Master Thesis - Fachbereich Informatik

114 CHAPTER 5. RESULTS AND EVALUATION
GTD [mm]
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ground truth distance
tube marker
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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Tube number
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Measurement distribution
Ground truth distribution
49 49.2 49.4 49.6 49.8 50 50.2 50.4 50.6 50.8 51
Length [mm]
Figure 5.9: (a) Ground truth distance GT D in mm for transparent tubes (50mm length,
∅8mm) at 30m/min. The measurements marked by a ‘+’ are all belonging to the same tube
that reached the maximum GT D at measurement 68. As one can see it is not systematically
measured wrong. A poor contrast region on the conveyor belt is rather the origin for the strong
deviations from the ground truth. (b) Gaussian distribution of all measurements compared to
the ground truth distribution.
possible at this velocity for transparent tubes so far and are therefore not considered in
Table 5.5.
The standard deviation σtube of transparent tubes moved at 40m/min is three times
larger than at 10m/min. This can be explained by the smaller number of per tube measurements.
The ground truth distance increases also with the velocity. Especially GT D
gets conspicuously larger, i.e. the measured lengths are larger than the ground truth
length on average. This trend can also be observed at the absolute value of GT Dmax and
GT Dmin. At a velocity of 40m/min the maximum ground truth distance is 0.75 which
is more than the allowed tolerance. In this context one has to keep in mind that these
values are only the extrema and do not describe the average distribution. This makes the
ground truth distance measure very sensitive to outliers. However, a large GT D value
does not have to mean poor accuracy automatically. On the other hand if the ground
truth distance is low in the extrema as with the black tubes in this experiment, this is an
additional indicator of high accuracy. The ground truth distance of the transparent tubes
at 30m/min is shown in Figure 5.9(a). The deviations are significantly larger compared
to Figure 5.8(a).
Instead of being approximately equally distributed as for the black tubes, the error of
transparent tubes seems to increase and decrease randomly, but always over a range of
consecutive measurements. This observation can be explained by the varying background
intensity at back light through the conveyor belt. The periodic intensity changes influence
the transparent tubes obviously much stronger than the black tubes since the detection
quality depends mostly on the image contrast. Figure 5.10 shows how the mean image
intensity of a moving empty conveyor belt changes over time. If a tube is measured at
a part on the conveyor belt that yields a poor contrast under back light, the GT D is
likely to increase. Having in mind each tube passes the measuring area 6 times in this
experiment, the probability is small that it is always measured at the same position on
the conveyor. The tube measured with the maximum GT D hasbeenmarkedintheplot
(b)