Title: Epipolar curves on surfaces

Authors: Peter J. Giblin and Richard S. Weiss
Affiliation: Computer Vision Research Laboratory, Dept. of 
Computer Science, University of Massachusetts, Box 34610, Amherst, MA
0l003-4610

Abstract: The view lines associated with a 
family of profile curves of the projection of a surface onto the retina
of a moving camera defines a multi-valued vector field on the surface.
The integral curves of this field are called epipolar curves and together
with a parametrization of the profiles provide a parametrization of regions of
the surface.  
We present an investigation of epipolar
curves on the object surface and in a related  
`spatio-temporal surface'.  Where the
epipolar plane is tangent to the surface,
the epipolar curve has a cusp and
the epipolar parametrization breaks down .
A description is given for the geometry of all of the generic cases 
where the epipolar parametrization breaks down.
These results give a systematic way of detecting 
the gaps left by reconstruction of a surface from profiles.

Keywords: surface reconstruction, epipolar constraint,
epipolar curve, spatio-temporal surface.