350 rub
Journal Achievements of Modern Radioelectronics №3 for 2017 г.
Article in number:
Method of measuring directional morphological multifractal signatures of the texture images
Keywords: fractal dimension fractal signature multifractal signature directional morphological multifractal signature local morphologic multifractal exponent
Authors:
V.А. Kuznetsov - Ph.D. (Eng.), Senior Lecturer, MTSC Air Forces «MAA named professor N.E. Zhukovsky and Y.A. Gagarin» (Voronezh) E-mail: kuzzviktor@mail.ru А.N. Pototskiy - Adjunct, MTSC Air Forces «MAA named professor N.E. Zhukovsky and Y.A. Gagarin» (Voronezh) E-mail: AntonPototskiy@mail.ru
Abstract:
The paper presents the results of the analysis of the limitations of current methods of fractal image processing, a brief description of produced with these characteristics - the fractal dimension, fractal signature, multifractal signatures, and directional fractal dimension and signature. The conclusions about the lack of informativeness of existing features for the analysis of real images. On the basis of the effective methods synthesized a new technique to account for the singular, multifractal and anisotropic properties of images. The comparative results of accuracy assessment of the extracted fractal features and enhanced functionality of the synthesized method. Investigated a new fractal feature - directional morphological multifractal signature, which characterize the fractal properties of the image, taking into account their mutual ties.
Pages: 39-52
References

 

  1. Mandelbrot B.B. Fraktalnaja geometrija prirody / Per. A.R. Logunova. Moskva-Izhevsk: Institut kompjuternykh issledovanijj. 2002.
  2. Pentland A.P. Fractal-based description of natural scenes // IEEE Trams. Pattern Anal. Mach. Intell. 1984. V. 6. № 6. P. 661-674.
  3. Peitgen H.-O., Saupe V. The Science of Fractal Images. Springer-Verlag. New York-Berlin-Heidelberg-London-Paris-Tokyo. 1988.
  4. Falconer K.J. The Geometry of fractal sets // Cambridge tracts in mathematics. V. 85. Cambridge: University Press. 1985.
  5. Novak M.M. Thinking in Patterns: Fractals and Related Phenomena in nature. Singapore: World Scientific. 2004.
  6. Voss R.F. Random fractals: Characterization and measurement // Physica Scripta. 1986. № 13. P. 27-32.
  7. Potapov A.A. Fraktaly v radiofizike i radiolokacii: topologija vyborki. Izd. 2-e, pererab. i dop. M.: Universitetskaja kniga. 2005.
  8. Potapov A.A., Gilmutdinov A.KH., Ushakov P.A. Fraktalnye ehlementy i radiosistemy: Fizicheskie aspekty. Monografija / Pod red. A.A. Potapova. M.: Radiotekhnika. 2009.
  9. Malinnikov V.A., Uchaev D.V., Uchaev Dm.V. Metodika poluchenija kanonicheskikh spektrov pri multifraktalnom analize cifrovykh izobrazhenijj // Obozrenie prikladnojj i promyshlennojj matematiki. 2006. T. 13. № 3. S. 516-517.
  10. Peleg S., Naor J., Hartley R. Multiple resolution texture analysis and classification // IEEE Trams. Pattern Anal. Mach. Intell. 1984. V. 6. № 4. P. 518-523.
  11. Xia Y., Feng D., Zhao R., Zhang Y. Multifractal signature estimation for textured image segmentation // Pattern Recognition Letters. 2010. № 31. P. 163-169.
  12. Jacquet G., Ohley W., Fortin C. Bone texture characterization by oriented fractal analysis // In Proceedings of the 18th IEEE on Bioengineering. 1988. P. 22-23.
  13. Yi W.J., Heo M.S., Lee S. Direct measurement of trabecular bone anisotropy using directional fractal dimension and principal axes of inertia // Oral Surg., Oral Medicine, Oral Pathology, Oral Radiology Endodontics. 2007. № 104. P. 110-116.
  14. Lynch J.A., Hawkess D.J., Bukland-Wright J.C. Analysis of texture in macroradiographs of osteoarthritic knees, using the fractal signature // Phys. Med. Biol. 1991. V. 36. № 6. P. 709-722.
  15. Podsiadlo P., Stachowiak G.W. The development of the modified Hurst Orientation Transform for the characterization of surface topography of wear particles // Tribology Lett. 1998. № 3. P. 215-229.
  16. Wolski M., Podsiadlo P., Stachowiak G.W. Directional fractal signature analysis of trabecular bone: evaluation of different methods to detect early osteoarthritis in knee radiographs // Proc. Inst. Mech. Eng. 2009. V. 223. № 2. P. 211-236.
  17. Wolski M., Podsiadlo P., Stachowiak G.W. Directional Fractal Signature Analysis of Self-Structured Surface Textures // Tribol Lett. 2012. № 47. P. 323-340.
  18. Russkin A.B. Sravnitelnyjj analiz metodov izmerenija fraktalnojj razmernosti dvumernykh signalov // Informacionno-izmeritelnye i upravljajushhie sistemy. 2009. T. 7. № 9. S. 10-19.
  19. Samarabandu J., Acharya R., Hausmann E. Analysis of Bone X-Rays Using Morfological fractals // IEEE Trans. Medical Imaging. 1993. V. 12. № 3. P. 466-470.
  20. Wu J.J. Analyses and simulation of anisotropic fractal surfaces // Chaos, Solitons and Fractals. 2002. № 13. P. 1791-1806.
  21. Brodatz P. Texture: A Photographic Album for Artists and Designers. Dover, New York. 1966. URL: http://sipi.usc.edu/database/database.