@InProceedings{Chum-BMVC03,
  IS = { zkontrolovano 25 Mar 2004 },
  UPDATE  = { 2003-10-09 },
  author =      {Chum, Ond{\v r}ej and Werner, Tom{\' a}{\v s} and 
                 Pajdla, Tom{\' a}{\v s}},
  title =       {Joint Orientation of Epipoles},
  year =        {2003},
  pages =       {73--82},
  booktitle =   {BMVC 2003: Proceedings of the 14th British
                 Machine Vision Conference},
  editor =      {Harvey, Richard},
  publisher =   {BMVA},
  address =     {London, UK},
  isbn =        {1-901725-23-5},
  volume =      {1},
  book_pages =  {813},
  month =       {September},
  day =         {9--11},
  venue =       {Norwich, UK},
  organization ={BMVA},
  annote = {It is known that epipolar constraint can be augmented with
    orientation by formulating it in the oriented projective geometry.
    This oriented epipolar constraint requires knowing the
    orientations (signs of overall scales) of epipoles and fundamental
    matrix.  The current belief is that these orientations cannot be
    obtained from the fundamental matrix only and that additional
    information is needed, typically, a single correct point
    correspondence. In contrary to this, we show that fundamental
    matrix alone encodes orientation of epipoles up to their common
    scale sign. We present two formulations of this fact. The
    algebraic formulation gives a closed formula to compute the second
    epipole from fundamental matrix and the first epipole.  The
    geometric formulation is in terms of the conic formed by
    intersections of corresponding epipolar lines in the common image
    plane; we show that the epipoles always lie on different antipodal
    components of the spherical interpretation of this conic. Further,
    we show that, under mild assumptions, fundamental matrix can
    discriminate between two classes of mutual position of a pair of
    directional cameras.},
  keywords =    {epipolar geometry, orientation, steiner conic},
  authorship =  {34-33-33},
  project =     {IST-2001-32184, MSM 212300013, MSMT Kontakt ME412,
                 GACR 102/01/0971, GACR 102/02/1539, GACR 102/03/0440, 
                 IST-2001-39184, MSMT Kontakt 22-2003-04, CTU 0306013},
  psurl       = {PDF},
}