We now consider how the camera motion can be computed from frontier
points,
, on curved surfaces. Since a frontier point does not move before and
after the camera motion,
and
vanish. Substituting
into (
3
), amd taking a vector product (
) with
, we find that the magnitude of motion,
, can be computed from the image measurements up to the depth to the
frontier point,
:
For the exact expression of
, see [
15
].
We next consider how the acceleration of the camera motion can be
computed from the frontier points. Substituting
into (
4
), and taking a vector product with
, the acceleration of the camera motion,
, can be computed from the image measurements as follows:
For the exact expression of
, see [
15
]. Note, even if the camera is uncalibrated, both
and
are computed from the changes in apparent contours in images up to the
depth
, and are independent of
,
and
.
J. Sato
