Master Thesis - Fachbereich Informatik

94 CHAPTER 4. LENGTH MEASUREMENT APPROACH
and background afterward. It is computed dynamically based on the regional mean of
the profile and a constant factor αpeak (see Equation 4.9). Although this parameter is
assumed to be constant it has to be trained once with respect to the conveyor belt used.
The teach-in of this parameter is very simple and intuitive. The visual system is set to
inspection mode, i.e. it is started as for standard measuring. The conveyor is empty, but
moving. The operator can adjust αpeak online starting at a quite low value. This value
is slightly increased as long as the system detects tubes (ghosts) where actually no tubes
are. Until now this procedure has to be performed manually, but one could think of an
automated version to reduce the influence of a human operator which is always a source
of errors.
To ensure the threshold has not become too large, several tubes are placed on the
conveyor. If the system is able to successfully detect all tubes (detection does not mean
the length has to be computed correctly in this context), the profile threshold factor is
assumed to be trained sufficiently. If the conveyor belt is not uniformly translucent, i.e.
the overall image brightness changes significantly over time, one has to assure that the
system is able to detect a tube both at the brightest and at the darkest region of the belt.
4.7.3. Perspective Correction Parameters
As introduced in Section 4.6.2 perspective effects in the measuring data can be reduced
using a perspective correction function fcor(x). This function has two parameters c1 and
c2 that have to be learned in the teach-in step from real data.
One intuitive method to do this is to measure a tube at a very slow conveyor velocity.
The result is a set of pixel length measurements (see Figure 4.25(a)) at almost every
position in the image. Then, the parameters of a second order polynomial f(x) =c1x 2 +
c2x + c3 can be computed using nonlinear least-squares (NLLS) methods. In this case, a
standard Levenberg-Marquardt algorithm [53] is used.
The resulting parameters c1 and c2 can be directly inserted into Equation 4.22 to compute
fcor(x).
For robust results this procedure can be repeated several times and the final parameter
set is averaged. Alternatively one could first acquire measurements of several tubes and
fit the correction function to the total data.
4.7.4. Calibration Factor
The most important parameter to be trained in the teach-in step is the calibration factor
that relates a length in the image to a real world length in the measuring plane ΠM. This
factor has been introduced as fpix2mm. The idea is to learn the calibration factor based
on correspondences between measurements and ground truth data.
In an interactive process the operator places a tube of known length onto the moving
conveyor. The velocity of the conveyor is set to production velocity, i.e. the velocity where
the tubes will be measured later. When the tube reaches the visual field of the camera
it is measured with the described approach, but at pixel level only. Once the tube has
left the measuring area, the total pixel length is computed and the user is asked to enter
the real world length of this tube into a dialog box. Again the input device is a standard
keyboard in the prototype version of the system.