Master Thesis - Fachbereich Informatik

84 CHAPTER 4. LENGTH MEASUREMENT APPROACH
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(a) (b)
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Figure 4.21: Effect of the weighting coefficient b in Equation 4.14. (a) Tube edge detection
results with a uniform weighted template (b = 0). (b) Results of a template with enhanced
ends (b = 3). (c) Corresponding cross-correlation results of (a), and (d) the cross-correlation
results of (b) respectively. The maximum in (c) and (d) corresponds to the pixel position
where the template matches best. In this example, the ridge closer to the observer is due to
a background edge while the ridge further away corresponds to the real tube edge.
Figure4.21showsanexampleofhowtheweightingofthetemplateendsimprovesthe
tube edge detection. In this example the right boundary contrast of a transparent heat
shrink tube is quite low. Using a uniformly weighted template, i.e. b = 0, the maximum
correlation score is reached at a background edge (see Figure 4.21(a) and (c)). In this
case, the tube would be measured larger than it really is. On the other hand, with
an enhancement of the template ends, the tube edge results in a larger score than the
background edge leading to a correct detection as can be seen in Figure 4.21(b) and (d).
The enhancement of the template ends is motivated in transparent tube characteristics.
For black tubes, b = 0 describes the response of the SOBELX operator best. However,
there is no disadvantage if using the same weighting coefficient as for transparent tubes.
Due to the strong contrast of black tubes, the curvature and size of the template are the
dominant factors influencing the matching results.
Template Rotation The templates generated by Equation 4.14 are symmetric along the
y-axis with respect to the template center. Thus, the ends of the template lie always on
one line perpendicular to the x-axis. In the ideal case, the edge response of a heat shrink
tube has the same characteristic. In practice, however, a tube can be slightly angular
within the guide bars, or the tube edge might be cut skew. In both cases the strong edge
responses at the ends do not have to lie on one line perpendicular to the x-axis as in the
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