CALIBRATION OF CLOSE-RANGE PHOTOGRAMMETRIC SYSTEMS 1485 
TABLE 1. NUMBERS OF PHOTOGRAPHS, MODELS, AND CORRESPONDING MEASUREMENTS. 
  
  
  
  
  
Number of Minimum Number of 
Photos Models Unknowns Object Total Point Model Point 
Points Measurements Measurements 
(e.g., mono-comparison) (stereo plotter) 
2 1 34 34 68 34 
3 3 51 17 51 51 
4 6 68 12 48 72 
6 13(11) 102 8(10) (60)48(60) 104(110) 
TABLE 2. RESULTS oF TEST CASES. 
Number of Photo Iteration RMS in um RMS for 24 (x, y, z) 
Photos Models Object Control Scale Sequence (photo scale) Check Points in um 
Points Points for all points (photo scale) 
Horizontal Vertical 
2 1 42 — 10H. 10V. 1:15 Ve Vu 1.7 0.8 0.5 
2 1 64 3H,3V 1:30 Va 5.3 45.0 27.8 
2 1 64 21H, 3V 1:30 Va, Vg 3.4 46.5 31.1 
2 1 64 10H, 10V 1:30 Vc 2.9 2.6 0.3 
9 1 64 10H 10V 1:30 Ve Vu 27 2.5 0.4 
3 3 62 2H,3V 1:30 Va 9.3 27.4 18.5 
3 9 62. 2H 3V 1:30 Ve Vu 7.3 46.4 24.2 
3 3 82 10H, 10V 1:30 VG 7.0 2.2 0.5 
3 3 69 16H 10V 1:30 Ve, Vs 6.7 1.5 0.3 
4 6 61 2H,3V 1:30 Vo 9.7 38.5 44.9 
4 6 61 29H.3V 130 Ve, Va 7.7 25.6 34.3 
4 6 61 10H, 10V 1:30 Va 6.7 2.0 2.6 
4 6 61 10H, 10V 1:30 Ve Vu 6.4 2.2 1.7 
6 11 33 29H. 3V 1:30 Va 8.4 26.4 60.8 
6 11 33 2H,3V 1:30 Ve Vu 7.8 18.3 56.1 
6 11 33 10H, OV 1:30 Va 7.9 5.5 1.0 
6 11 33 16H 10V 1:30 Ve Vu 6.2 1.2 1.2 
  
more, the same cases were computed with minimum control (two horizontal and three vertical 
control points). The results are listed in Table 2, based on PSK—measurements (c — 3 um). 
Following common photogrammetric practice, no variance-covariance matrix was obtained 
for computational reasons, which explains why no standard deviations for the unknowns are 
given. The quality ofthe method, however, is apparent from the RMS values for all points and 
forthe check point residuals. The increase in RMS values forall points with more photographs 
was expected as all points were transformed in all models. Even so, they are very small. 
The actual fitting into the control was somewhat weak when using minimum control, which 
might partly be caused by uncertainties of the control point coordinates. However, with ten 
control points in both planimetry and height an excellent fit has been obtained. 
CoNcLUDING REMARKS 
Although computer intensive, the method described is an excellent tool for close-range 
photogrammetry, especially when using non-metric cameras, as it does not assume a constant 
interior orientation when taking different photographs. The step-by-step iteration procedure 
permits a simple basic calibration if the job athand does not require more. As planimetric and 
vertical control are treated separately, the minimum control requirement can easily be met 
without much surveying work. If the object is placed on a plane surface, three bolts with 
predetermined height can be placed conveniently around it, and a ruler or similar object of 
known length, located on the plane surface is all that is needed for defining the object space 
coordinate system. Usually, this is sufficient for close range work, as any local system is 
permissible. The results proved that high accuracies can be obtained with this method. 
In closing I would like to acknowledge the efforts of Mr. H. Moniwa, graduate student at 
U.N.B., in connection with this research, which in part was sponsored by the National Re- 
search Council of Canada.