slope classes were consequently produced (see Figures 5.2 to 
3.3) 
  
Figure 5.2 
Normal view of a shaded relief representation of the test area computed from the 
DTM. 
Accuracy analysis of the DTM. The "absolute" accuracy of 
the produced DTM can only result from the comparison with 
the real terrain. Since that is not possible, the accuracy of the 
DTM has to be established by a comparison with height 
measurements of the same terrain obtained by an independent 
method with a higher order of accuracy. Such a method is the 
tacheometric field survey. 
  
Figure 5.3 
Perspective view of the test area computed from the DTM. 
To facilitate the accuracy evaluation of the DTM, 743 ground 
points (check points) were measured by tacheometric field 
survey. The vast majority of these points (about 90%) lies on 
the three rocks. The height accuracy of the tacheometric survey 
was at the 10 cm level. The heights obtained by the 
tacheometric survey were compared with the heights 
interpolated from the DTM at the same planimetric positions. 
Therefore the data that was used for the accuracy evaluation of 
the DTM consisted of height differences at the check points. It 
has to be mentioned that the two methods of computing the 
heights namely the tacheometric and the DTM interpolation are 
totally independent since for the DTM generation, no ground 
survey was applied but only GPS and photogrammetry. 
22 
For the statistical analysis of the height differences the 
following are considered (Petrie and Kannie, 1990): algebraic 
mean (M), mean error (me), root mean square error (rms) and 
standard deviation (o). These statistical expressions were 
calculated for all the height differences (n = 743 points). 
The better statistical way to describe the accuracy of the DTM 
is the standard deviation o. As can be seen from Table 5.2, the 
standard deviation is 23 cm when all the check points are taken 
into account. 
Table 5.2 
Statistical properties of the check points, for the total number of check points, 
and for the total number except the 8 blunders (reduced). 
  
  
  
  
  
  
  
  
  
  
  
  
number | algebraic | mean standard max 
of check mean error rms | deviation height 
pts M(m) me (m) (m) c (m) difference 
(m) 
total 743 -0.001 0.16 0.23 0.23 1.97 
reduced 735 0.01 0.15 0.19 0.19 0.71 
Table 5.3 
Number (and percentage) of check points that have height differences smaller than 
a particular multiple of the standard deviation. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
mean standard standard | maximum | maximum 
error error error error error 
K « |l « 20] « [3o] « Mo] 
[0.6745 of 
total 447 581 714 734 737 
(60.296) (78.296) (95.196) (98.896) (99.2%) 
reduced 362 $15 707 729 735 
(49.896) (78.296) (96.296) (99.2%) (100%) 
Table 5.4 
Number (and percentage) of check points that have height differences larger than a 
value. 
>0.2 >0.3 204 05m | »075 »4 21.5 
m m m m m m 
total 228 91 36 20 8 4 2 
(30%) | (12%) (4%) (2%) (1%) | (0.4%) | (0.2%) 
reduced 220 83 28 12 0 0 0 
(29%) | (11%) | (3%) (1%) (0%) (0%) (0%) 
  
  
  
  
  
  
  
  
  
  
Table 5.3 indicates that the distribution was indeed normal in 
all the cases. From the same table it can be observed that 
outliers exist when all the check points are considered. Eight 
points have height differences over 75 cm (see Table 5.4). 
When the eight points that show the maximum height 
differences that can be regarded as blunders were re-observed in 
the stereo-model, it was discovered that they all lie at an area 
of one of the two big rocks that is covered by shadow. That was 
quite expected because it is very difficult to observe points in 
the shadow. It was also found that most of the points that show 
large height differences lie in shadow areas. 
When the eight points were regarded as blunders and were 
removed from the data set (reduced case) the standard deviation 
improved from 23 cm to 19 cm (see Table 5.2). In this case 3% 
of the height differences are over 40 cm, 11% over 30 cm, and 
29 over 20 cm (see Table 5.4). It is speculated that the removal 
of all the points that have been observed in the shadow can 
improve the accuracy by few more centimetres. In this case the 
areas in shadow can be re-observed using another stereo-model 
of the same strip since the sun angle and-as a result-the position 
of the shadow changes. 
From the preceding discussion it can be concluded that the 
standard deviation was at the 19 cm level and it can be even 
better if additional points are observed in another stereo-model 
at the areas that were covered by shadow. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996 
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