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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
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Figure 7. Initial (upper) and corrected DEM (lower)
comparison with the manually collected TIN.
Visualization and statistics of the DEM collected
with the “TIN” method on the Softplotter.
5. RESULTS
Although the tests conducted returned a number of measures
for statistical analysis, only the most important are
summarized in the following table.
LA
Lh
X
DEM type |Mean SD RMS MAD Range Kurtosis|
m m m m m
2 Iitial9590-0.54 1.75 182 142 1025 245
©
* Corrected :
a 95% -0.11 0.59 0.60 0.36 1243 16.92
= Initial 9594|-0.10 0.93 0.94 86% 2082 14.2]
> Corrected
a Tas, | 009, 058. 0359 036. 2074 2878
95%
> Initial 95%|-0.09 0.87 0.88 062 2033 12.87
f Corrected .
95%, -0.09 0.56 0.56 0.35“ 20.70 30!
Table 1. Comparison of the initial and corrected by the
proposed method DEMs, against the manually
collected TIN.
These statistical measures are well known and widely used,
but a brief explanation is given. Mean is a measure of central
tendency, and shows if there is a significant systematic shift
of the surface, indicating a gross error. It is a measure of
accuracy, although it is highly dependent on the outliers.
Considering the expected accuracy (0.36 meters) and human
operator's precision (0.147 meters), all DEMs have mean
close to zero, except the artificially distorted DEM, which
correctly indicates a large error. Generally speaking all
software packages are able of producing DEMs with mean
better than the operator's precision. Balanced errors such as
these in the artificially distorted DEM cannot be detected by
the mean.
SD and MAD from the mean, are measures of the DEM's
dispersion. They are a measure of precision. SD shows the
magnitude of the variations from the mean value, while MAD
is a measure of the mean difference.
RMS error is the most appropriate measure when comparing
with reference data. It is the DEM's accuracy. In this
particular case where the mean is small, there is negligible
difference between RMS and standard deviation.
Range shows the maximum variation and is a measure of
dispersion of the differences between the compared DEM
with the reference.
Kurtosis is a numerical value of how close the error
distribution plot is to the Gaussian plot. If kurtosis is equal to
1, the plot is exactly the Gaussian plot. If lower than 1 then it
is very wide (hence large errors and very big standard
deviation) and if larger than one is very thin and high,
meaning that all the values are concentrated close to the mean
(hence small errors).
Conclusions that can be drawn comparing values of table |
are the following:
Arithmetic mean was improved in all cases by the algorithm,
especially in the artificially distorted DEM, where the
improvement was noticeable.
In all case the algorithm improved SD, irrespectively from
the beginning value of the initial DEM. The final values were
0.56-0.59 meters.
Exactly the same holds with RMS. The only difference is that
the RMS is a bit bigger than SD because it ‘encloses’ the
mean.
In all case the algorithm improved MAD, irrespectively from
how erroneous was the initial DEM. The final value was 0.36
meters, which is equal to the expected DEM accuracy,
accordingly to ISM (1998) and equal to one pixel in ground
units (for the particular project parameters).
Algorithm has not improved range at all. Actually in the
distorted DEM there was a noticeable deterioration. It is
suspected that the large values appearing in range is a side
