V.A.Malinnikov, D.V.Uchaev

Moscow State University for Geodesy and Cartography, Moscow, the Russian Federation


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.