@InProceedings{Bujnak-Kukelova-Pajdla-CVPR-2012,
  IS = { zkontrolovano 14 Jan 2013 },
  UPDATE  = { 2012-10-10 },
  author = {Bujnak, Martin and Kukelova, Zuzana and Pajdla, Tom{\'a}{\v s}},
  title = {Making Minimal Solvers Fast},
  booktitle = {CVPR 2012: Proceedings of the 2012 IEEE Computer Society
               Conference on Computer Vision and Pattern Recognition},
  year = {2012},
  pages = {1506-1513},
  publisher = {IEEE Computer Society Press},
  address = {New York, USA},
  month = {June},
  organization = {IEEE Computer Society},
  annote = {In this paper we propose methods for speeding up minimal
    solvers based on Gr\"{o}bner bases and action matrix eigenvalue
    computations.  Almost all existing Gr\"{o}bner basis solvers spend
    most time in the eigenvalue computation. We present two methods
    which speed up this phase of Gr\"{o}bner basis solvers: (1) a
    method based on a modified FGLM algorithm for transforming
    Gr\"{o}bner bases which results in a single-variable polynomial
    followed by direct calculation of its roots using Sturm-sequences
    and, for larger problems, (2) fast calculation of the
    characteristic polynomial of an action matrix, again solved using
    Sturm-sequences. We enhanced the FGLM method by replacing time
    consuming polynomial division performed in standard FGLM algorithm
    with efficient matrix-vector multiplication and we show how this
    method is related to the characteristic polynomial method. Our
    approaches allow computing roots only in some feasible interval
    and in desired precision. Proposed methods can significantly
    speedup many existing solvers. We demonstrate them on three
    important minimal computer vision problems.},
  authorship = {34-33-33},
  book_pages = {3696},
  day = {16-21},
  doi = {10.1109/CVPR.2012.6247853},
  isbn = {978-1-4673-1228-8},
  issn = {1063-6919},
  keywords = {Minimal problems, Gr\"{o}bner basis},
  prestige = {important},
  project = {FP7-SPACE-218814 PRoVisG, FP7-SPACE-241523 PRoViScout, SGS12/191/OHK3/3T/13},
  psurl = {[10.1109/CVPR.2012.6247840.pdf]},
  venue = {Providence, USA},
  ut_isi = {000309166201083},
}