Susumu Hattori 
  
Listed in Table 1 are the results obtained in the orientation/triangulation adjustments for Kobe-AT, based 
on four different models: 1D perspective model (Eqs. 2), the parallel perspective model (Eqs. 4), the 1D 
affine model (Eqs. 3) and the 2D affine model (Eqs. 5). Both internal and external measures of accuracy 
are listed. The internal precision (RMS 1-sigma) is obtained via the covariance matrix of parameters from the 
"bundle adjustment’, whereas the external accuracy is quantified through the RMS value of ground check point 
discrepancies. The time variation of parameters in the 1D perspective and 1D affine models was assumed to 
be linear. Fig.3a shows the disposition of GCPs and check points for Kobe-AT. Three patterns of control were 
tested, as indicated in Table 1 and Fig. 3a. These comprised four, six and nine GCPs. All other control points 
were used as check points. 
With the exception of the case of the 1D perspective model with 4 GCPS, all models yielded sub-pixel external 
accuracies. Although there is little to distinguish the results of each algorithm, the 2D affine model produced 
the most consistently accurate ground point coordinates in the orientation /triangulation for the Kobe-AT test 
area. 
Table 1: Orientation accuracy for Kobe-AT 
  
  
  
  
  
  
  
  
  
  
4GCPs 6GCPs 9GCPs 
To internal external oo internal | external To internal external 
model | (um) | accuracy | accuracy || ( pm) | accuracy | accuracy || (um) | accuracy accuracy 
H V H V {HV IH] V H.|Vv.lH V 
1p 4 3.4 | 10.7 | 5.7 13.5 3.9 3 {89537174 4.1 2.8 | 8.3 ] 5.1 6.4 
PP 4 6.6 | 24.5 | 7.7 | 8.7 4 2.9 | 83.6 | 5.3 |.7.7 4 2.8 | 8.3 | 5.3 6.2 
la 3.8 3.3] 8.9 | 5.8 |. 6.9 3.8 2.8 1 7.9 1 5.5 1 6.6 3.9 2.7 | 7.8 | 5.2 6.2 
2a 3.9 3 36 | 58] 65 3.9 2.8 | 7:8 | 5.3 | 6.5 4 2.7 | 7.6 | 4.9 5.9 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Unit of accuracy is meter 
lp — 1D perspective model, pp — parallel perspective model, 1a = 1D affine model 2a = 2D affine model 
The counterpart of Table 1 for Kobe-Osaka is Table 2, which confirms that the 2D affine model yields the 
optimum results. Not only did the 2D affine model produce the most accurate ground point coordinates, it 
proved to be the most stable algorithm. The accuracy discrepancy between Kobe-Osaka and Kobe-AT could 
be anticipated due to the differences in area, but a contribution also likely comes from limitations in the affine 
modelling over the larger image scene. 
Table 2: Orientation accuracy for Kobe-Osaka 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
4GCPs 6GCPs 9GCPs 
00 internal | external To internal external To internal external 
model || (um) | accuracy | accuracy (um) | accuracy | accuracy || ( pm) | accuracy | accuracy 
H V H V H V H V H V HY 
1p 4.6 |4.3| 129 | 5.4 | 34.2 58 {57 17.9] 5.5 | 26.7 5.5 | 4.6 | 14.1| 5.2] 25 
PP 5 6 | 19.8 | 8.8 | 19.8 5.6 | 5.9 | 18.2 | 8.6 | 10.1 4.9 4 | 10.9 [5.5 | 9.4 
la 4 4 110.4 | 5.9 | 9.1 4.5 14.1] 10.8 | 5.5 ] 10.3 45 1.3.7! 97 153, 9 
2a 4.7, | 4.4 [ 11.3 | 7.1 -| 103 4.5 “1 3.7 9.8 6 9.5 48 13.6 | 9.7 | 5.6] 8.7 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
5.2 Orientation of MOMS-2P images 
The MOMS-2P 3-line stereo imaging sensor scans the ground in along-track mode, with the ground resolution 
of the forward- and backward-looking linear arrays of 2976 pixels being 18m x 18m and the sensor inclinations 
being +/-21.4°. The view angle is about seven degrees, which is significantly wider than SPOT. MOMS-2P 
operated from the MIR space station, which has an orbit height of about 400km and an orbit inclination of 
91.6". The stereo image pair used in the present experiment covered a 150km long, 50km wide strip over 
southeastern Germany and part of Austria. The maximum height difference in the underlying terrain was 
180m. Some 58 GCPs were surveyed by GPS and Fig.4 shows their distribution. The orientation/triangulation 
adjustments, again utilising the same four mathematical models, were conducted in the UTM coordinate system. 
The resulting triangulation accuracies are shown in Table 4. 
In the case of MOMS, the 1D and 2D affine models, along with the parallel projective model, display slightly 
better accuracy than the 1D projective model. For practical purposes, however, the accuracies produced by 
these three models can be considered equivalent. This is perphaps a consequence of the field view angle being 
a relatively wide 7°. Thus, the strength of the affine model does not show up. 
  
364 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.