The 3D reconstruction is a bundle adjustment method 
performing the transformation between the image coordinate 
system and the object coordinate system. This is an intersection 
using the exterior parameters also obtained in the previous 
calibration. 
To obtain a representative measure of accuracy of the system 
a targeted object is imaged inside the actual area. Calculated 
coordinates are compared to the given values and the deviations 
are used to estimate the accuracy. The given values are found 
by accurate photogrammetric methods. 
The precision of measured coordinates is estimated from 
repeated measurements. 
Results of this analysis are given in table 1. 
  
  
  
  
X Y Z XYZ 
Accuracy (RMSE) 0.056 0..101 0.082 0.141 
Precision (O0) 0.051 0.035 0.135 0.148 
  
Table 1. Results from accuracy investigation (all in mm.). 
Different methods can be applied to verify the 3D model. In 
our set-up, 3D graphics software was used to generate grid 
models for visual verification. A more sophisticated approach 
is surface modelling by generating synthetic images (Thune, 
1991). Perspective views can be generated from the estimated 
object model using the pixel values and the camera model in a 
simple ray casting technique. 
3.8 Data analysis. 
The initial task of our system was to obtain characteristic 
parameters of the functioning of the teatcup liner. Using 3D 
object models from different phases of the milking process, it 
is possible to estimate variable parameters like shape and size 
of the surface. From these the required data of tension in the 
liner and the distribution of the pressure from the liner on the 
teat can be obtained by means of a physical model. This work 
is performed by the Dept. of Agricultural Engineering at AUN. 
An example of result from this analysis is given in figure 11. 
4. Conclusions 
This paper descibes the work of designing a videometric system 
to meet the special requirements of measuring a moving surface 
inside a small vacuum chamber. 
The work consists of a system component description and an 
analysis of each component regarding mainly their influence on 
the overall accuracy. 
Binary radiometric resolution of the images and use of only one 
videoframe are the main contributors to the accuracy loss. 
These choices were made in order to handle the dataflow from 
the fast moving dynamic scenes and still be inside the accuracy 
requirements. 
Results from the calibration of the system with both mirrors 
and CCD-camera indicates considerable local distortions in the 
images. These were probably caused by low-cost optics and 
mirrors which were impossible to model by global parameters. 
Both the resulting spatial accuracy and precision of the system 
were inside 2/10 mm and satisfied the requirements. 
When higher accuracy standards are required other choices can 
be made and another more sophisticated mathematical model 
used. 
The data provides for a new analysis of the dynamics of the 
teatcup liner, and, the results are promising so far. 
  
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Figure 11. Estimated 3D model of the teatcup liner (upper plot) 
and pressure from the liner on the teat (lower plot). 
5. Acknowledgements 
Most of the experimental and practical image acquisition work 
were done in close cooperation with Mr. Odd Rgnningen at 
Dept. of Agricultural Engineering, AUN. He also initiated the 
project and made use of the data in his further research on the 
milking process. 
Prof. @.Andersen gave valuable support during the calibration 
work. 
6. References 
Baltsavias, E.P., and Stallmann, D., 1990. Trinocular vision for 
automatic and robust 3-D determination of the trajectories of 
moving objects. In: Close-Range Photogrammetry Meets 
Machine Vision, A.Gruen, E.P. Baltsavias, Editors, Proc.SPIE 
1395, pp.620-629.