114 
Table 3 Correlation matrix for the 12 parameters 
  
Q $ K Xo Yo Zo Xo Vo f al az Di 
1.00 
o 
$ |-0.38 1.00 
K |-0.33 0.99 1.00 
Xo| 0.33 -0.48 -0.47 1.00 
Yo 
Zo 
  
0.69 -0.45 -0.45 0.18 1.00 
-0.82 0.41 0.38 -0.20 -0.94 1.00 
Xo|-0.16 0.91 0.92 -0.09 -0.34 0.25 1.00 
yo|-0.99 0.34 0.28 -0.32 -0.60 0.78 0.12 1.00 
f |-0.62 0.40 0.40 -0.14 -0.98 0.93 0.30 0.54 1.00 
a1|-0.56 -0.01 -0.09 -0.19 -0.02 0.35 -0.20 0.67 0.02 1.00 
a2|-0.39 0.58 0.60 -0.91 -0.39 0.37 0.24 0.35 0.37 0.09 1.00 
pi| 0.61 -0.28 -0.21 0.25 0.12 -0.25 -0.14 -0.63 0.05 -0.43 -0.15 1.00 
  
  
  
  
Table 3 shows a correlation matrix for the first image (Fig. 4) with 12 parameters. Strong correlation betweenw andy, 
can be found and although strong correlation can be found also between some other parameters, these relationships 
consist of more than two parameters, andthe value of w can be estimated as the zenith angle. Consequently, in 
order to reduce interior parameters, let w be the known value. Since x and ÿ can be estimated as the horizontal 
angle and 0 degrees respectively, let these values be the initial values because of the X,Y axis for the CCD camera and 
the video theodolite are not perfectly parallel with the test course. : 
Furthermore, since the information which is acquired from the goal and course lines in the orientation image give two 
dimensional coordinates, let be 8 parameters, the exterior parameters (X,, Y,,Z,, « , ¢ ), principal point (x,,Y,) and focal 
length (f) are unknown parameters in this investigation. In order to get stable solution, x, 256 was used 
simultaneously as a additional constrain equation with collinearity equation. 
Table 4 shows the calibration results and the accuracy for the orientation image with 16 control points. 
Table 4 Calibration results and accuracy of a goal image 
(a) Calibration results 
  
  
  
  
  
  
E Y, Zs $ K x0 v0 f 
0.258m -1.615m 0.650m -0°53'44"-0"6'3" 256.0 pic 218.2pc . 16.182 
(b) R.M.S.E. 
Xe Yo Lo $ K x0 vo f 
  
  
  
105.460mm 17.074mm 6.253mm 0.049" 0.048? 0.233 pic 1.221 pic . 0.155mm 
  
Figure 6 shows sequential images during the simulated 100 meter race. Since the doll was running on a parallel plane 
perpendicular to the camera, X and Z coordinates for the doll's feature points (head and right-toe) in each sequential 
image were calculated from the following two-dimensional projective transformation. The feature points were extracted 
manually. 
841X * àzy —asıf 
xz fas 842X * a25y — aol (Vz Vo) 
(1) 
Z= Zu + FE yo) 
842X * a25y — aol 
where ; 
Xo, Yo, Zo ; camera position 
  
  
  
X , Y ,Z ; object coordinates of the feature points 
X y ; image coordinates of the feature points 
f ; focal length 
aij; rotation matrix with three parameters,o,o,« 
  
Figure 7 Multiexposure station Video theodolite 
However, each sequential image was taken at a different exposure station as indicated in figure 7 dueto the discord 
between the center of the theodolite and the lens of the CCD camera. Then each camera position have to be corrected to 
response to the moving theodolite by following equation. 
JAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences’, Zurich, March 22-24 1995