User manual

Small Vision System User Manual 35
3.2 Horopter
Stereo algorithms typically search only a window of disparities, e.g., 16 or 32 disparities. In this case,
the range of objects that they can successfully determine is restricted to some interval. The horopter is the
3D volume that is covered by the search range of the stereo algorithm. The horopter depends on the
camera parameters and stereo baseline, the disparity search range, and the X offset. Figure 3-3 shows a
typical horopter. The stereo algorithm searches a 16-pixel range of disparities to find a match. An object
that has a valid match must lie in the region between the two planes shown in the figure. The nearer plane
has the highest disparity (15), and the farthest plane has the lowest disparity (0).
Plane of
closest
match
Plane of
furthest
match
16 dis
p
arities
Figure 3-3 Horopter planes for a 16-pixel disparity search.
The placement of the horopter can be varied by changing the X offset between the two images, which
essentially changes the search window for a stereo match. Figure 3-5 shows the raw disparities for a
typical stereo head. The cameras are slightly verged, so a zero disparity plane (where an object appears at
the same place in both images) occurs at some finite distance in front of the cameras. If the stereo
algorithm is searching 5 disparities, then without any X offset, it will search as shown in the top red arrow,
that is, from disparity 0 to disparity 4. By offsetting one image in the X direction by n pixels, the horopter
can be changed to go from –n to 5-n raw disparities. This search range is indicated by the lower red arrow.
Generally, it is a good idea to set the X offset to compensate for camera vergence or divergence, that
is, to set it so that the furthest horopter plane is at infinity. The reason that this is a good idea is because
it’s usually possible to control how close objects get to the camera, but not how far away. The offset that
puts the far horopter plane at infinity is called X
0
. With this offset, a disparity of 0 indicates an infinitely
far object.
The horopter can be determined from Equation (1). For example, if the disparity search window is 0-
31, the horopter (using the graph above) will be from approximately 1 meter to infinity. The search
window can be moved to an offset by shifting the stereo images along the baseline. The same 32 pixel
window could be moved to cover 10-41 pixel disparities, with a corresponding horopter of 0.8 meters to
2.2 meters.