University of Technology, Gratz, Austria},
  annote = {Many vision tasks require efficient solvers of systems of
    polynomial equations.  Epipolar geometry and relative camera pose
    computation are tasks which can be formulated as minimal problems
    which lead 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 work 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\"{o}bner 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.  },
  note =        {out of proceedings},
  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 },