Master Thesis - Fachbereich Informatik

56 CHAPTER 4. LENGTH MEASUREMENT APPROACH
However, this scale factor may differ depending on the image position. It is expected
that the distance between pL and pR will be slightly shorter at the image boundaries and
maximal at the image center due to perspective.
4.2.4. Edge Model
Thetubeedgesaremodeledasramp edges as introduced in Section 2.3.1, since this model
describes the real data most adequate both for transparent and black tubes. The slope of
the ramp determines the sharpness of an edge. As steeper the rise (or fall respectively) as
sharper the edge. Obviously, the edge position can be located much more precise if the
ramp has only a minimum spatial extension.
As mentioned before in the technical background section there are several factors that
can cause ramp edges including the discrete pixel grid, the camera focus, and motion blur.
The first factor can be reduced if using a high-resolution camera (reminding the trade off
between resolution and speed as discussed in Section 3.2.1). The camera focus depends
mainly on the depth of an object. In this application, the depth of an object does not
change over time, since all tubes in a row have the same diameter and are lying on the
planar conveyor belt which is parallel to the image plane. In the following it is assumed
that the camera and the optical system are adjusted in way that a tube is imaged as sharp
as possible. Motion is another common parameter influencing the appearance of an edge.
Since the tubes are inspected at motion (up to 40m/min), a short shutter time (exposure
time) of the camera is required. If the shutter time is too large, light rays from one point on
the tube contribute to the integrated intensity values of several sensor elements along the
moving direction. Especially the left and right tube boundary considered for measuring
are affected by motion blur as they lie in the moving direction.
Therefore, it is assumed that the shutter of the camera is adjusted to a very small
exposure time to suppress motion blur as much as possible. A short shutter time requires
a large amount of light to enter the camera at one time. The iris optical system has to be
wide open (corresponding to a little F-number) and the illumination must be sufficiently
bright.
4.2.5. Translucency
Translucency is the main property to distinguish between transparent and black tubes.
Black tubes do not transmit light leading to one uniform black region with strong edges
in the image under back light. In this case, the local edge contrast at a certain position
depends on the background only. On the other hand, transparent tubes transmit light.
However, some part of the light is also absorbed or reflected in directions that do not
reach the camera. Therefore, a tube will appear darker in the image compared to the
background. It will even be darker at positions where the light has to go through more
material. This leads to two characteristic dark horizontal stripes at the top and bottom of
a transparent tube as can be seen in Figure 4.5. This model knowledge has been exploited
to define a robust feature for edge localization which can still be detected in situations
where the contrast at the center of the edge is poor.
The printing on the tubes also reduces the translucency and is therefore visible on
transparent tubes in the image. On average it covers about 8% of a tube’s surface along
the perimeter for 6, 8, and 12mm diameter tubes.