Master Thesis - Fachbereich Informatik

86 CHAPTER 4. LENGTH MEASUREMENT APPROACH
curvature
4.5
4
3.5
3
2.5
2
1.5
1
0.5
3
x 10
5
0
0 50 100 150 200
x
250 300 350 400
(a) Left tube side
curvature
3
x 10
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
350 400 450 500 550
x
600 650 700 750
(b) Right tube side
Figure 4.23: Curvature of best matching template depending on the x-position of the match.
one has to consider 2 × 10 × 3 templates if k = 3. Since correlation is an expensive
operation, the processing time increases significantly even if the local ROIs are relative
small. It turned out that not more than 15 templates can be checked at each side without
skipping frames at a frame rate of 50fps at an AMD Athlon 64 FX-55 processor with 2GB
RAM.
One thinkable optimization is to reduce the curvature resolution, i.e. quantize the same
range of curvatures to ≤ 5 templates at each side. Obviously this reduces the accuracy of
the edge localization and is no satisfying solution in this application.
Instead one can apply model knowledge to exclude several curvatures depending on
the horizontal image position. It can be assumed that the curvature is maximal at the
image boundaries and decreases toward the image center. Real sequences support this
assumption. Figure 4.23 shows the occurrence of different curvatures with respect to x.
The data was acquired over several sequences including transparent and black tubes. It
turns out that the curvature decreases linearly within a certain band. The upper and lower
boundary of this band determine which curvatures can be excluded at a given position.
The range distance of curvatures dψ at a position x is defined as:
dψ(x) =ψmax(x) − ψmin(x) (4.16)
where ψmax(x) andψmin(x) are the maximum and minimum curvature occurring at
this position. dψ is the average range distance over all x. This range must be checked
each time and is covered by n templates. In practice n = 5 is used, since as mentioned
before the maximum number of templates that can be processed with the given hardware
in real-time is 15 (in addition to all further processing that is needed), and 5 curvatures ×
3 rotations = 15 templates to be checked each frame at one tube side. To yield the desired
resolution over the whole range of curvatures, the total number of curvatures Nψ,total is
computed as follows:
Nψ,total = n(ψmax − ψmin)
dψ
(4.17)