@Article{Kukelova-etal-CVIU-2009,
  IS = { zkontrolovano 09 Apr 2010 },
  UPDATE  = { 2009-10-15 },
  author = {Kukelova, Zuzana and Byrod, Martin and Josephson, Klas and Pajdla, Tomas and Astrom, Kalle},
  title = {Fast and robust numerical solutions to minimal problems for cameras with radial distortion},
  year = {2010},
  month = {February},
  pages = {234--244},
  journal = {Computer Vision and Image Understanding},
  publisher = {Elsevier},
  address = {San Diego, USA},
  issn = {1077-3142},
  volume = {114},
  number = {2},
  annote = {A number of minimal problems of structure from motion for
    cameras with radial distortion have recently been studied and
    solved in some cases. These problems are known to be numerically
    very challenging and in several cases there were no practical
    algorithms yielding solutions in floating point arithmetic. We
    make some crucial observations concerning the floating point
    implementation of Groebner basis computations and use these new
    insights to formulate fast and stable algorithms for two minimal
    problems with radial distortion previously solved in exact
    rational arithmetic only: (i) simultaneous estimation of essential
    matrix and a common radial distortion parameter for two partially
    calibrated views and six image point correspondences and (ii)
    estimation of fundamental matrix and two different radial
    distortion parameters for two uncalibrated views and nine image
    point correspondences. We demonstrate that these two problems can
    be efficiently solved in floating point arithmetic in simulated
    and real experiments. For comparison we have also invented a new
    non-minimal algorithm for estimating fundamental matrix and two
    different radial distortion parameters for two uncalibrated views
    and twelve image point correspondences based on a generalized
    eigenvalue problem.},
  keywords = {radial distortion calibration, minimal problems, Groebner basis},
  authorship = {30-30-20-10-10},
  project = {FP7-SPACE-218814 PRoVisG, MSM6840770038},
  prestige = {important},
  note = {in press, DOI: 10.1016/j.cviu.2008.11.008},
}