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ON THE TECHNIQUE FOR TERRAIN ROUGHNESS DETERMINATION
lom Ionescu
University of Civil Engineering
Faculty of Geodesy, Laboratory of Photogrammetry and Remote Sensing
B-dul Lacul Tei 124, Sect. 2 Bucharest
ROMANIA
KEY WORDS: Roughness. Spectral analysis, Power spectrum, F iltering, Frequency.
ABSTRACT
In analogy with electric signal, the roughness of terrestrial relief can be defined as a component similar to the noise
present at the signal during the transmission process. According to this concept, the paper presents a technigue of the
roughness determination using spectral analysis of dense sampled terrain profiles. The periodogram is used to make
it evident. It aids to find out roughness specific frequency. Afterwards, the separation of the roughness is achieved by
filtration process in the frequency domain, carried out with Butter worth filter, followed by inverse Fourier (ransiorm.
The results obtained are illustrated through the graphical representations and the comparisons made between the
initial profiles and the filtered profiles.
1.INTRODUCTION
The terrestrial relief is a complex spatial surface with a
high degree of variability, that includes in this structure
different types of forms. From the geomorphologic point
of view, the relief form is the descriptive element of the
particular aspects of the terrestrial surface, according to
the gemesis. Besides genesis, that is considered an element
of great importance, different parameters that describe
their geometric features are used for the analysis of relief
forms. It is obvious that the number of proposed
parameters for this aim is considerable. Based both on
the describing capacity of terrain variations and on the
easiness of application of some modern analysis methods,
respectively of classification, three parameters are
considered to be most significant out of the multitude of
parameters: the dimension or the vertical amplitude
( relief ), defined as the value differences of the height
extreme values, the slope standing for the first order
derivative of the height and wawelenght or the mean
distance between successive extreme local heights of
terrain profile ( Frederiksen. P, Jacobi. 0, Kubik. K,
1984).
The relief form in geomorphological space, evaluated from
the geometric point of view, under their dimentional
aspect or as size order, cover a very large range. Thus,
according to G-scale used im a taxonomic hierarchic
classification based on the size order and the geometric
topological complexity ( Dikau. R, 1990 ) in
geomorphological space, there are: mega (> 10'* mp ),
macro ( 10'? - 10% mp ). meso ( 10* - 10* mp), micro
(10% - 10° mp), mano ( 10° - 10" mp ) and picoforms
(< 10? mp ). The roughness or the small size terraim
variations cam be included im nanoform classes, taking
this hierarchy as refference.
The terrestrial suríace is a suming ( superposition ) oí
components of different sizes amd configurations, view ed
from the structural point of view. Its representations
under profile form, reveals spatial development of this
similar to the variations of an electrical signals. If a
comparison of different components conformly to this is
performed, the roughness can be asimilated with the
present moise in the structure of the signal during
transmission process. Described according to the above
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
mentioned parameters, within the signal theory context,
it represent the random variations of very little amplitude
and period or high frequency relief.
Considering the analogy between terrain profile and
electrical signal as main hypothesis, the paper presents a
technique of roughness determination with the specific
means of spectral analysis.
2. ROUGH NESS DETERMENATION USING
SPECTRAL ANALYSIS
Spectral analysis has numerous applications in different
domains of science and technique. It forms a distinctive
chapter with theoretical basis within modern measurig
techniques. Its use in the field of photogrammetry,
includes mainly applications connected with the digital
elevation models ( DEM ) technologies. A short survey
points out: the interpolation interpretation. smoothings
amd parametrical transformations as types of discrete
convolution ( Kratky. V. 1980 ), sampling interval
determination ( Jacoby. 0, 1980, Kraus. K. 1984,
Hassan.M.M, 1986 ). data filtering ( Hassan. M.M, 1988a,
1988b ) and accuracy of DEM’ s estimation ( Frederiksen.
P, Jacobi. 0, Justensen. J. 1978, Frederiksen. P,1981,
Jacobi. 0, 1980, Tempfli. K, 1930, 1982, Frederiksen.P,
Jacobi. 0, Kubik. K. 1984) , terrain types classification
(Ayeni. 0, 1976, Jacobi. 0, 1980, Frederiksen. P, Jacobi.
0, Kubik. K, 1984), slope and terrain curvature mapping
(Papo. II. B, Gelbman. F, 1984).
The main operating tools from spectral analysis
represented by series and Fourier transforms have the
capacity of achieving a link between the domain of signals
existence ( space or time ) and frequency, domain in which
the signals can be represented. Simultaneously with this
special property, Fourier transform have the property of
being able to be used at the identification of some signals
of different frequency. additively combined and then,
because it enable the spectral estimation obtaining, at
their separation through filtering operations.
The applications of these concepts at the study of relict
components, on an analysis process is based, within which
samples of a finite lenght signal ( 0,L ), Zi terrain heights
are considered. Their uniform gathering along profiles to
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