Master Thesis - Fachbereich Informatik

4.5. MEASURING POINT DETECTION 83
occurrence
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012
curvature
(a)
occurrence
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.025 -0.02 -0.015 -0.01
curvature
-0.005 0 0.005
Figure 4.19: Histogram of template occurrence for (a) left and (b) right tube side. It can
be seen that only a small range of curvatures can be observed. This reduces the number of
templates that have to be tested each time.
120
100
80
60
40
20
0
0
2
x
4
6
8
0
10
20
30
40
50
60
y
70
10 80
Figure 4.20: If the height weighting coefficient gets too large (here: b = 20), the center of
the tube edge does not contribute to the matching score anymore.
Template Weighting The weighting coefficient b in Equation 4.14 is important for transparent
tubes. Due to a poor contrast, the overall edge response of a transparent tube might
be low. If considering only the center region of an edge, the contrast might be even lower
than a background edge at worst case. The cross-correlation only computes the similarity
of a template at a certain location in the image. The maximum response is taken as match,
since it is assumed that there must be a tube edge in the search region, even if the same
or another template matches the real tube edge perfectly, but with a lower score. Finally
this will lead to a wrong measurement.
With model knowledge about the tube characteristics one can assume that the contrast
at the edge ends is significantly stronger. If the template is weighted uniformly at the
center and the ends, the correlation score depends on the whole edge equally. On the
other hands, if the ends of the template are weighted stronger than the center, a template
that perfectly fits the tube edge will yield a larger score, since background edges are usually
uniform. Thus, the template is designed to prefer tubes edges.
The weighting coefficient b hastobelargerthanonetoyieldthedesiredeffect.Onthe
other hand, b must not be too large as well, since then the ends get too much influence. In
the extreme case, the template equals two spots at a certain distance that do not represent
a tube edge anymore (see Figure 4.20).
(b)