Master Thesis - Fachbereich Informatik

82 CHAPTER 4. LENGTH MEASUREMENT APPROACH
# templates ψmin ψmax χ a b
Left: 30 0.0 0.02 0.00066 −1 3
Right: 30 −0.02 0.0 0.00066 1 3
Table 4.3: A set of 30 templates with curvatures equally distributed between ψmin and ψmax
at a curvature resolution (step size) χ has been used to determine the occurrence of certain
curvatures empirically.
side a>0 is used to model the positive response of dark-bright edges. Figure 4.18 shows
some examples that visualize Equation 4.14 and the effect of the different parameters.
Template Dimension A constant template width of 11pixels is used, which is large
enough to represent both straight and maximal curved tube boundaries. The template
height is defined over the global ROI height. Assuming the guide bars are always arranged
so that the guide bar distance is only slightly larger than the tube’s perimeter, the global
ROI height is a good reference on the tube size. It is possible to compute a well guess of
the tube height by the following equation:
where HROIG
HT = γHROIG
is the global ROI height and γ a factor between 0 and 1.
(4.15)
Curvature Thequestionis,whatrangeofcurvaturesoccursinpracticeandhowmany
templates are needed to cover that range. Therefore, several test sequences with both
black and transparent tubes of different diameter have been captured. 30 templates of
different curvature have been generated for both tube sides. The parameters can be found
in Table 4.3.
Foreachmeasurableframethecurvatureofthetemplatethatreachesthemaximum
correlation value is taken into account to build a histogram of curvature occurrence both
for the left and ride tube side. The normalized cross-correlation (see Equation 2.31) is
used as measure evaluating the match quality of each template at a certain location. The
results can be found in Figure 4.19.
It shows, the occurring curvatures are limited to a small range denoted as Rψ, left and
Rψ, right with Rψ, left =[0, 0.005] for the left and Rψ, right =[−0.005, 0] for the right
side respectively. In order to reduce the number of templates all curvatures outside this
range can be ignored.
Another important criteria is the step size or curvature resolution χ, i.e. how many
steps between ψmin and ψmax are taken into account. Theoretically one could quantize
the curvature ranges into very small steps. However, since correlation is an expensive
operation one has to make a compromise between accuracy and performance. It was
observed that if more than 15 templates have to be tested at each tube side per frame, the
system starts to drop frames, i.e. this is a quantitative indicator that the overall processing
time exceeds the current frame rate. Therefore the total number of templates is restricted
to 10 in this application. The corresponding step size between two curvatures is 0.0005.