Image Processing Reference
In-Depth Information
Fig. 13.7. The system graph summarizes a stereo camera set-up with both cameras as well as
the corresponding epipoles,
E
L
,E
R
,
marked
13.4 Reconstructing
3
D by Stereo, Triangulation
In this section we will discuss how to estimate the position of a point in the world
by means of two images. The ideas behind stereo processing can also be extended to
three or more cameras, although we will not elaborate on them to limit the scope. To
be precise, two images taken by two perspective cameras located at different places
but observing the point simultaneously will be assumed. The issue of taking pictures
simultaneously is evidently an approximation of the reality. When the points in the
view fields of the two cameras move much slower than a camera, even one camera
taking pictures at two different locations and two different times can be viewed as a
reasonable approximation of a stereo system. The points of interest in our system are
listed below and are also marked in Fig. 13.7:
P
An arbitrary point in the common view field of the cameras
P
L
The image of
P
in the left camera
P
R
The image of
P
in the right camera
O
L
The projection center of the left camera
O
R
The projection center of the right camera
E
L
The image of
O
R
in the left camera, the left epipole
E
R
The image of
O
L
in the right camera, the right epipole
O
L
The image of
O
L
in the left camera
O
R
The image of
O
R
in the right camera
O
W
The projection centre of a fictitious world frame
In Fig. 13.7 we have only shown the left and the right coordinate frames, whereas we
have only marked
O
W
for simplicity because the world frame can be eliminated by
transferring the reference to one of the camera frames, here the left. We will elaborate
on this further below.
