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tion DEMs offer the base conditions to perform such an analysis. High resolution describes very fi ne structural levels that stem from different processes. For example, a micro-fold may result from a landslide or from erosion. Thus, the imprint of this feature will not be contained in the same spatial context regarding its relation to coarser features. Although high resolution provides a much better visual rendering of the territory and of its structures, the relations between topographical structures and formations are more compli-cated. Hence they represent a new challenge for quantitative geomor-phology and geomorphometry.

A first attempt to address this challenge was carried out through the development of form indicators, also known as geomorphometry indicators (e.g., Wood, 1996). Geomorphometric indicators are spatial features that can be extracted from a DEM, such as slope, aspect, and curvature. These indicators are geometric because they are computed using the adjustment of a mathematical surface on elevation models. The detection of geomorphological features using this type of indica-tors (as well as hydro-morphological indicators such as the wetness index, watersheds, and streams) is complicated because such indices are dedicated to local scale analysis only. Moreover, in high resolution DEMs, features are nested one into the other, making the interpreta-tion of indicators difficult. This is a computational scale problem (see Lassueur et al., 2006, and References therein) also observed in the use of geomorphometric indicators for the prediction of environmental parameters such as wind speed (Foresti et al., 2011) and orographic precipitation (Foresti and Pozdnoukhov, in press). Wilson and Gallant (2000) showed that the characterization of landscape processes and features based on one specific scale is far too simple to model our environment. In recent years, multiresolution analysis tools based on a generalization of Evans' (1972) geomorphometric indicators have been developed ( Wood, 1996). These tools provide multiple results for one indicator at multiple scales. There is no feature extrac-tion, but rather a multiscale/multiresolution topographical analysis and the extraction of a geometric network. These methods rely essentially on a geometrical analysis, while Jordan and colleagues combined geomorphometric indicators and digital image processing techniques (including edge detectors, histogram slicing, and gradient filters) to detect tectonic faults with DEMs ( Jordan et al., 2005; Jordan, 2007 ).

To enable the detection of a phenomenon and its underlying fea-tures, it is necessary to identify the specific scales at which signi ficant features and their intrinsic relations emerge. A way to move toward the extraction of geomorphological indicators at different scales is to consider DEMs in the frequency domain. Indeed, our environment is composed of frequency information characterizing either the spa-tial domain (as it is considered in this paper) or the temporal domain (e.g. earthquakes or mass movements). A limitation is that almost no natural phenomenon related to Earth science is stationary and  homogeneous, and this made many studies fail. Real phenomena con-sist of a nesting of processes and structural elements, which are inter-dependent, have various scales, and interact in the natural system. This means that the size and shape of every structure depends on the phenomenon it belongs to, but本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。