User manual

Small Vision System User Manual 33
3.1 Disparity
The figure below displays stereo geometry. Two images of the same object are taken from different
viewpoints. The distance between the viewpoints is called the baseline (b). The focal length of the lenses is
f. The horizontal distance from the image center to the object image is dl for the left image, and dr for the
right image.
Figure 3-1. Definition of disparity: offset of the image location of
an object.
Normally, we set up the stereo cameras so that their image planes are embedded within the same plane.
Under this condition, the difference between dl and dr is called the disparity, and is directly related to the
distance r of the object normal to the image plane. The relationship is:
(1) r = bf / d , where d = dl - dr .
Using Equation 1, we can plot range as a function of disparity for the STH-V1 stereo head. At their
smallest baseline, the cameras are about 8 cm apart. The pixels are 14 um wide, and the standard lenses
have a focal length of 6.3 mm. For this example, we get the plot in Figure 3-2. The minimum range in this
plot is 1/2 meter; at this point, the disparity is over 70 pixels; the maximum range is about 35 meters.
Because of the inverse relationship, most of the change in disparity takes place in the first several meters.
The range calculation of Equation (1) assumes that the cameras are perfectly aligned, with parallel
image planes. In practice this is often not the case, and the disparity returned by the Stereo Engine will be
offset from the ideal disparity by some amount X
0
. The offset is explained in the section below on the
horopter, and in the section on calibration.