degrees. The geometric configuration of the image ac- 
quisition is shown in figure 1. 
2.4 Determination of image coordinates 
Two different procedures were used for the measure- 
ment of the image coordinates of the signalized points. 
One set of image coordinates was obtained using a chain 
code algorithm /Lenz 1987/. At first, for each image 
point a surrounding box is drawn interactively. By means 
of histogram analysis within this window, a greyvalue 
threshold is automatically determined, discriminating 
pixels belonging to the image point from those belonging 
to the background. This yields a closed boundary line 
passing between image point pixels and background 
pixels. In the next step, a more precise boundary line is 
determined separately for the x- and y-axis by means of 
linear greyvalue interpolation. For the determination of 
the x-coordinate of the image point only the vertical 
boundary line elements are shifted, and vice versa. From 
the two refined boundary lines, the centre coordinates 
of the enclosed image point are determined with subpi- 
xel accuracy by calculating the 0^ and 1* order momen- 
tums from the line integrals. 
A second set of image coordinates of the same eight 
images was derived using least squares matching /Fórst- 
ner 1982/. A template showing a black circle with a 
diameter of 10 pixels on a white background was gene- 
rated. Although a method for the automatic detection of 
approximate signal positions in the images can easily be 
set up, for reasons of simplicity the results of the first 
described algorithm were used as initial values for the 
matching procedure. Plausibility checks for the results 
were carried out as described in Heipke, Kornus /1991/. 
A theoretical comparison between the two algorithms 
reveals that 
- leastsquares matching determines the centre of the 
circular signal as projected into the image, chain 
code matching determines the centre of the distor- 
ted signal; although the difference between the two 
positions is not significant in most cases, only the first 
position is correct. 
- least squares matching uses all pixels of the signal, 
chain code matching uses only the signal contour. 
Thus, in the latter case radiometric errors within the 
signal (eg. reflections) can be tolerated. 
- only least squares matching produces an accuracy 
estimate for the results. 
   
- chain code matching runs substantially faster. 
A comparison between the two sets of image coordinates 
resulted in a root mean square error of 0.06 um for each 
coordinate. From the above observations and these re- 
sults, it is clear that both algorithms give excellent results 
for the measurement of image coordinates of signalized 
points. In a particular project the more suitable algo- 
rithm has to be chosen according to additional criteria. 
3. RESULTS 
3.1 Results of calibration 
  
The two questions to be investigated here were the 
accuracy of the determined calibration parameters of 
the ProgRes 3000 and their stability over time. For all 
computations the bundle adjustment programme CLIC 
developed at the Chair for Photogrammetry and Remote 
Sensing, Technical University Munich /Miiller, Stephani 
1984/ was used. 
In order to impose little constraint on the solution, only 
five control points were introduced, one in each corner 
of the testfield and one in the middle. In a first compa- 
rison both sets of image coordinates were used. Since the 
results did not show any significant differences, only the 
coordinates obtained with the chain code algorithm are 
considered in the following. The calibrations were car- 
ried out in three different epochs over three weeks. The 
results are presented in table 1. For each epoch the 
values and theoretical standard deviations of the princi- 
pal distance, the location of the principal point, and the 
maximum effect of distortion (radial and tangential) are 
given. Also the estimated standard deviation of the 
image coordinates o, is included. The following conclu- 
sions can be drawn from the results: 
- A calibration of the parameters of interior orienta- 
tion and lens distortion is necessary, if precise three 
dimensional object point coordinates are to be de- 
termined. The location of the principal point differs 
by more than 119 um (about 40 pixels) from the 
centre of the chip, the distortion amounts to a maxi- 
mum of approximately 75 um (about 25 pixels). 
- The results show a very stable behaviour over time. 
Therefore, a calibration has to be carried out in 
extended time intervals only.