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- rotation (X-axis, Y-axis, Z-axis, positive 
directions) 
- principal distance 
An implementation of an algorithm for finding 
initial values based on the method described in 
(Haralick et al, 1991) is planned. 
43.4 The calibrated parameters The result from 
the calibration phase can be divided in two parts: 
- Inner orientation parameters 
- Outer orientation parameters 
The inner orientation parameters are the principal 
distance, the principal point, radial distortion 
coefficients and the scale difference in x and y. In a 
metric camera with fiducial marks these parameters 
are defined and constant and indifferent to camera 
movement. In a high speed camera this is not the 
case. It is especially the principal point which is 
unstable due to the lack of fiducial marks. In the 
present version the principal point is not regarded as 
constant while the other parameters are. 
The outer orientation describes the position and the 
direction of the camera in the object coordinate 
system. If the calibration is done with the same set-up 
of the cameras as the actual test set-up, these outer 
orientation values can be used as approximate values 
for the 3D calculations. They are not used for any 
other purpose. 
4.4 3D - Calculations 
The actual 3D calculation is done either as a result 
from the bundle adjustment or as a resection from 
the known orientation parameters and image 
coordinates. There are two reasons not to make a new 
bundle adjustment for each frame: time and stability. 
The time requirements for the system will probably 
permit an adjustment for each frame, but if a few 
hundred frames are measured the time saving is still 
considerable. Another reason is the stability of the 
system. If a new adjustment is done for each model, 
the measuring noise might give a larger instability 
than using a constant setting for all frames. An error 
in the constant settings will obviously create an error, 
but this error will have a uniform structure through 
the sequence and the local errors between frames 
might be smaller than with a new bundle adjustment 
for each frame. 
The 3D coordinates are calculated from, at least, two 
images. The coordinates for the point is measured in 
the images and the object space coordinates are 
computed as the intersection of the rays. To be able to 
do this, the inner and outer orientation of the 
cameras must be known. The inner parameters are 
taken from the calibration phase as well as the 
approximate values for the outer orientation if the 
calibration is done with the same set-up as the test 
run. When using high speed film cameras, the inner 
orientation is normally not stable since there are no 
reference marks (fiducial marks) to define the 
principal point. Due to this, the principal point must 
  
   
   
    
  
  
  
    
   
    
   
   
  
  
  
  
  
    
     
    
    
    
    
   
   
   
   
   
    
  
   
   
   
    
    
   
  
    
   
be re-calibrated during the 3D calculations. If the 
cameras are fairly stable, i.e. the inner and outer 
orientation parameters do not change, the 3D 
calculations are performed without recalculating the 
outer orientation for each image frame. If the 
deviations to the known object points are too large 
the outer orientation parameters will be recalculated. 
  
fig6 Control point configuration 
4.4.1 Control point configuration The purpose of 
the control points in the 3D calculation are to connect 
the image coordinate systems to the object coordinate 
system. In the case of additional calibration of the 
principal point they also serve this purpose. The 
minimum configuration for the control points are 
three points, but in order to achieve some 
redundancy and control of the calculations this 
number should be increased to at least six points, 
preferably three behind the test object and three in 
front of the object. They should be as well distributed 
as possible under the given practical conditions over 
the image plane. An example of acceptable control 
point configuration is shown in fig 6. 
4.5 Self Diagnosis and Quality Reports 
The philosophy of the system is that an operator 
should be avle to run through an image sequence 
with as little interaction as possible. This means that 
errorneous measurements or changes in the inner or 
outer orientations must be diagnosed and corrected 
automatically as fas as possible by the system. Two 
types of diagnosis is made: 
4.5.1 Internal Diagnosis By looking at the residu- 
als for each computed 3D point indicates if an error 
are present. If more than two cameras are used it will 
normally be possible to detect the erroneous 
measurement. In the camera calibration on known 
test-fields, a re-weighted least squares procedure is 
used to reduce the effect of the errors. 
45.2 External Diagnosis In each frame a few stable 
known coordinates will always be seen. They will be 
used as a measure of stability during the sequence. 
When the 3D calculations are done, these points will 
be compared with their true values and if drifted