IS = { zkontrolovano 15 Dec 2007 },
  UPDATE  = { 2007-12-11 },
  key =         {Kukelova-Pajdla-OMNIVIS2007},
  author =      {Kukelova, Zuzana and Pajdla, Tomas},
  title =       {Two Minimal Problems for Cameras with Radial Distortion},
  year =        {2007},
  pages =       {8},
  booktitle =   {OMNIVIS 2007: Proceedings of The Seventh Workshop on Omnidirectional Vision, 
                 Camera Networks and Non-classical Cameras},
  publisher =   {IEEE Computer Society Press},
  address =     {Los Alamitos, USA},
  isbn =        {978-1-4244-1631-8},
  book_pages =  {2240},
  month =       {October},
  day =         {20},
  venue =       {Rio de Janeiro, Brazil},
  organization ={IEEE Computer Society},
  annote = {Epipolar geometry and relative camera pose computation for
    uncalibrated cameras with radial distortion has recently been
    formulated as a minimal problem and successfully solved in
    floating point arithmetics. The singularity of the fundamental
    matrix has been used to reduce the minimal number of points to
    eight.  It was assumed that the cameras were not calibrated but
    had same distortions. In this paper we formulate two new minimal
    problems for estimating epipolar geometry of cameras with radial
    distortion.  First we present a minimal algorithm for partially
    calibrated cameras with same radial distortion. Using the trace
    constraint which holds for the epipolar geometry of calibrated
    cameras to reduce the number of necessary points from eight to
    six. We demonstrate that the problem is solvable in exact rational
    arithmetics.  Secondly, we present a minimal algorithm for
    uncalibrated cameras with different radial distortions. We show
    that the problem can be solved using nine points in two views by
    manipulating polynomials by a sequence of Gauss-Jordan
    eliminations in exact rational arithmetics. We demonstrate the
    algorithms 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 },
  note =        {CDROM},