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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.