3 SIMULATION 
3.1 Assumptions 
The simulation assumes that a setup of 2, alternatively 3 
cameras is placed in alternatively 1, 2 and 4 positions 1m 
above a test field (volume: 1x1x1 m3) with camera axes 
directed towards the centre of the field, see fig. 1. (Principle 
distance =1800 pixels, image format: 1000x1000 pixels). 
Thus a near normal configuration is the case. The result is 
derived by bundle adjustment (Hädem, 1989) and shown in 
fig.s 2 and 3. 
Two alternative configurations of object points are assumed, 
as illustrated by fig.s 1a and 1b. 
Two alternatives of object control are assumed: 
- "given points only": the object points are given except 
the 6 endpoints of distances fig.1c (i.e. the testfields fig.s 
1a and 1b get 8 and 21 given points, respectively); 
- "given distances only": the distances fig. 1d are given 
(i.e. all the object points are unknowns). 
Two alternatives mentioned as constrained and not constrained 
relative orientation, are assumed (for those cases where the 
setup of cameras have been placed in several positions): 
- constrained relative orientation: It is assumed that the 2 
(3) cameras of a setup retain their relative orientation 
when the setup is moved to another position to taking a 
new set of pictures; 
- Dot constrained relative orientation: No such assumption. 
5 unknown camera parameters are assumed: those of inner 
orientation (xy, Y,,c), affinity and lack of orthogonality (see 
eq.s (A1) in the Appendix). In fig.s 2 and 3, these parameters 
are assumed to be different from camera to camera, except for 
the lower row where it is assumed that they are global. 
3.2 Summary and conclusions 
On the basis of the graphs in fig.s 2 and 3, a summary and 
some concluding comments will be given. In the following, 
Ore((-) indicates the mean of actual o,,, taken from the graphs. 
The results 1) - 5) assume local camera parameters. 
1 ) The ratio Orel (in X- or Y-direction)/ Orel (in Z-direction) is: 
0.27 in the "given points only" cases, 
0.42 in the "given distances only" cases 
showing that the accuracy of distances in different 
directions is rather inhomogenous. 
2) Theratio c 
0.55 
showing that the geometry in the "given distances only" 
cases is far from being optimal. 
rel (given points on) Sie (given distances only) IS: 
3 ) The ratio Orel (27 object points) ^9 rel (14 object points)!S: 
0.76 in the "given points only" cases 
0.92 in the "given distances only" cases 
4 ) The ratio Orel (constr. rel. or) 9rel (not constr. rel. or.) IS. 
0.99 in the "given points only" cases, 
0.74 in the "given distances only" cases. 
The effect of constraints is more significant in the 
"given distances only" cases, recalling that these cases 
have a less optimal geometry. 
     
  
5) The ratio c 
0.81 
rel (setup of 3 cameras)" rel (setup of 2 cameras) IS: 
6 ) The ratio Orel (global camera par/ Orel (local camera par.) is: 
0.87 in the "given distances only" cases. 
7 ) When global (instead of local) camera parameters are 
assumed, there is less frequent ill-conditioning. 
The main conclusions are: 
1) The use of a) constrained relative orientation, b) more 
than 2 cameras in a setup, and c) different positions and 
rotations of the setup strengthens the geometry. 
2 ) The use of given distances (in stead of given points) 
requires careful geometrical considerations of their 
placement in object space. 
3) The assumption of local (in stead of global) camera 
parameters weakens the geometry and decreases the 
relative accuracy. 
4) "The near normal case" gives inhomogenous relative 
accuracy. 
Although many interesting simulation results have been 
obtained so far, there are still many questions left. Thus, it is 
desirable to perform further investigations on the use of: 
other camera orientations (position and convergence) to get 
better intersection conditions, 
- other configurations of given distances (position and 
direction), 
- alarger number of object points for different cases of type 
of control (points and distances), 
- other types of additional parameters (like global or local 
radial distortion and decentering). 
- constraining precalibrated relative positions of targeted 
points on reference bar, 
- constraining geometrical information (e.g. linearity, see 
Zielinski, 1992); geometrical figures may be placed in 
different positions in the object space. 
Such investigations should be followed up by real experiments. 
4 EXPERIMENTAL ACCURACY RESULTS FOR A 
PHOTOGRAMMETRIC STATION. 
To indicate the accuracy potential of a high precision 
calibrated photogrammetry system, some of the results from 
an accuracy test of the Metrology Norway System (MNS see 
Pettersen, 1992a and 1992b, Amdal, 1992, and Axelsson, 
1992) is reported. The MNS is an on-line photogrammetry 
system based on high resolution CCD cameras (Kodak Megaplus 
with 12.5 mm lens) interfaced to a VME computer, measuring 
coordinates of laser spots or Light Emitting Diodes (LEDs). 
Using the Light Pen (see Pettersen, 1992b) turns the system 
into a "Hand-Held Coordinate Measuring Machine" (CMM), 
allowing the use of standard CMM accuracy tests for evaluating 
the accuracy of the MNS. The CCD cameras in the MNS are 
laboratory calibrated by Metronor AS, employing an optical 
calibration method which differs from the test field approach 
studied in the simulations. This one time calibration process, 
which involves measuring more than 10 million calibration 
points for each camera, turns the high resolution CCD camera 
into a photogrammetric camera.