chosen. The overlap between two neighbouring photos in 
a flying line is approx. 60%. These four photos are 
digitized using the photo scanner PS1 with pixel size 15 
x T5 um? and 8 bits per pixel (i.e. 256 grey value steps). 
The algorithm of the image pyramid is used to deter- 
mine the initial DTM in all tests. A horizontal plane is 
utilized as the initial height surface in the top level. 4 
and 5 levels of image pyramid are employed for the 
windows A,C and B, respectively. With that, the 
precision of initial DTM is 2%, H1.2m) and 3%, H 
(71.8m) respectively, where the notion H means the 
flying height above ground and will be used in the 
following text. That also corresponds to the precision of 
x-parallax about 1.5 pixels and 1.1 pixels in the top 
level. 
DTMs with the grid size 0.5 x 0.5 m? in these three 
windows were measured by an operator on the analytical 
. Stereo plotter WILD AC3 to compare with the computed 
DTM by FV. The measuring precisions (Tab. 1) show 
the different quality of texture in these windows: A and 
B are approximately the same, C is inferior. 
  
  
     
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| 00,200 | GZ,0P | O70 mas 
window k n [m] [m] [m] 
A 320 | 1943 0.07 0.03 0.08 
B 209 936 0.08 0.04 0.11 
C 300 | 920 0.14 0.08 0.16 
  
  
  
  
  
  
  
      
      
     
   
    
   
    
   
   
   
   
     
   
   
   
   
    
  
   
   
   
  
Tab. 1: Statistic data of the height measurements in the 
windows A,B,C with the grid size 0.5x0.5m^ by an 
operator on the analytical stereo plotter WILD AC3. 
k = number of Z-points, n = number of Z-measurements, 
Go. z.0p = the global precision of each single Z-measure- 
ment, 
O7 OP. 07, OP,max 7 ‘he mean and maximal value of the 
standard deviations of the mean Z-values. 
The following data will be given in the following tables 
to judge the precision of the computed DTM by FV: 
& = the standard deviation of unit weight 
a (grey value); 
67,FS.Ó7 ps, max = the mean and maximum of the 
standard deviations of the Z-values, 
determined in the computation of FV; 
= the standard deviation a posteriori of 
the computed Z-value (Zi ). by FV and 
Spg / Sop 
of the mean ( Zor). of the height 
observations measured by an operator 
on the grid point i, i = 1 (1) Æ (both are 
derived from the measured DTM by 
operator); 
az, = the maximum of the absolute values of 
,max 
the resolved height differences (az, ) 
1i=1(l)k; 
974 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
   
AZ ts, = the constant height difference between 
both DTM (Zgg). and (Zop)., i=1 (1) & 
and it's standard deviation, 
where (Zss), - (Zor). = (az, * AZ. One can find the 
related detailed descriptions in [3]. 
Parts of the test results for the window C will be 
analyzed briefly as follows. They are in good agreement 
with the other ones for the window C and the ones for 
the windows A and B. 
Tab. 2 shows the test results using 2 images, where 2x2 
pixels per G-facet and 4x4 pixels per Z-facet are used, 
denoted by 
P:G:Z=1:2°. 4" 
One sees clearly that all computations converge in 2 or 3 
iterations. 6, becomes larger from the upper level to the 
lower one. That is caused obviously by the low-pass 
image filtering from the lower levels to the upper ones, 
where image noise is damped down. 
The standard deviations of heights, that are determined 
by FV, become smaller from the upper level to the lower 
one, i.e. from coarse resolution to fine one. The standard 
deviations a posteriori se; of the computed Z-values by 
FV in the 1st level are less than or equal to 3 cm 
(70.05 Y o FD that corresponds to 0.3 pixel in the image 
space. Also AZ -0, ie. there exists no offset between 
both DTM (rs) and (Zo ).. The value az, e" 
i i 
equal to 13 cm in the Ist level. 
Furthermore, 82.3% of the resolved height differences 
are located in the interval +6cm (70.197. H); Te. 0.6 
pixel. 
Tab. 3 shows the test results using 4 images. Comparing 
with the ones using 2 images (Tab. 2), the precision of 
the object surface reconstruction using 4 images is better 
than the one using 2 images with respect to &, and Spg- 
All standard deviations a posteriori, spg. of the com- 
puted heights by FV in the 1st level are smaller than 
3cm, i.e. 0.05% H or 0.3 pixel in the image space, 
where the constant height difference AZ 
significant, i.e. AZ —0. 
Tab. 4 shows the test results using 4 images and the 
very high resolution of 2x2 pixel per Z-facet and with G- 
facet — Z-facet, denoted by 
is not 
P:GtUZ2]:22993?. 
This is the maximum resolution applicable for FV using 
the S-model as the object grey value model. In that case, 
all computations converge in 2 or 3 iterations. As before 
(Tab. 2 and 3), 6j becomes larger from the upper level 
to the lower one. The standard deviations a posteriori 
Sps Of the computed heights by FV in the 1st level are 3- 
) — OX o/ 
4cm (=0.05-0.07%, 
space. So, the precision of FV at maximum resolution is 
only slightly less than the one with the lower resolution 
H), i.e. 0.3-0.4 pixel in the image