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A Fractal Method for Digital Elevation Model Construction and its Application to a Mountain Region
Author(s) -
Brivio Pietro Alessandro,
Marini Daniele
Publication year - 1993
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.1250297
Subject(s) - fractal , fractal dimension , digital elevation model , fractal analysis , interpolation (computer graphics) , fractal landscape , rendering (computer graphics) , fractal dimension on networks , computer science , terrain , algorithm , geometry , raster graphics , computer graphics (images) , mathematics , artificial intelligence , geology , mathematical analysis , image (mathematics) , remote sensing , geography , cartography
This paper presents and discusses the results of a methodology for the construction of Digital Elevation Models (DEM), based on mathematical principles of fractal geometry. Classical approaches to DEM are founded on numerical methods of interpolation or approximation of data extracted from contour lines of standard topographic maps. Fractal geometry opens a new and innovative approach in which the irregularity, erraticity and self similarity of fractal structures mimics at best the typical behaviour of high mountain profiles. The adoption of fractal methods requires the identification of the fractal dimension D for a given data set. The determination of the fractal dimension D can be achieved applying some special mathematical method on finite set of samples. Different methods. for D estimation are presented. Once the fractal dimension is given, it is possible to reconstruct a surface relief using different fractal methods which interpolate the original set of elevation data. Our research has also investigated two different interpolation methods, fBm and IFS, both confirming that the fractal approach is very well suited for high relief terrain modeling. Photo realistic rendering of the computed DEM allows to appreciate the quality of the reconstruction through visual inspection.