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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
Figure5: Frequency distribution of correlation coefficients of least squares matching in complex areas with small and large building 
and trees, sub-matrix for least squares matching 10x10 pixels; step width = 3 pixels 
4. Accuracy Analysis 
The accuracy analysis shall lead to the optimal matching 
procedure. As reference for the investigation manually 
measured, randomly spaced points in the stereo model have 
been used. 
The reference height model must be available in a grid mode. 
For this reason, the reference DSM has been interpolated by 
Delauny triangulation to a point raster with 20cm spacing. 
The generated DSM has been checked against the manually 
measured reference height model separately for the open area 
and the area with man-made objects and trees. For this the 
Hannover program for analysis of height models can use a layer 
with different point classes (Jacobsen 2007). Table 3 shows the 
results of the comparison. 
Class 
Number of 
measured 
points 
RMSE 
cm 
Bias 
cm 
man-made objects 
and trees 
1839 
13.4 
0,0 
open area 
1222 
10.6 
0.4 
Table 3: RMS discrepancies against reference height model 
The root mean square errors (RMSE) of the differences have to 
be seen in relation to the 9.4cm GSD together with the height to 
base relation of the DMC, being 3.2 for the used 60% endlap. 
The standard deviation of the x-parallax corresponds to the 
vertical root mean square error divided by the height to base 
relation. So a RMSE of 13.4cm for the height differences 
corresponds to 0.44 GSD standard deviation of the x-parallax 
and 10.6cm RMSE correspond to 0.35GSD. 
The standard deviation of the height (Sz) can be estimated with: 
c h 
Sz = — • spx (l) 
where h is the flying height above ground, b is the base length 
and spx the standard deviation of the x-parallax. 
As expected, the root mean square error in open area is smaller 
than root mean square error for the area with buildings and trees, 
which is influenced by discontinuities. 
$ ¿l' Ip n* $ Jb <$> $ 
5- 55 ? 55' & 55' 55' O' 0- <5' Cr 0 <5- 0- <5- 
Figure 6: Frequency of distribution of the height differences [m] 
between the matched DSM and the reference DSM in the area 
with man-made objects and trees 
80 t— — - mm ■ 
70 
$ ¡S' $ ov? & $ $ $ ^ 'S 3 ^ ^ 
55- J5' 55' 0 55' 55' 55' J5* O' O' <5- <5' ' J ' O'“ <5 ; 
Figure 7: Frequency distribution of the height differences [m] 
between the matched DSM and the reference DSM in open 
areas 
The frequency distribution in open area (figure 7) is close to 
normal distribution, while the frequency distribution shown in 
figure 6 is a little asymmetric, caused by vegetation. 
As tolerance limit for analysis a maximal absolute value of the 
height difference of 0.5m has been used, larger height 
differences have been handled as blunders. Only very few 
points exceeded this limit. 
5. Comparison between matched and reference DSM 
The reference height model is not free of errors; this should be 
respected for the accuracy analysis. 
The accuracy of the manual pointing is estimated with a 
standard deviation of the x-parallax of 0.25 GSD, multiplied 
with the height to base relation of 3.2 it leads to a standard 
deviation of the height measurement of 0.8 GSD or 7.5cm. If 
this is respected for the values shown in table 3, the standard 
deviation of the DSM in the area with man-made objects and 
trees is 11.1cm, corresponding to a x-parallax accuracy of 
0.37GSD, and for the open area 7.5cm, corresponding to a x- 
parallax accuracy of 0.25GSD. This means, for the open area 
the manual pointing and the automatic image matching are on 
the same accuracy level, while in the build up area the manual 
pointing is more precise, mainly because of problems at 
discontinuities. 
6. Visual inspection 
The visual comparison of the DSM generated by manual 
measurement and the matched DSM shows the following for 
the matched DSM: 
The base of the buildings is wider than its original length, 
mainly caused by occlusions, but in most cases the roof is 
shown very well. 
Sun shadows leads to matching failures. 
The building footprints in most cases can be extracted 
from the generated DSM, but not in any case with 
satisfying details.