Skip to main content
SpringerLink
Log in

On image analysis in fractography (Methodological Notes)

  • Physical Foundations of Strength and Plasticity
  • Published:
Russian Metallurgy (Metally) Aims and scope

Abstract

As other spheres of image analysis, fractography has no universal method for information convolution. An effective characteristic of an image is found by analyzing the essence and origin of every class of objects. As follows from the geometric definition of a fractal curve, its projection onto any straight line covers a certain segment many times; therefore, neither a time series (one-valued function of time) nor an image (one-valued function of plane) can be a fractal. For applications, multidimensional multiscale characteristics of an image are necessary. “Full” wavelet series break the law of conservation of information.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. B. Merkov, Image Recognition. Introduction to Statistical Educaiton Methods (Editorial URSS, Moscow, 2011).

    Google Scholar 

  2. N. N. Krasil’nikov, Digital Image Processing (Vyuzovskaya Kniga, 2001).

    Google Scholar 

  3. A. S. Viktorov, Landscape Picture (Mysl’, Moscow, 1986).

    Google Scholar 

  4. Yu. A. Krupin and V. G. Sukhova, Computer Metallography (ID MISiS, Moscow, 2009).

    Google Scholar 

  5. A. S. Mel’nichenko, Statistical Analysis in Metallurgy and Materials Science (ID MISiS, Moscow, 2009).

    Google Scholar 

  6. Digital Image Transformation, Ed. by R. E. Bykov (Goryachaya Liniya-Telekom, Moscow, 2003).

    Google Scholar 

  7. Yu. L. Klimontovich, Introduction to the Physics of Open Systems (Yanus-K, Moscow, 2002).

    Google Scholar 

  8. B. Mandelbrot, Fractal Geometry of Nature (IKI, Moscow, 2002).

    Google Scholar 

  9. Physical Encyclopedia, Ed. by A. M. Prokhorov (BRE, Moscow, 1998), Vol. 5, p. 371.

  10. Probability and Mathematical Statistics. Encyclopedia, Ed. by Yu. V. Prokhorov (BRE, Moscow, 1999), p. 777.

    Google Scholar 

  11. M. Shreder, Fractals, Chaos, Power Laws (RKhD, Moscow, 2001).

    Google Scholar 

  12. O. I. Shelukhin, A. M. Tenyakshev, and A. V. Osin, Fractal Processes in Telecommunications (Radiotekhnika, Moscow, 2003).

    Google Scholar 

  13. M. A. Shtremel’, “Generalization of the Pareto distribution in statistical metallography problems,” Zavod. Lab. 71 (8), 25–31 (2005).

    Google Scholar 

  14. D. Yu. Ivanov, Critical Behavior of Nonidealized Systems (Fizmatlit, Moscow, 2003).

    Google Scholar 

  15. A. N. Pavlov and V. S. Anishchenko, “Multifractal analysis of complex signals,” Usp. Fiz. Nauk 177 (8), 859–876 (2007).

    Article  Google Scholar 

  16. F. Mun, Chaotic Oscillations (Mir, Moscow, 1990).

    Google Scholar 

  17. R. M. Rangaiyan, Analysis of Biomedical Signals. Practical Approach (Fizmatlit, Moscow, 2007).

    Google Scholar 

  18. A. A. Potapov, Fractals in Radiophysics and Radiolocation: Topology of Sample (Universitetskaya Kniga, Moscow, 2005).

    Google Scholar 

  19. G. A. Kukharev, Biometric Systems. Methods and Means of Identification of Personality (Politekhnika, St. Petersburg, 2001).

    Google Scholar 

  20. B. Yane, Digital Image Processing (Tekhnosfera, Moscow, 2007).

    Google Scholar 

  21. Novel Image Processing Methods, Ed. by A. A. Potapov (Fizmatlit, Moscow, 2008).

    Google Scholar 

  22. A. S. Potapov, Image Recognition and Machine Perception. General Approach Based on the Principle of the Minimum Description Length (Politekhnika, St. Petersburg, 2007).

    Google Scholar 

  23. D. Forsait and Zh. Pons, Computer Vision. Modern Approach (Vil’yams, Moscow, 2004).

    Google Scholar 

  24. A. A. Koronovskii and A. E. Khramov, Continuous Wavelet Analysis and Its Applications (Fizmatlit, Moscow, 2003).

    Google Scholar 

  25. A. A. Bol’shakov and R. N. Karimov, Methods of Processing of Multidimensional Data and Time Series (Goryachaya Liniya-Telekom, Moscow, 2007).

    Google Scholar 

  26. S. Welsteed, Fractals and Wavelets for Image Compression in Action (Triumf, Moscow, 2003).

    Google Scholar 

  27. K. Blatter, Wavelet Analysis. Fundamentals of Theory (Tekhnosfera, Moscow, 2006).

    Google Scholar 

  28. V. P. D’yakonov, Mathcad 11/12/13 in Mathematics: AHandbook (Goryachaya Liniya-Telekom, Moscow, 2007).

    Google Scholar 

  29. N. P. Klepikov and S. N. Sokolov, Analysis and Planning of Experiments Using the Method of Maximum Likelihood (Nauka, Moscow, 1964).

    Google Scholar 

  30. A. A. Greshilov, Incorrect Problems of Digital Processing of Information and Signals (Radio Svyaz’, Moscow, 1984).

    Google Scholar 

  31. A. N. Tikhonov and M. V. Ufimtsev, Statistical Processing of Experimental Results (MGU, Moscow, 1988).

    Google Scholar 

  32. V. Yu. Trebizh, Analysis of Time Series in Astrophysics (Nauka, Moscow, 1992).

    Google Scholar 

  33. V. Yu. Trebizh, Introduction to the Statistical Theory of Inverse Problems (Fizmatlit, Moscow, 2005).

    Google Scholar 

  34. M. A. Shtremel’, “Boundaries of the possibilities of diffractometer analysis of a fine structure,” Dokl. Akad. Nauk SSSR 203, 570 (1972).

    Google Scholar 

  35. V. V. Ovchinnikov, Mössbauer Methods of Analysis of the Atomic and Magnetic Structure of Alloys (Fizmatlit, Moscow, 2002).

    Google Scholar 

  36. I. D. Grachev, M. Kh. Salakhov, and I. S. Fishman, Statistical Regularization during Processing of Experimental Data in Applied Spectroscopy (KGU, Kazan, 1986).

    Google Scholar 

  37. M. A. Shtremel’ and D. A. Kozlov, “On criteria and plans of optimum X-ray diffraction measurement of texture,” Zavod. Lab., No. 5, 15–21 (1991).

    Google Scholar 

  38. K. Chui, Introduction to Wavelets (Mir, Moscow, 2001).

    Google Scholar 

  39. A. S. Monin and D. M. Sonechkin, Climate Oscillations according to Observation Data: Ternary Solar and Other Cycles (Nauka, Moscow, 2005).

    Google Scholar 

  40. G. A. Sobolev and A. V. Ponomarev, Physics of Earthquakes and Precursors (Nauka, Moscow, 2003).

    Google Scholar 

  41. J. C. Russ, Fractal Surfaces (Plenum, New York, 1994).

    Book  Google Scholar 

  42. V. S. Sizikov, Mathematical Methods of Processing Measurement Results (Politekhnika, St. Petersburg, 2001).

    Google Scholar 

  43. E. Terner, I. Kerube, and J. Wilson, Biosensors: Fundamentals and Applications (Mir, Moscow, 1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National University of Science and Technology MISiS, Leninskii pr. 4, Moscow, 119049, Russia

    M. A. Shtremel’

Authors
  1. M. A. Shtremel’
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Shtremel’.

Additional information

Original Russian Text © M.A. Shtremel’, 2014, published in Deformatsiya i Razrushenie Materialov, 2014, No. 10, pp. 2–9.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shtremel’, M.A. On image analysis in fractography (Methodological Notes). Russ. Metall. 2015, 771–777 (2015). https://doi.org/10.1134/S0036029515100158

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0036029515100158

Keywords

Search

Navigation