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The whole system is controlled by an industrial 
PC with image processing boards. The image 
processing components are a digital multiplexer, 
a camera interface and a  transputer based 
processing board. The cameras deliver a digital 
signal, which is shuffled by the interface board 
into the memory of the transputer board. The 
number of cameras to be used is independent of 
the processing unit and the measuring frame and 
has to be applicated to the complexness of the 
tubes to be measured. The more bends the tubes 
can have the more cameras are necessary to be 
sure that every bend point can be recorded by at 
least two cameras. 
The whole background of the measurement frame is 
white to achieve a high contrast between tubes 
and background. In the images the tube is 
projected as a black polygon on a white 
background (Fig.2a). 
  
Fig.2a: Tube in digital image 
2.3 Software 
The processing of the digital images captured by 
the CCD-cameras runs in several steps. 
In the first processing stage in every image the 
center line of the tube is extracted (Fig.2b). In 
à second stage these center line is splitted up 
into straight parts and bends. Following straight 
parts are connected, the intersection is the 
projection of a bend point into the image 
(Fig.2c). The result of the image processing are 
the image coordinates of these intersection 
points. 
      
  
Fig.2b: Extracting tube center line 
  
  
Fig.2c: Intersecting straight tube parts 
If every image is processed, image coordinates of 
bend points are available. The 3-D-coordinates of 
these bend points can be derived by ray 
intersection in space. Therefore the interior and 
exterior orientation of the cameras has to be 
known. 
These orientation parameters can be derived 
simply by a spatial resection of the images over 
the reference points. Therefore the reference 
points are also measured in the images. This 
system calibration is not performed every time a 
tube is measured, but only if a change in the 
orientation is detected. This changes can simply 
be detected by a continues observation of the 
image coordinates of some reference points. If 
any changes occur, a calibration can be started. 
The major difficulty of this system is the 
matching of homologous bend points in the images. 
If a plane modelled by two following straight 
tube parts is perpendicular to an image plane, 
the bend point between the two straight parts can 
not be detected in the image. This case occurs 
very often, if the tube is bended very complex. 
In that case a special algorithm has to match the 
homologous projections of bend points. This is 
done by a ray intersection and the restriction of 
a minimized spatial distance of projection rays. 
Every intersection of two projection rays with a 
spatial distance under a predefined threshold is 
calculated. The resulting  3-D points were 
combined to clusters with a predefined maximum 
radius. Now homologous points can be detected as 
matching the same cluster. 
The resulting 3-D coordinates of the bend points 
can be used to derive the distances between bend 
points and the bend angles. These are the 
parameters to control the bend roboters and can 
be used for a nominal and actual shape 
comparison. 
2.4 Practical Experiences 
First practical experiences have shown, that this 
method can be established to control the shape of 
automatically bended tubes. The achievable 
accuracy of a single bend point in the images is 
about + 0.1 pixel, the global accuracy depends on 
the projecting scale. The first established 
system with 6 CCD cameras and a measurement 
volume of 1.5 m x 1.0 m x 0.5 m achieves an 
accuracy of t 0.5 mm for one coordinate. 
The limits of the system are bend angels less 
then 10 degrees and straight parts shorter than 
30 mm. Those bendpoints are hardly to detect in 
the images and can therefore not be measured with 
a sufficient accuracy.