Multifractal formalism in image and time series analysis

Audrey L. Karperien; Herbert F. Jelinek; Helmut Ahammer

doi:10.4064/bc109-0-3

Multifractal formalism in image and time series analysis

Audrey L. Karperien, Herbert F. Jelinek, Helmut Ahammer

Medical University of Graz

Research output: Book chapter/Published conference paper › Conference paper › peer-review

Abstract

Multifractal analysis explores patterns to discover within them characteristic sets of multiple fractal dimensions. Using computer software, patterns are resolved over decreasing scales and examined under various distorting lenses to make multifractal spectra that can sometimes tell much about the state of a system, including physiological systems. Here we review some key tenets of the multifractal formalism using box-counting as the basis for software-based multifractal analysis, and discuss some applications to cell morphology, retinal pathology, cancer, and heart rate variability.

Original language	English
Title of host publication	Banach Center Publications
Editors	Grzegorz Banaszak, Jan Milewski, Przemysław Waliszewski
Place of Publication	Poland
Publisher	Institute of Mathematics, Polish Academy of Sciences
Pages	23-45
Number of pages	23
Volume	109
ISBN (Print)	9788386806331
DOIs	https://doi.org/10.4064/bc109-0-3
Publication status	Published - 2016
Event	Arithmetic methods in mathematical physics and biology - Banach Centre, Będlewo, Poland Duration: 03 Aug 2014 → 08 Aug 2014 https://ammpb.wmi.amu.edu.pl/abstract.htm

Publication series

Name	Arithmetic Methods in Mathematical Physics and Biology
Publisher	Institute of Mathematics, Polish Academy of Sciences
Volume	109
ISSN (Print)	0137-6934

Conference

Conference	Arithmetic methods in mathematical physics and biology
Country/Territory	Poland
City	Będlewo
Period	03/08/14 → 08/08/14
Other	The conference aims to present recent applications of: Algebraic Number Theory, Arithmetic and Algebraic Geometry, Fractal Geometry, Nonlinear Dynamic Systems, Cellular Automata, Graph Theory and Cryptography to Mathematical Physics and Biophysics, Nonlinear Biology, and Complexity in Biology and Physics and to foster research and cooperation between scientists representing various areas of natural sciences based on the applications of both arithmetic and algebraic methods.
Internet address	https://ammpb.wmi.amu.edu.pl/abstract.htm

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10.4064/bc109-0-3

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Karperien, A. L., Jelinek, H. F., & Ahammer, H. (2016). Multifractal formalism in image and time series analysis. In G. Banaszak, J. Milewski, & P. Waliszewski (Eds.), Banach Center Publications (Vol. 109, pp. 23-45). (Arithmetic Methods in Mathematical Physics and Biology; Vol. 109). Institute of Mathematics, Polish Academy of Sciences. https://doi.org/10.4064/bc109-0-3

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abstract = "Multifractal analysis explores patterns to discover within them characteristic sets of multiple fractal dimensions. Using computer software, patterns are resolved over decreasing scales and examined under various distorting lenses to make multifractal spectra that can sometimes tell much about the state of a system, including physiological systems. Here we review some key tenets of the multifractal formalism using box-counting as the basis for software-based multifractal analysis, and discuss some applications to cell morphology, retinal pathology, cancer, and heart rate variability.",

author = "Karperien, {Audrey L.} and Jelinek, {Herbert F.} and Helmut Ahammer",

note = "Includes bibliographical references; Arithmetic methods in mathematical physics and biology ; Conference date: 03-08-2014 Through 08-08-2014",

year = "2016",

doi = "10.4064/bc109-0-3",

language = "English",

isbn = "9788386806331",

volume = "109",

series = "Arithmetic Methods in Mathematical Physics and Biology",

publisher = "Institute of Mathematics, Polish Academy of Sciences",

pages = "23--45",

editor = "Grzegorz Banaszak and Jan Milewski and Przemys{\l}aw Waliszewski",

booktitle = "Banach Center Publications",

address = "Poland",

url = "https://ammpb.wmi.amu.edu.pl/abstract.htm",

}

Karperien, AL, Jelinek, HF & Ahammer, H 2016, Multifractal formalism in image and time series analysis. in G Banaszak, J Milewski & P Waliszewski (eds), Banach Center Publications. vol. 109, Arithmetic Methods in Mathematical Physics and Biology, vol. 109, Institute of Mathematics, Polish Academy of Sciences, Poland, pp. 23-45, Arithmetic methods in mathematical physics and biology, Będlewo, Poland, 03/08/14. https://doi.org/10.4064/bc109-0-3

Multifractal formalism in image and time series analysis. / Karperien, Audrey L.; Jelinek, Herbert F.; Ahammer, Helmut.
Banach Center Publications. ed. / Grzegorz Banaszak; Jan Milewski; Przemysław Waliszewski. Vol. 109 Poland: Institute of Mathematics, Polish Academy of Sciences, 2016. p. 23-45 (Arithmetic Methods in Mathematical Physics and Biology; Vol. 109).

Research output: Book chapter/Published conference paper › Conference paper › peer-review

TY - GEN

T1 - Multifractal formalism in image and time series analysis

AU - Karperien, Audrey L.

AU - Jelinek, Herbert F.

AU - Ahammer, Helmut

N1 - Includes bibliographical references

PY - 2016

Y1 - 2016

N2 - Multifractal analysis explores patterns to discover within them characteristic sets of multiple fractal dimensions. Using computer software, patterns are resolved over decreasing scales and examined under various distorting lenses to make multifractal spectra that can sometimes tell much about the state of a system, including physiological systems. Here we review some key tenets of the multifractal formalism using box-counting as the basis for software-based multifractal analysis, and discuss some applications to cell morphology, retinal pathology, cancer, and heart rate variability.

AB - Multifractal analysis explores patterns to discover within them characteristic sets of multiple fractal dimensions. Using computer software, patterns are resolved over decreasing scales and examined under various distorting lenses to make multifractal spectra that can sometimes tell much about the state of a system, including physiological systems. Here we review some key tenets of the multifractal formalism using box-counting as the basis for software-based multifractal analysis, and discuss some applications to cell morphology, retinal pathology, cancer, and heart rate variability.

UR - https://www.impan.pl/en/publishing-house/banach-center-publications/all/109

U2 - 10.4064/bc109-0-3

DO - 10.4064/bc109-0-3

M3 - Conference paper

SN - 9788386806331

VL - 109

T3 - Arithmetic Methods in Mathematical Physics and Biology

SP - 23

EP - 45

BT - Banach Center Publications

A2 - Banaszak, Grzegorz

A2 - Milewski, Jan

A2 - Waliszewski, Przemysław

PB - Institute of Mathematics, Polish Academy of Sciences

CY - Poland

T2 - Arithmetic methods in mathematical physics and biology

Y2 - 3 August 2014 through 8 August 2014

ER -

Multifractal formalism in image and time series analysis

Abstract

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