Consider an instantaneous motion of a camera, so that the
view point 
at time 
moves to 
at time 
.
Suppose an apparent contour, 
, in an image at time 
corresponds to a contour generator, 
,
on the surface.
The two projection centers, 
and 
,
define a family of epipolar planes, 
.
Then, the contour generators, 
and 
,
at time 
and 
cross over an epipolar plane,
, at 
and 
respectively.
Since 
and 
are on the
same epipolar plane, 
, their projections, 
and 
, are on the corresponding epipolar lines
in images.
In the infinitesimal limit, this provides a natural spatio-temporal
parameterisation of the image and contour generators.
This parameterisation of curved surfaces and image sequence
with respect to 
and 
parameters is called the
epipolar parameterisation [5],
and the trajectory of a surface point,
, with a fixed 
parameter is called the
epipolar curve. The epipolar parameterisation can be
obtained from the extracted epipolar geometry. Since it enables us to identify
correspondences between the changes in apparent contours and
the changes in contour generators,
the epipolar parameterisation is
useful for recovering the surface geometry from apparent contours.