Master Thesis - Fachbereich Informatik

5.3. EXPERIMENTAL RESULTS 107
The tolerances for these lengths differ, i.e. the 30mm tubes are allowed to deviate only
up to 0.5mm around the target length while 70mm tubes have a larger tolerance of 1mm.
The measuring precision can be directly linked to these tolerances. Accordingly the system
must measure smaller tubes with a higher precision then larger ones.
In this scenario, the accuracy and precision is evaluated based on the mean and standard
deviation of a sequence of tubes measured online that approximately meet the given target
length. Corresponding ground truth data is available.
Performance Finally, it is of interest to determine the performance of the system in
terms of the average per frame processing time ΩTIME. It is investigated how the total
processing time is distributed over the different stages of the inspection including radial
distortion compensation, profile analysis, edge detection and template matching, as well
as the total length computation and tracking.
5.3. Experimental Results
In this section the experimental results of the different scenarios are presented and discussed.
Further discussion as well as an outlook on future work is given in Section 5.4.
5.3.1. Noise
The influence of noise on the measuring accuracy is tested on synthetic sequences. Rectangles
of 200 pixels width are placed on a uniform background with a contrast of 70 gray
levels between the object and the brighter background. The image size is 780 × 160, and
the sequence is analyzed like a real sequence with two differences. First, the perspective
correction function is disabled, since the synthetic ‘tube’ is not influenced by perspective,
i.e. the width of the rectangle is constant independent of the image position. Furthermore,
the dynamic selection of template curvatures based on the image position does not work
as well in this scenario, since the model knowledge assumptions do not hold. Thus, in
this experiment all templates are tested at each position (computation time is not critical
here).
Gaussian noise of standard deviation σN has been added to the ideal images, with
σN ∈{5, 10, 25}. Sample images of each noise level are shown in Figure 5.4(a)-(d).
The measuring results are evaluated using the root-mean-square-error between the
ground truth length of 200pixels and the result of the single measurements. The results
show that in the ideal (noise free) case, the pixel length is always measured correctly.
Under the presence of noise, the measured length varies at subpixel level. Figure 5.4(e)
shows how the measurements differ in accuracy and precision under the presence of noise.
The maximum deviation from the target length occurs at the largest standard deviation
(σN = 25). The RMSE results can be found in Figure 5.4(f). For sequences with only
a little amount of noise (σN = 5) the RMSE is acceptable low with 0.122. If one pixel
represents 0.12mm in the measuring plane, the real world error is about 1/100mm. Even
under strong noise (σN = 25), which is far beyond the noise level of real images, the
measuring error is 0.252pixels or 0.03mm in the example. This is still significantly below
the human measuring variance.