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"Humanities and Science University Journal" №19 (Physical and mathematical, biological and technical science), 2016

Digital Image Analysis Based on Direct Multifractal Transform

N. B. Ampilova, V. D. Sergeev, I. P. Soloviev
Price: 50 руб.
 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 exponential law. In this work, we consider methods of obtaining classifi cation signs based on the calculation of alpha-divergences (Rényi divergences), the Hausdorff dimension of measure support, and averaged singularity exponents. A discrete normed measure and the sequence of measures obtained from the initial one by the direct multifractal transform are considered for any given image. In the fi rst method, we compare two images by calculating the 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 Hausdorff 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, Rényi divergences, direct multifractal transform, Hausdorff dimension.
REFERENCES
1. Gonzalez, R.C., & Woods, R.E. Digital image processing (3rd ed.). 2008: PrenticeHall.
2. Katok, A., & Hasselblatt, B. Introduction to the modern theory of dynamical
systems. 1995: Cambridge university press.
3. Bashkirov, A.G. Renyi entropy as statistical entropy for complex systems. Theoretical and Mathematical Physics. 2006, 149(2), 299–317. doi:10.1007/s11232-006-
0138-x
4. Vstovsky, G.V. Elements of information physics. 2002, Moscow: Moscow State
Industrial University.
5. Ampilova, N.B., & Soloviev, I.P. On application of entropy characteristics to texture analysis. WSEAS Transactions on Biology and Biomedicine, 2014, 11, 194–202.
6. Hero, A.O., Bing, Ma, Michel, O., & Gorman, J. Alpha-Divergence for Classifi cation, Indexing and Retrieval. 2001, Ann Arbor: The University of Michigan.
7. Jizba, P., & Arimitsu, T. The world according to Rényi: thermodynamics
of multifractal systems. Annals of Physics. 2004, 312(1), 17–59. doi:10.1016/j.
aop.2004.01.002
8. Billingsley, P. Ergodic theory and information. 1965, New York: John Wiley &
Sons. doi:10.1002/bimj.19680100113
9. Chabra, A.B., Meneveau, C., Jensen, R.V., & Sreenivasan, K.R. Direct determination of the f(α) singularity spectrum and its application to fully developed turbulence.
Physical Review A, 1989, 40 (9), pp. 5284–5294.
10. Falconer, K.J. Fractal Geometry. Mathematical Foundations and Applications.
1990, New York: John Wiley & Sons.
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