ons 
ter) 
ru (X-X)) «rj (Q(-Yy r4 -Zy dt 
r4 (X- X9) *r4 (Y -Yy) *r4(Z-Z9) 
ra (X-X) +r,,(Y-Yp) +7 (Z-Zo) d 
x2xo-f 
  
  
yof ro (XX) r4 (Y- Y) r4 (Z-Z,) % (5) 
dx- -bx «b,y byx r^ «box r* bx r* © 
«br 2x2) +2b,x y, -bgx RA 
dy- -b,y +bx br +b,y 7 +b;y 7 m 
+2D,XY,+b,(T 242y) by, 
The first steps involved in the calibration process are similar to 
the procedure for the measurements. The process of calibration 
is described in figure 8. 
  
     
     
   
  
  
  
    
  
     
Image param. 
  
Image 
acquisition 
  
  
    
Grabbing par. 
     
Digital images 
     
Measurement par. 
    
    
Target 
location 
  
Image coord. 
| D4 | Image coord. 
    
        
  
   
Calibration 
& orientation 
adjustment 
Image coord. 
     
Results 
Statistical 
analysis 
Figure 8. Decomposition of the calibration process. 
  
  
  
  
Prelim. Results 
values 
  
  
  
Di Cal.& Or. par. 
  
  
  
In order to eliminate effects of syncronization of the 
videosignal (i.e. line-jitter) which are not investigated here, a 
sequence of images of the calibration frame is captured. The 
target location is established as described earlier and the mean 
values of the image coordinates are used in the following 
adjustment as observations. The stochastic model used in this 
investigation assume the observations to be uncorrelated and 
having a normal distribution with equal variance. These are 
truly only assumptions, but common practice in similar 
investigations. 
The on-the-job calibration is performed by placing a calibration 
frame with accurately determined targets in the measuring 
space. This frame is targeted as described in 3.2 and the 
geometry is shown in figure 9. 
The programme used is a least squares bundle adjustment 
adapted to our task. Both interior and exterior orientation can 
be estimated and the desired number of additional parameters 
can be included in the mathematical model. Only parameters 
being significantly different from zero remain in the model 
throughout the adjustment. 
Results from our system show considerable differences between 
the two imaginary cameras. This can be explained by different 
optical conditions for the two cameras, concerning both the 
mirror arrangement and the two halves of the camera optics. 
Further investigations of other additional parameters must be 
made if higher accuracy is required from the system. 
  
  
  
  
  
  
Loy 
  
  
  
  
  
  
  
  
  
  
Upper targets 
  
    
  
  
  
Lower targets / 
Section A-A 
  
  
  
  
Figure 9. Calibration frame. 
3.7 3D-model calculation. 
The observed image coordinates must be corrected because the 
functional model of the imaging system is not a pinhole model. 
Mirror and lens distortion, affinity, lack of orthogonality and 
the center of the frame memory are parameters estimated in the 
calibration that form the transformation between observed and 
the corrected image coordinates. 
One central problem is finding corresponding points (targets) in 
the two (or more) images. Using targets of identical size and 
shape, methods like feature based image matching 
(Forstner,1986) are not the most suitable. Introducing 
topological constraints like epipolar geometry will be a more 
effective approach here. Because of prior knowledge of the 
object geometry the identification of the targets in the images 
can be performed by using the perspective equations between 
object and images. 
  
        
    
  
    
Cal. and or.par 
  
Correction 
of image 
  
     
coordinates 
Bundle 
adjustment 
   
    
  
      
       
    
  
Graphic 3D object coord. 
verification 
  
  
  
Figure 10. Decomposition of 3D model calculation.