International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
not very good. Also the high number of required iterations is an 
indication of a relatively poor result. Compared to the analysis 
with image 334, however, this result is a significant 
improvement. It should be recalled that the obtained rms 
corresponds to only 7/4 of a pixel Figure 7 shows the 
orthoimage and the model grey values, both computed with the 
initial DTM, and the model grey values, computed with 
DTMi s, 534m2- 
  
  
  
  
  
  
  
Image | Comment |lterations | Zo[m] | rms[m] 
334ml | only scale factor no conv. no conv. no conv. 
334m2 | linearly changed 42 79.5 242.7 
  
  
Table 3. Results with modified image 334 
   
   
£3 
  
Figure 7. Image 334m2: orthoimage (1.), model grey values of 
initial DTM (m.) and of DTMi, s 5345 (r.) 
     
Figure 8. Model grey values of DTM|i s, 53445 (1.), enlargement of 
marked area (m.) and same area in orthoimage (r.) 
The orthoimage shows less contrast than the orthoimage in 
figure 6. This happens, due to the used scale factor (rm = 0.3). At 
the beginning the model grey values show the already reported 
strips caused by manual measurement (figure 7 centre). The 
model grey values computed with DTM, 53445" (figure 7 right 
and figure 8 centre) show again some blobs. The resulting 
DTMi s. 3342 i8 illustrated in figure 9. 
  
Figure 9. DTMis 3345» (height-exaggeration factor 2x) 
In comparison with DTM, s 33s (figure 3), DTM, s, 3349» exposes 
the consequences of contrast reduction of image 334. The 
resulting DTM is smoothed. 
In order to demonstrate that the linear modification applied to 
image no. 334 does not have a negative effect if orthoimage and 
model grey values are of approximately equal brightness, we 
have also applied the modification to image no. 338. As 
expected, the result does not show significant changes to the 
computation with the original image (see analysis no. 3, table 
1). After 19 iterations the accuracy parameter Z, has the value 
of 42.6 metres and a rms of about 148.7 metres. 
3.4 Two-image analysis 
The advantage of applications using multiple images with 
different exterior orientations is that an additional geometric 
stabilisation constraint, the correspondence between the images, 
is added to the determination of the surface. In addition, further 
images provide independent grey value information for the 
reconstruction of the unknown DTM heights. Compared with 
the one-image analysis, it is unnecessary to introduce a known 
height as a scale factor, because homologous image rays 
intersect in the appropriate object point. In this way, the 
definition of absolute heights is guaranteed. 
If we use the two described original images, the computation 
failed as expected. For this reason, we carried out the two- 
image analysis using the modified images 334m2 and 338m3. 
The analysis converges after only four iterations (table 4). 
  
Images Comment Iterations Zo [m] rms [m] 
  
  
  
  
  
  
334m2 / 338m3 | linearly changed 4 -19.2 140.1 
  
  
832 
Table 4. Result of a two-image analysis using modified images 
The fast computation and the values of the accuracy parameters 
are indications of a good reconstruction. DTM; 334m2. 338m 
(figure 10) shows that the poor grey value information of image 
334 could be overcome by the second image. 
  
Figure 10. DTMys, 334m2. 338m3 (height-exaggeration factor 2x) 
3.5 Radius of convergence 
To investigate the radius of convergence of MI-SFS, we have 
inserted different initial DTMs into the algorithm. These DTMs 
differ from the manually measured DTM by an offset a, and a 
scale factor m. The height differences are chosen in a way that 
the mean position change of a surface element in the two 
images is a multiple of the pixel size. As mentioned in section 
3.2, a pixel change in the images conforms with a height change 
of about 360 metres. Using equation 7, 15 different initial 
DTMs were computed (table 5). 
The results of the two-image analyses assuming Lommel 
Seeliger reflectance and computed with different initial DTMs 
are presented in table 5. The numerical results show, that the 
radius of convergence of MI-SFS is approximately four pixels 
which conforms with an offset a, of about 1440 metres. It 
should be noted, that the algorithm produces a correct result 
also starting from a horizontal plane located at the average 
height in the investigated area (third line of table 5). 
whe 
  
Tal