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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 1, Pages 91–102 (Mi sjvm428)  
This article is cited in 1 scientific paper (total in 1 paper)

Estimation of fractal dimension of random fields on the basis of variance analysis of increments

S. M. Prigarinab, K. Hahnc, G. Winklerc

a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
c Institute of Biomathematics and Biometry Helmholtz Zentrum Muenchen, Neuherberg, Germany
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Abstract: This paper deals with estimating the fractal dimension of realizations of random fields. The numerical methods in use are based on analysis of the variance of increments. To study the fractal properties, we propose the use of a specific characteristic of random fields called “variational dimension”. For a class of Gaussian fields with homogeneous increments, the variational dimension converges to the Hausdorff dimension. Several examples are presented to illustrate that the concept of variational dimension can be used to construct effective computational methods.
Key words: computation of dimension, random fields, Hausdorff dimension, fractal analysis, variational dimension.
Received: 12.01.2010
Revised: 15.04.2010
English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 1, Pages 71–80
DOI: https://doi.org/10.1134/S1995423911010071
Bibliographic databases:
Document Type: Article
MSC: 28A80, 62M10, 65C05
Language: Russian
Citation: S. M. Prigarin, K. Hahn, G. Winkler, “Estimation of fractal dimension of random fields on the basis of variance analysis of increments”, Sib. Zh. Vychisl. Mat., 14:1 (2011), 91–102; Num. Anal. Appl., 4:1 (2011), 71–80
Citation in format AMSBIB
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\by S.~M.~Prigarin, K.~Hahn, G.~Winkler
\paper Estimation of fractal dimension of random fields on the basis of variance analysis of increments
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 1
\pages 91--102
\mathnet{http://mi.mathnet.ru/sjvm428}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 1
\pages 71--80
\crossref{https://doi.org/10.1134/S1995423911010071}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952460768}
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  • https://www.mathnet.ru/eng/sjvm/v14/i1/p91
    • This publication is cited in the following 1 articles:
    1. Appice A., Ciampi A., Fumarola F., Malerba D., “Missing Sensor Data Interpolation”: Appice, A Ciampi, A Fumarola, F Malerba, D, Data Mining Techniques in Sensor Networks: Summarization, Interpolation and Surveillance, Springerbriefs in Computer Science, Springer, 2014, 49–71  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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