Susumu Hattori 
  
  
  
-40km |OI12GCPs 
e 9 GCPs 
^ Check Point 
/ Flight Direction 
® 0 of satellite 
  
  
  
  
  
-50km 
  
  
I I 
40km 0 -80km 
Figure 4: Disposition of GCPs and Check Points for MOMS-2P images 
Table 3: Orientation result for MOMS-2P Image Pair 
  
  
  
  
9GCPs 12GCPs 
00 internal external To internal external 
model | (um) | accuracy accuracy (um) | accuracy accuracy 
H V H V H V H V 
  
lp 2.3 | 10.8 | 13.1 | 14.2 | 14.3 2.3 9.3 | 11.4 | 12.4 | 10.6 
PP 3.9 16 1182 | 11.6 | 112 3.7 | 13.9 | 16.8 | 10.8 |. 10.5 
la 24 | 10.7 | 14.4 | 11.8 | 12 2.4 8.8 12 | 11.1 | 10.3 
2a 3.8..].13.9.] 17.5 1 11.5.] 11.3 3.6 ]| 12.3 | 16.4] 10.5. ]1 10.5 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
6 CONCLUDING REMARKS 
The reported investigations have revealed the following properties of affine-based orientation/triangulation of 
satellite line scanner imagery: 
e Affine projection is linear with regard to object point coordinates and thus closed-form orientation is 
possible. The inclination angle and the focal length are however necessary for image transformation from 
central perspective to affine projection. 
e The precision of affine-based orientation corresponds well to that of central projection-based methods. As 
compared to the central projection models without exterior orientation constraints, the affine approach is 
generally more stable. 
e The rank of affine-based observation equations is four, while that of central projection-based equivalents 
is seven. The degrees of freedom within a model formed by two overlapping affine images is 12 and the 
minimum number of required GCPs is four. On the other hand, the model created by two central perspective 
images has 15 degrees of freedom if interior orientation is treated as unknown, and the minimum required 
number of GCPs to orient the model is five. The burden of control surveying is, therefore, of little difference 
for the two orientation methods. 
e Corrections to linear distortions in parameters( e.g. Earth rotation effect, uncertainty of geoid) are auto- 
matically incorporated in the affine observation equations. 
e A major shortcoming of affine projection-based orientation is that the images taken with a sensor with a 
relatively wide field view angle, e.g. seven degrees for the MOMS-2P sensor, are not completely subject 
to affine geometry, but stand between affine and central projection. This produces measurement errors 
due to height differences and so these must be eliminated via iterative image transformations from central 
perspective to affine projection. 
e The affine projection-based orientation needs to utilise either a local tangent plane XYZ coordinate reference 
system or a Gauss-Krueger projection coordinate system such as UTM; the model is not suited to earth 
centered coordinate systems since the satellite is assumed to fly in space at a constant velocity. Height 
errors due to earth curvature must of course also be compensated. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 365