APPLICATION
OF MULTIFRACTAL APPROACH IN GENERALIZING RIVER NETWORK CARTOGRAPHIC IMAGES
V.A.Malinnikov, D.V.Uchaev
D-Uchaev@yandex.ru
In the present
article multifractal approach to generalization of
hydrographic networks images is formulated. The
given approach represents natural summarizing of cartographic objects
generalization fractal techniques. The
substantive provision of fractal geometry consists of that natural object
possess property of self-similarity, i.e. look approximately equally at
different scale levels. The fractal
dimension serves as quantity indicator of fractal objects self-similarity, and,
hence, the quantitative characteristic of objects generalization degree. Fractal
dimension shows as the object change sizes at generalization. For
example, the line with small value of fractal dimensions keeps the length
during generalization, and the line with fractal dimension 1,5 decreases in
sizes with a map scale reduction. Thus, fractal
dimension is the convenient tool of the cartographic objects procedure analysis
simplification at generalization.
However,
despite of essential successes reached in the field of cartographical
generalization with introduction of the theory of fractals, it has not found wide application by development
of natural object generalization effective algorithms. By
authors of the given work opinion, the reason of it is covered in idealization
of natural object self-similarity property. The
self-similarity for the majority of mapped objects carries a statistical
property and is found out only on the certain range of scales. All
this testifies to insufficiency of one fractal dimension use at generalization
of natural structures.
In the present
work the opportunities of multifractal
approach used for generalization of hydrographic networks images are analyzed. The
essence of multifractal approach consists in use not
one, but the whole spectrum of fractal dimensions, reflecting the statistical nature
of river network self-similarity. Owing to the
entered approach it was possible to reflect the structural organization of
river networks. Besides it, as a result of the
conducted researches, the correlation is received quantitatively connecting an
exponent of the hydrographic network image generalization
with its basic quantitative characteristics.
The approach
generated in given work to generalization of river networks images in essence represents one of the multifractal technique application first attempts at
generalization of natural objects images. Authors
of the article express confidence, that the ideas which have been set up in
given work, will subsequently receive the development at effective algorithm
elaboration of the such natural object automated generalization, as ocean and
sea coasts, lakes, mountain ridges, borders of the states, conducted on natural
orienting points, etc.