The magnitude of camera motion,
computed from the frontier points is next used for recovering the depth
to curved surfaces.
If the point
on the contour generator is not a frontier point,
and
in (
3
) and (
4
) do not vanish. As it has been shown in [
5
], since the viewing ray,
, is always tangent to the surface at a point
, the change
must be parallel to the viewing ray,
:
Substituting ( 1 ), ( 2 ) and ( 3 ) into ( 7 ), we have:
For the exact expression of
, see [
15
]. Thus, the following proposition holds:
Note, the computation of depth,
, is independent of the calibration matrix,
, camera rotation matrix,
, and camera position,
. That is the relative depth,
, to curved surfaces can be computed uniquely even for an uncalibrated
camera with unknown translational motion.
J. Sato
