Research output: Contribution to journal › Article › peer-review
Digital image analysis based on direct multifractal transform. / Ампилова, Н.; Сергеев, В.; Соловьев, И.
In: УНИВЕРСИТЕТСКИЙ НАУЧНЫЙ ЖУРНАЛ, No. 19, 2016, p. 23-32.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 7611116