Digital image analysis based on direct multifractal transform

Research output

Abstract

Now it is widely accepted that many digital images are phase portraits of complex dynamical systems. The distribution of system trajectories in the phase space may be described by a measure that follows an exponent law. In this work we consider methods of obtaining classification signs based on the calculation of alpha-divergences (Regny divergences), the Hausdorf dimension of a measure support and averaged singularity exponents. For an given image a discrete normed measure and the sequence of measures obtained from the initial one by the direct multifractal transform are considered. In the first method to compare two images we calculate alpha-divergence between the measures from corresponding sequences. The obtained vector is a characteristic of similarity of images structures. In the second method we calculate the Hausdorf dimension of the measure support and the averaged singularity exponent. The results of numerical experiments for Brodatz textures and biomedical preparation images are given.
Original languageEnglish
Pages (from-to)23-32
JournalУНИВЕРСИТЕТСКИЙ НАУЧНЫЙ ЖУРНАЛ
Issue number19
Publication statusPublished - 2016

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Image analysis
Dynamical systems
Textures
Trajectories
Experiments

Scopus subject areas

  • Computer Science(all)

Cite this

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title = "Digital image analysis based on direct multifractal transform",
abstract = "Now it is widely accepted that many digital images are phase portraits of complex dynamical systems. The distribution of system trajectories in the phase space may be described by a measure that follows an exponent law. In this work we consider methods of obtaining classification signs based on the calculation of alpha-divergences (Regny divergences), the Hausdorf dimension of a measure support and averaged singularity exponents. For an given image a discrete normed measure and the sequence of measures obtained from the initial one by the direct multifractal transform are considered. In the first method to compare two images we calculate alpha-divergence between the measures from corresponding sequences. The obtained vector is a characteristic of similarity of images structures. In the second method we calculate the Hausdorf dimension of the measure support and the averaged singularity exponent. The results of numerical experiments for Brodatz textures and biomedical preparation images are given.",
keywords = "Image analysis, probabilistic measure, multifractal spectrum, Regny divergences, direct multifractal transform, the Hausdorf dimension",
author = "Н. Ампилова and В. Сергеев and И. Соловьев",
year = "2016",
language = "English",
pages = "23--32",
journal = "УНИВЕРСИТЕТСКИЙ НАУЧНЫЙ ЖУРНАЛ",
issn = "2222-5064",
publisher = "Санкт-Петербургский университетский консорциум",
number = "19",

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TY - JOUR

T1 - Digital image analysis based on direct multifractal transform

AU - Ампилова, Н.

AU - Сергеев, В.

AU - Соловьев, И.

PY - 2016

Y1 - 2016

N2 - Now it is widely accepted that many digital images are phase portraits of complex dynamical systems. The distribution of system trajectories in the phase space may be described by a measure that follows an exponent law. In this work we consider methods of obtaining classification signs based on the calculation of alpha-divergences (Regny divergences), the Hausdorf dimension of a measure support and averaged singularity exponents. For an given image a discrete normed measure and the sequence of measures obtained from the initial one by the direct multifractal transform are considered. In the first method to compare two images we calculate alpha-divergence between the measures from corresponding sequences. The obtained vector is a characteristic of similarity of images structures. In the second method we calculate the Hausdorf dimension of the measure support and the averaged singularity exponent. The results of numerical experiments for Brodatz textures and biomedical preparation images are given.

AB - Now it is widely accepted that many digital images are phase portraits of complex dynamical systems. The distribution of system trajectories in the phase space may be described by a measure that follows an exponent law. In this work we consider methods of obtaining classification signs based on the calculation of alpha-divergences (Regny divergences), the Hausdorf dimension of a measure support and averaged singularity exponents. For an given image a discrete normed measure and the sequence of measures obtained from the initial one by the direct multifractal transform are considered. In the first method to compare two images we calculate alpha-divergence between the measures from corresponding sequences. The obtained vector is a characteristic of similarity of images structures. In the second method we calculate the Hausdorf dimension of the measure support and the averaged singularity exponent. The results of numerical experiments for Brodatz textures and biomedical preparation images are given.

KW - Image analysis

KW - probabilistic measure

KW - multifractal spectrum

KW - Regny divergences

KW - direct multifractal transform

KW - the Hausdorf dimension

M3 - Article

SP - 23

EP - 32

JO - УНИВЕРСИТЕТСКИЙ НАУЧНЫЙ ЖУРНАЛ

JF - УНИВЕРСИТЕТСКИЙ НАУЧНЫЙ ЖУРНАЛ

SN - 2222-5064

IS - 19

ER -