@TechReport{Chum-TR-2003-10,
  IS = { zkontrolovano 07 Dec 2003 },
  UPDATE  = { 2003-12-03 },
author =      {Chum, Ond{\v r}ej and Werner, Tom{\' a}{\v s} and 
               Pajdla, Tom{\' a}{\v s}},
title =       {On Joint Orientation of Epipoles},
institution = {Center for Machine Perception,  K13133 FEE
               Czech Technical University},
address =     {Prague, Czech Republic},
year =        {2003},
month =       {April},
type =        {Research Report},
number =      {{CTU--CMP--2003--10}},
issn =        {1213-2365},
pages =       {13},
figures =     {5},
authorship =  {34-33-33},
psurl       = {[Chum--TR-2003-15.pdf
]},
project =     { IST-2001-32184, MSM 212300013, GACR 102/02/1539,
                GACR 102/01/0971, BeNoGo IST-2001-39184, 
                MSMT Kontakt ME412, MSMT Kontakt 22-2003-04},
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},
}