Master Thesis - Fachbereich Informatik

4.4. TUBE LOCALIZATION 67
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1
Psmooth = P ∗
Ksmooth
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1
Ksmooth
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...
�
1
Ksmooth
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Ksmooth times
(4.5)
The idea of this low pass filtering operation is to reduce the high-frequency components
in the profile, thus, especially the structure of the background pattern.
Obviously, this step also blurs the tube edges, and therefore reduces the detection precision
significantly. Having in mind the goal of the profile analysis, it is intended to verify
whether a measurement is possible in the current frame or not. In a next step, the proper
measurements have to be performed on the original image data and not on the profile.
However,knowledgeofthisfirststepdoesnothavetobediscardedandcanbeusedinstead
to optimize the following. In other words, if it is possible to predict a tube’s boundaries
reliable, but not precise, this information is then used to define a region of interest (ROI)
as close as possible around the exact location.
Step 2: The next step is to detect strong changes in the profile. Large peaks in the first
derivative of the profile indicate such changes and can be considered as candidates for
tube boundaries. Therefore, a convolution with a symmetric 1D kernel approximating the
first derivative of a Gaussian is performed:
Pdrv = Psmooth ∗ Dx
(4.6)
The odd symmetric 9 × 1 filter kernel Dx is given by the following filter tab as proposed
in [25] for the design of steerable filters:
tab 0 1 2 3 4
value 0.0 0.5806 0.302 0.048 0.0028
With this kernel a dark-bright edge results in a negative response while a bright-dark
edge leads to a positive response. The intensity of the response is proportional to the
contrast at the edge.
Assuming the potential tube boundaries have a sufficient contrast, only the strongest
peaks of Pdrv are of interest for later processing. To simplify the task of peak detection,
theabsolutevaluesofthedifferentiatedprofilearetakenintoaccountonly. Thisisdenoted
as follows:
as P +
drv
P +
drv = |Pdrv| (4.7)
Note that the information of the sign of a peak in Pdrv is still useful for later classification
and has not to be discarded.
Step 3: A thresholding is performed on P +
drv to eliminate smaller peaks that correspond
for example to changes in intensity due to the background pattern or dirt:
� +
P
Pthresh(x) = drv (x)
0
+
, if P drv (x) >τpeak
, otherwise
(4.8)