E
L(m)
2.00 216.00 240.00
80 0.90 1.00
L
80 090 1.00
E
L(m)
2.00 216.00 240.00
:
moderate
HC -1/ E13 *(V2- 1) (£1 fe)? =
21/ E1*9,414 Cf | fe ) ?^ ] (16)
After obtaining filtered profiles, by their subtract from
initial profiles, the heights differences ( dhrj) which
represent the roughness values, are determinated. As
parameter for global caracterisation of the roughness,
rooí mean square ( rms ) height differences is used:
e = LD (dhr)? /N 1°? (17)
3. RESULTS AND CONCLUSIONS
Efficiency of periodogram use im height informations
analysis has been demonstrated within the studies
concerning detection and filtering of errors im DEM' s
data ( Hassan. M. M, 19992, 1998b ), The application of
its highlights properties of the parts in a signal to the
question of determining roughness or high frequency
relief, is based on some observation as follows:
-power specírum estimations corresponding to low
frequencies (fig. 2b amd 3b ) convey in periodogram curve,
tlie contribution forms which are superior as size order to
roughness. Within this frequencies area, roughness inílu-
ence is very little, even insignificant. Adequate spectrum
oí minimum frequency defines either a maximum or a
peak of curves.
-if within the analysed terrain profile there is only one
kind of form dimensionaly superior to roughness ( only
one low frequency oscillation ) in the maximum point,
periodogram gets quikly lower to a little amplitude value
characterised by a high level frequency. In the case are
more kinds of superior forms ( different low frequency
oscillations ) in the above mentioned area, there will be
either peaks or local maximus at frequencies that
correspond them.
-on going, from low amplitude value, periodogram
relatively displays mon - uniformaly . having low
amplitudes, as well. This is high frequencies area or
descriptor of roughness contribution to periodogram
configuration. Frequency corresponding to ils starting
point, that makes an utmost change in periodogram, is
cutt-off frequency ( fc ). According to that mentioned in
the end of chapter 2.1, this frequency level has been used
as a control parameter of filtering process alome by
Butter worth filter, through which roughness is separated.
Two exemples of separating roughness parts are displayed
in figures 2 and 3. The first profile processed in this way
is a plane terrain and the second one a moderate variable
terrain. They are succesively conveyed:
-periodogram from input data which make obvious
roughness and its frequency level (figures 2b, 3b):
-periodograms corresponding to profiles data resulted
after filtering is applied ( figures 2c, Jc );
-configur ation of the two filtered profiles ( 2d. 3d );
-graphics of roughness values ( 2e, Je).
The two profiles are sampled £o an interval As = 0.5m
between height samples and roughness amplitude
component within the 0 - 1.0m range, is considered.
The roughmess is determined in different types of
applications from the fields how are for exemple: geology.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
geomorphology, planetary geology or radar remote
sensing. In accordance with the nature of the applications
its components separations resolutions, can vary at
centimetre to metre scale. Taking into account this aspect,
Zi( s ) height profiles must be sampled to fulfil all imposed
accuracy conditions by asked resolution.
The plane coordinates and heights accuracies which can
be achieved using photogrammetric methods are
dependent on various interrelated factors, but chiefly:
( 1) the scale and resolution of the aerial photography:
( II) the flying height at which the photos was taken;
(III) the base / height ratio of the overlapping photos;
( IV ) the accuracy of the stereoplotting equipment used
for the measurements ( Kennie.M.J.T, Petrie.G, 1990 ).
Out of mentioned factors, for roughmess a great
importance have, the scale and resolution of the aerial
photography. Its separation entail the aerial photos at
large scale with a very good resolution.
The aerial photos in the area scale 1: 2000 - 1: 4000,
exploited using enlargement factors of 5 or 6, can assure
obtaining the components of the 0.15 - 1.0m range, with
enough accuracy. But, in the case of the high resolution
applications, where the roughness is determinated at
centimetric scale, are necessary special photos, at very
large scale, obtained with means wich allow taking of the
photographic registrations from small altitude. It is
enlightening the results obtained using the close - range
aerial photos maked with 70mm metric cameras attached
to either end of a 6.2m boom, mounted under a helicopter
(Wall.S.D. Farr. T.G, Muller.J-P, Lewis.P, Leberl.F.V.
1991 ). Also. are of maintained concerning (o very high
resolution determinations. the possibilities offered by
close - range photogrammetry, wich can to provide a
precision of Imm ( Kirby. P.R, 1991 ).
Complex numbers involved in the FFT, require twice
storage and computational time that real numbers use.
For increasing of the data processing efficiency, there is
an alternative, the Fast Harley Transform (FHT)
( Watson D.F, 1992 ). This uses only real numbers so is
twice as fast while using only one - halí the storage.
For technique in this paper presented, must be underlined
that an exact correlation between the input data quality
amd asked resolution is ome out of the fundamental
factors. Using the height samples having the improper
accuracy , can be lead (o ambigous situations when the
roughness are mixed and confused with measuring errors.
REFERENCES :
[ 1] Ayeni.0,1976. Objective terrain description and
classification for digital terrain models, XIII Congress of
the 1.S.P, Com. III Helsinki;
I 21 Dikau.R, 1990, Geomorphic landform modelling
based on hierarchy theory. Proceedings of the spatial data
handling, Zurich;
[ 31 Davenport. W.IB, Root. W.L, 1958, An introduction
to the theory of random signals and noise, Mc.Graw - Hill
N.Y;
| 41 Frederiksen.P, Jacobi.O. Justensem.J. 1973.
Fourier - (ransíormation von hóhenbeobachtungen Zív.
mo. 2;
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