Cruz, Santiago 
been measured, several transformations can be made and the user can decide the best solution. The conformal and affine 
transformations between the corner coordinates computed for a frame and the "calibrated" ones for the camera will give 
residuals. But two additional transformations have been considered. A two-dimensional projective transformation 
allows correction for lack of parallelism between two planes. This can be useful when a paper print (without the edges 
cropped) is scanned. This can correct for errors introduced in the optical enlargement of the paper print. Also a bilinear 
transformation (see Ghosh, 1987) can partially correct for some non-linear errors. But special care has to be taken 
because both transformations have 8 parameters. With 4 corners only 8 equations can be written and there will not be 
residuals. 
3 SOME EXAMPLES OF AUTOMATIC INNER ORIENTATION 
The method presented in this paper has been tested with some examples. Several photographs taken with non-metric 
cameras have been oriented. The cameras are RICOH KR10M (35 mm format) and a HASSELBLAD 500 CM (70 mm 
format). Several frames had been measured in an analytical plotter (Wild AP1 used like monocomparator), so values for 
"calibrated" corners were available for both cameras. The frames (slide and negative films) were scanned with two 
desktop scanners AGFA ARCUS II (at 600 dpi maximum optical resolution) and AGFA ULTRA-HORIZON (at 1200 
dpi). Several examples are shown in figures 4, 6 and 7 with the results of different transformations (4 and 6 parameters) 
in Table 1. In general errors are higher in 70 mm film format than in 35 mm format. Figure 6 shows an example of inner 
orientation in a 70 mm frame. Typical marks of the Hasselblad frame (slits at the left edge and special frame corners) do 
not disturb the application of the method. In this case the error is slightly higher than the pixel size (21 um) using the 4- 
parameters transformation (table 1). 
  
  
  
  
  
Figure 6. Inner orientation in photograph taken with Hasselblad 500 CM and scanned at 1200 dpi. 
  
  
  
  
  
  
  
  
  
  
Affine Tr. (6-par.) Confomal Tr. (4-par.) 
; Ox (mm) Oy (mm) Ox (mm) Oy (mm) 
Ex. 1 (Fig. 4) +0.008 +0.014 +0.015 +0.010 
Ex. 2 (Fig. 6) +0.014 +0.018 +0.026 +0.028 
Ex. 3 (Fig. 7A) +0.012 +0.004 +0.023 +0.015 
Ex. 4 (Fig. 7B) +0.001 +0.068 +0.101 +0.121 
  
  
  
Table 1. Coordinate transformation errors (in terms of cx and oy) for the examples of figures 4, 6 and 7. 
©; 600 dpi; '?: 1200 dpi 
  
154 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 
  
  
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