DIGITAL ANALYSIS AND BASIC SHAPE RELIEF EXTRACTION FROM DTM 
A. Dupéret * *, B. Deffontaines ” 
* ENSG (IGN France), 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, F-77455 Marne la Vallée Cedex 
2, France — alain.duperet@ensg.ign.fr 
^ Ecole Pratique des Hautes Etudes, Laboratoire de Géomorphologie et Environnement Littoral, 15 boulevard de la 
Mer, F-35800 Dinard, France - benoit.deffontaines@ephe.sorbonne.fr 
ICWG IVIV 
KEY WORDS : Geomorphology, Analysis, Global-Environmental-Databases, Algorithms, Automation, DEM/DTM, GIS, 
Landscape 
ABSTRACT : 
Geomorphometry, by its analytical approach, contributes towards understanding landscape shapes and processes that generate them. 
The automation of reliefs feature extraction is in a transition period and has now to lead the users to practical solutions in their 
systems. This corresponds also to the emergence of a great variety of acquisition modes for DTM, and a fast-growing production of 
elevation data. The scope of this study aims to provide a practical illustration of geomorphometric descriptive parameters extraction. 
First, on the basis of simple criteria linked to the digital representation of the altitude, for which a hypothesis of modelling by 
polynomial regional so-called "translated functions” is introduced, the various slopes and curvatures will be represented analytically. 
From this base, more complex and pertinent criteria for geomorphometric features will be suggested. The survey will provide an 
analytical foundation for the description of the relief aimed at all those who study relief evolution processes. From the geographer 
point of view, this approach confirms past evolutionary processes leading to present landscape shapes and explains the role of these 
shapes in current and ongoing erosion phenomena by using digital data. The analytical geometric analysis provided and the objects 
recognized help the settlement of environmental database. Therefore, the D'TM finds its place as an operationnal cornerstone data in 
the GIS, dedicated to the standard geo-spatial applications, and joins the tools involved by the resource and environmental 
  
monitoring. 
1. FROM GEOGRAPHY TO GEOMORPHOMETRY 
Geography is the scientific study of the distribution of physical, 
biological and anthropogenic phenomena on the surface of the 
Earth. Traditionally determinist, recent trends have led to the 
development of more and more quantitative tools. An optimal 
analytical method should reconcile these two approaches, 
quantitative analyses being more adapted when there is a need 
for greater objectivity and precision in the perception of these 
phenomena in relation to the relief of the terrain (Depraetere, 
1984a & 1984b). Geomorphology is the science which studies 
the relief of the terrain and the geological formations which 
shape it (Derruau, 1974; Dewolf, 1982; Joly, 1997...). The 
geomorphologist describes the relief of the terrain in view of his 
experience and his specialized discipline : historic, dynamic, 
structural or climatic geomorphology. This natural subjectivity 
combined with observations in the field can easily be 
standardized with digital data, particularly in hydrology. Thus, 
with the help of modern means of calculation, the Digital 
Terrain Model (DTM) has taken on a preponderant role 
The description of the landscape can be based on various types 
of classification ; one of them is the parametric approach, which 
divides and classifies the terrain in terms of particular attributes 
based on sampling. The DTM is of this type, especially since a 
careful choice of the grid and its spacing is essential to be 
consistent with the characteristics and scale of the features to be 
studied. In the case of geomorphology, this parametric approach 
  
is thus called geomorphometry. 
The first part offers a possible mathematical model of the 
terrain's surface. Parametric indicators will next be defined to 
determine the relief. The following chapters are largely inspired 
by the work of H.M. Dufour (1988a & 1988b) and C. 
Depraetere (1984a), who have both profoundly influenced 
modern geomorphometry ; their contributions will therefore not 
be systematically mentioned, but the objective is to present a 
global synthesis of their works. 
2. POLYNOMIAL DESCRIPTION OF A SURFACE 
The representative function of altitude must take into account 
the different discontinuities in the terrain : 
e Talus, cliffs directly related to altitude, 
e Breaks in slope lines (concave, convex), 
e Breaks in curved lines. 
Mathematically, linear functions can be used to describe 
inclined or horizontal planes ; slope and orientation are thus 
constant and the vertical curves of slope lines or the horizontal 
curves of contour lines are zero. Quadratic functions produce 
more varied shapes, which can be used to better describe 
topographic shapes, although the latter derived remain constant. 
The surfaces thus modelled will therefore have constant curves, 
which is doubtless not the usual case. Cubic functions may lend 
themselves to represent surfaces whose contour lines and slope 
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