Master Thesis - Fachbereich Informatik

54 CHAPTER 4. LENGTH MEASUREMENT APPROACH
(a) Ideal tube model (b) Perspective tube model
Figure 4.3: (a) In the ideal model, the (parallel) projection of a 3D tube corresponds to a
rectangle in the image. The distance d between the left and right edge is equal at each height.
Under a perspective camera, objects closer to the camera appear larger in the image. Hence,
the distance d1, belonging to the points on the tube edges that are closest to the camera,
is larger than d2, and d2 is larger than d3 (the distance of the edge points that are farthest
away). Note, the dashed lines are not visible in the image under back light, and the tube
edges appear convex.
Only one tube is visible completely (with left and right end) in each image at one
time
There is a clear spacing between two consecutive tubes
The guide bars cover the upper and lower border of each image
The guide bars are parallel and in horizontal direction
The moving direction is from the left to the right
The mean intensity of the background (conveyor belt) is brighter than the foreground
(heat shrink tubes)
There is a sufficient contrast between background and objects
The video capture rate is fast enough to take at least one valuable image of each
tube segment so that a length measurement can be performed. (Potentially the
production speed has to be reduced to qualify this constraint)
The image is not distorted, i.e. straight lines in the world are imaged as straight
lines and parallel lines are also parallel in the image
In this application, the variety of image situations to be observed is highly limited and
constraint by the physical setup (see Chapter 3). Thus, it is possible to reduce the number
of potential situations to nine defined states. Each image can be categorized into exactly
one of these states as shown in Figure 4.2 by means of synthetic representatives. Only
four of the nine states are measurable, i.e. state (d), (e), (f) and (g) respectively. In these
states a tube is completely in the image.
4.2.3. Tubes Under Perspective
Under ideal conditions, i.e. with a parallel projection, a tube on the conveyor is represented
by a rectangle in the image plane with the camera setup used (see Figure 4.3(a)). Due