Master Thesis - Fachbereich Informatik

66 CHAPTER 4. LENGTH MEASUREMENT APPROACH
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(a) transparent, 50mm length, ∅8mm (b) black, 50mm length, ∅8mm
gray level profile
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(c)
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gray level profile
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Figure 4.13: Sample images with 11 equally distributed vertical scan lines used for profile
analysis within a certain region of interest. (c) and (d) show the resulting profiles of image
(a) and (b) respectively.
ˆPy(x) =I(x, y) (4.3)
where I(x, y) indicates the gray level value of an image I at pixel position (x, y). Since
a single scan line (e.g. ˆ P h/2 with h the image height) is very sensitive to noise and local
intensity variations, the localization of the tube boundaries based on the profile of a single
row can be error-prone. Hence, a set of n parallel scan lines is considered. The mean
profile Pn of all n lines is calculated by averaging the intensity values at each position:
Pn = 1
n
n�
ˆPyi
i=1
(d)
(4.4)
One property of the resulting profile Pn is the projection of a two-dimensional to an onedimensional
problem which can be solved even faster (processing speed is a very important
criteria at this step of the computation). Since further processing steps with respect to Pn
are independent of the number of scan lines n (n ≥ 1), Pn is denoted simply as P in the
following. A more detailed view on the number of scan lines and the scan line distribution
with respect to robustness and performance is given in Appendix A. In the following Nscan
denotes the number of scanlines used.
4.4.2. Profile Analysis
Step 1: The first step is smoothing the profile P by convolving with a large 1D mean
filter kernel of dimension Ksmooth: