366 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
TABLE 6. NoN-METrIC CAMERAS: COMPARISON BETWEEN EXPERIMENTAL AND 
PREDICTED ACCURACIES IN MICROMETERS (A = EXPERIMENTAL VALUES; 
B = SIMULATION PREDICTOR; C= KARARA/ABDEL-AZIZ PREDICTOR) 
  
Plane 1 Plane 2 
XYZ rX rY rz rXYZ rX rY rZ 
  
Kodak A 24.1 10.1. 194 10.1 19.8 6.5 16.0 9.7 
B 426 137 342 196 380 136 3289 182 
ec 37.1 120 331 114 312 199 258 117 
Crown A 943 101 31.7 8.3 
B 32.2 103 259 144 
EC. 28.1 9.1 25.1 8.6 
Pentax A 7.4 2-2 6.7 2.2 9.6 3.6 8.6 2.4 
B 10.9 3.5 8.8 4.9 9.7 3.5 7.4 4.7 
C 9.5 3.1 8.5 2.9 8.0 3.9 6.6 3.0 
Hass. A 179 5.3 «16.7 3.8... 17.0 54 15.2 5.4 
500 B 17.1 5.4... 13:7 76 . 152 5.5 11.6 7.3 
C 14.9 4.8 13.3 46 12.5 5.2 10.3 4.7 
Hass. A 13.8 49 124 34 12.0 24 111 3.7 
MK70 B 14.0 A5: 112 62 12.5 4.5 9.5 6.0 
€ 19.9 3.9 109 37 10.2 4.9 8.5 3.8 
  
Table 6 gives the experimental and predicted accuracies computed from the values of To 
(Table 5) and Equations 22 and 23 (Analog formulas were established for the plane 2). 
It can be observed that, for the corresponding value of r (base-to-object distance), the two 
predictors give nearly the same results, at least for rXYZ, rX, and rY. However, there is some 
disagreement for rZ (vertical). The value o, for the Kodak camera (Table 5) is probably 
over-estimated. The value to use in the predictors is 10 wm rather than 15.6 um. 
It is also interesting to compare the accuracy of non-metric and metric cameras. If we use 
2.5 pm for o,, we find (Figures 11 and 12) for minimum accuracy of metric cameras 
(r = 0.73), rXYZ = T.0 um, rX = 2.25 um, rY = 5.6 um, and rZ = 3.1 pm. 
From all of the results obtained by Karara/Abdel Aziz, only the ones for the Pentax camera 
give for the same measurement effort the same accuracy as metric cameras. All the other 
cameras give a lower accuracy. 
Maximum accuracy with non-metric cameras. All the Karara/Abdel Aziz trials correspond 
to minimum accuracy conditions, that is, to minimum measurement redundance (one setting 
per image point, one target per object point, one frame per station). 
Added to these results are two trials performed at the IGN. The conditions of the picture 
taking and measuring process are summarized as follows: 
Camera Lens Focal length r (gr) Measuring process 
Hasselblad 500 Planar 100 mm 0.29 12.5 3 frames/station and 
Hasselblad 500  Distagon 40 mm 0.44 18 3 setting/image point 
After averaging the settings for each frame, the three frames of each station were super- 
posed by the means of a homography. The computation conditions were analogous to those 
of Karara and Abdel Aziz (particularly for the Distagon camera where an image-refinement 
method was practiced, i.e., plate-residual filtering and correction). The number of control 
points was 27. 
It can be seen (Table 7) that the maximum accuracy obtained from the best non-metric 
cameras is nearly the same as that obtained for metric cameras. 
Note that the RMS values of plate residuals were 3.05 um for the Planar and 2.98 um for 
the Distagon. Thus, in contrast to minimum accuracy conditions, it is impossible to predict 
real accuracy from such values. The maximum accuracy is obtained for o = 1.23 pum (metric 
cameras) and the use of the value 3 um would lead one to underestimate the accuracy. This 
is not an isolated observation, and is also valid for metric cameras. In other words, the value 
of a to use for accuracy prediction can be derived only from experimental accuracy studies. 
NON-SYMMETRICAL CASE OF THE STEREOPAIR AND MULTI-STATION GEOMETRY 
Studies of the non-symmetrical case of the stereopair are currently (August 1975) 
underway at the University of Illinois. As for multi-station geometry, it is currently used by