49 
8.2.3 Fiducial Marks 
The image co-ordinate system is defined by fiducial marks in the camera 
frame, which was filed to form small corners. There are eight marks in each 
camera, and their positions define the image co-ordinate system. The co-ordi 
nates of the fiducial marks were determined in the following way. A series of 
exposures towards a bright and unfocussed background was made in each 
camera. The fiducial marks in these photos were measured in a comparator 
and then transformed to one and the same system. Because of film shrinkage, 
setting, rounding-off etc the transformed co-ordinates differ between the pic 
tures. (see formulas 8.3.1 and 8.3.2) 
On each picture all measurements were repeated to estimate the standard 
deviation sj, which contains the effects of setting errors, rounding-off errors 
and accidental errors inherent in the comparator. 
The variation of the co-ordinates of the fiducial marks between the pictures 
gives us a possibility of estimating a standard deviation, s 2 , which also contains 
the effect of film shrinkage and possible errors introduced by the camera during 
exposure. 
The co-ordinates of the fiducial marks are the averages of all transformed 
measurements and the precision of the averages is calculated from the standard 
deviations of the transformed co-or-dinates. Testing the equality Si = s 2 , the dif 
ference between Si and s 2 is highly significant. The standard deviation of the 
averages is 0.58 and 0.59 jum for the two cameras. The number of degrees of 
freedom is 480 and 528 respectively. The standard deviation of a single deter 
mination of the fiducial co-ordinates is 3.17 jum and 3.42 jum respectively. 
8.2.4 Fiducial Transf ormations 
The calibration of the stereocamera is based on three pairs of pictures of the 
test object, no. 1 and no. 2 with aperature f:45, and no. 3 with f: 11. The first 
Table 7. Fiducial transformations. Stereo-Medical-Nikkor. 
Pair of pictures 
Cam 1 
Cam 2 
Scale 
S scale 
Scale 
S scale 
1 
.999622 
.001214 
1.001074 
.000290 
2 
.999818 
.001214 
1.001129 
.000220 
3 
.999684 
.001244 
1.000728 
.000354 
Mean 
Variance between 
Variance within 
.999708 
10036 10-12 
.001217 
1481087 10-12 
1.000977 
47257 10-12 
.000293 
85849 10-12