Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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On Application of Fractal Analysis Methods to Biomedical Preparation Images

Author(s):

N. Ampilova

Russia, 198504, Petergof, Universitetski pr.28
Saint-Peterburg State University
Faculty of Mathematics and Mechanics

n.ampilova@spbu.ru

Igor P. Soloviev

St. Petersburg State University
Math.& Mech. Faculty
Computer Science Dept.

soloviev@math.spbu.ru

Yuri V. Shupletsov

St. Petersburg State University
Math.& Mech. Faculty
Computer Science Dept.

shupaag@mail.ru

Abstract:

We investigate a possibility to apply fractal and multifractal methods to analyze some classes of biomedical preparation images. The Modified Fractal Signature method based on the calculation of the Minkovsky dimension is used. The method is alternative to well-known box dimension calculation. Generalized dimensions (Regny spectrum) and multifractal spectrum are calculated to obtain valuable features for multifractal sets. Different methods for multifractal spectrum calculation are considered. The results of numerical experiments show that for the images under study the direct calculation of multifractal spectrum (pointwise dimensions calculation and the computing thermodynamic averages) is more preferable than the obtaining the spectrum from generalized dimensions with the following using the Legendre transform.

References:

  1. Ampilova N., Gurevich E., Soloviev I. Application of Modified Fractal Signature & Regny Spectrum Methods to the Analysis of Biomedical Preparations Images. Proc. 6 Int. Conf. CEMA11, 6-8 Oct. 2011, Sofia, Bulgaria. p. 96-100
  2. Ampilova N., Soloviev I., Shupletzov Y. Multifractal spectrum as a classification sign for biomedical preparations images. Proc. 7 Int. Conf. CEMA12, 8-10 Nov. 2012, Athens, Greece. p. 98-101
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