Master Thesis - Fachbereich Informatik

4.6. MEASURING 91
fcor(x) =−(c1x 2 + c2x)+c1s 2 + c2s (4.22)
where s is the x-coordinate of the peak of f(x) withs = −c2/(2c1), i.e. the point where
the first-derivative of f(x) is zero. Thus, fcor is the 180 ◦ rotated version of f(x) whichis
shifted so that fcor(s) = 0 as can be seen in Figure 4.25(b).
This function applied to the measurements has the effect of all values being adjusted
to approximately one length l(s). The corrected length values lcor(x) areshowninFigure
4.25(c). As one can see, the mean value over all measurements describes the data
much better after perspective correction.
To reduce the computational load the correction function is computed only once for
each position at discrete steps and stored in a look up table for fast access.
4.6.3. Tube Tracking
Assuming a sufficient frame rate, one tube is measured several times at different positions
while moving through the visual field of the camera. One constraint in Section 4.2.2
regarding the image content states that only one tube is allowed to be measurable at one
time. The question is whether the current measurement belongs to an already inspected
tube or if there is a new tube in the visual field of the camera. Since there is no external
trigger, this task has to be solved by the software.
Consecutive tubes appear quite equal in shape, size, or texture (especially black tubes).
Itisdifficultuptoimpossibletofindreliablefeaturesinformofanuniquefingerprint
that can be used to distinguish between tubes. In addition the extraction and comparison
of such fingerprints would be computational expensive. Standard tracking approaches
such as Kalman filtering [24] or condensation [8] are also not suited in this particular
application, since such approaches are quite complex and are worthwhile only if an object
is expected to be in the scene over a certain time period. At faster velocities, however, a
tube is in the image for about 4-7 frames only.
Since processing time is highly limited, it is a better choice to develop fast heuristics
based on model-knowledge that replace the problem of tube tracking by detecting when
a tube has left the visual field. Therefore, the following very fast heuristics have been
defined:
1. Backward motion
2. Timeout
Backward motion Since the conveyor moves always in one direction (e.g. from left to
right in the image), it is impossible that a tube moves backward. Thus, if the horizontal
image position of the tube at time t is smaller than at time t − 1(i.e. thetubewouldhave
moved further to the left), this can be used as indicator that the current measurement
belongs to the next tube. The position of a tube can be defined as the x-coordinate of
the left measuring point. Hence with the image content assumption the tube measured at
time t − 1 has left the visual field if xpL (t)