User manual

Small Vision System User Manual 38
3.3 Range Resolution
Often it's important to know the minimal change in range that stereo can differentiate, that is, the range
resolution
of the method. Give the discussion of stereo geometry above, it's easy to see that that range
resolution is a function of the range itself. At closer ranges, the resolution is much better than farther
ranges.
Range resolution is governed by the following equation.
(2)
∆ r = (r
2
/bf) ∆d
The range resolution, ∆r, is the smallest change in range that is discernable by the stereo geometry,
given a change in disparity of
∆d. The range resolution goes up (gets worse) as the square of the range.
The baseline and focal length both have an inverse influence on the resolution, so that larger baselines and
focal lengths (telephoto) make the range resolution better. Finally, the pixel size has a direct influence, so
that smaller pixel sizes give better resolution. Typically, stereo algorithms can report disparities with
subpixel precision, which also increases range resolution.
The figure below plots range resolution as a function of range for the STH-MD1 (MEGA-D) stereo
head, which has a baseline of 9 cm. The Stereo Engine interpolates disparities to 1/16 pixel, so
∆d is 1/16 *
7.5 um = 0.08533 um. The range resolution is shown for a sampling of different lens focal lengths. At any
object distance, the range resolution is a linear function of the lens focal length.
Equation 2 shows the range resolution of a perfect stereo system. In practice, video noise, matching
errors, and the spreading effect of the correlation window all contribute to degrading this resolution.
Range resolution is not the same as range accuracy, which is a measure of how well the range
computed by stereo compares with the actual range. Range accuracy is sensitive to errors in camera
calibration, including lens distortion and camera alignment errors.
Figure 3-6. Range resolution as a function of range. This plot assumes a baseline of 90
mm, and a pixel size of 7.5 um, with subpixel resolution of 1/16 pixel.