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Figure 1: Real digital images. Upper row: images 1-4 from left to right. Lower row: images 5-8 from left to right. 
5.1 Testfield block 
The object was a 3-D testfield at Helsinki University of Technology, containing 161 known 3-D points with an accuracy 
of about 0.03 mm. The camera was a digital camera, Olympus Camedia C-1400L with a zoom lens. The image size was 
1280x1024 pixels, and the nominal focal length varied from 1400 to 4000 pixels. 
Eight images were taken, images 1-4 with the smallest zoom, and images 5-8 with the largest zoom. The images were 
taken from clearly different positions and orientations. The images are shown in Figure 1. The unknown interior orienta- 
tions of the images were partially the same: affinity and non-orthogonality were kept the same, whereas principal point 
and focal length were kept different between image sets 1-4 and 5-8. In both image sets, five non-linear lens distortion 
coefficients were taken into account, three for radial distortion, and two for tangential distortion. The effect of the lens 
parameters was controlled in all adjustment methods with one fictitious observation equation per parameter (Heikkili, 
1992). 
Measurements. The images were measured manually with a computer program which had a zoomable measurement 
window. The measurement accuracy was supposed to be less than half a pixel. 398 image points from 97 different object 
points could be measured. Approximate values for the singular correlations were computed for all possible image pairs 
with at least eight corresponding points. This gave 27 image pair combinations, from which 50 image triplets could be 
formed in this example. 
Adjustments. The projective adjustment was performed three times. In the first adjustment (Projective 1), only the ob- 
servations belonging to the most optimal image pairs were used. In the second adjustment (Projective 2), extra constraints 
3 were used where possible, to maximize the number of observations in the adjustment. The extra interior orientation 
constraints for the trifocal planes (equation 1) were also used in the second projective case. 
Because the data and the number of equations were different between different cases, a subset of common data between 
all adjustments was extracted from the original data, to get more comparable cases. This common data contained 319 
image point observations from 77 object points. The third projective case (Projective 3) used this common data, adjusted 
with all possible constraints. 
The physical and bundle adjustments were performed twice, first with all possible data (Physical 1 and Bundle 1) and then 
with the smaller common data (Physical 2 and Bundle 2). The characteristics of all adjusted cases are in Table 2. 
To get the resulting 3-D models from different adjustments comparable, the models were first transformed to the known 
testfield co-ordinate system by using a seven-parametric similarity transformation. The root mean square error (RMSE) 
between the transformed co-ordinates and the true co-ordinates was then computed. 
Data usage. The data usage is summarized in Table 2. It can be seen from this table that the adjustment based on the 
projective singular correlation always missed some data (except in the Projective 3 case). There were 97 object points, 
but in the first projective case all observations of ten object points were totally missed from the adjustment. Similarly, 
some correlation equations between some image observations were also missed. This can be seen by comparing the 
redundancy numbers of the cases. For example, in the bundle adjustment, the maximum redundancy of 456 was obtained, 
whereas the best projective redundancy (in Projective 2) was only 432. Thus, at least 24 useful equations between image 
observations were missing because the corresponding singular correlation matrices were not taken into the adjustment, or 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 647