Skip to main content
Log in

On estimation of the image complexity by two-dimensional variations

  • Theory and Methods of Information Processing
  • Published:
Journal of Communications Technology and Electronics Aims and scope Submit manuscript

Abstract

General principles of solution of the problem of distorted image reconstruction on the basis of both deterministic and probabilistic approaches are considered. The importance of choosing the mathematical characteristics of two-dimensional functions that can be used as the basis for estimation of their complexity is noted. It is proposed to estimate the image complexity with the help of two-dimensional Kronrod variations. The results of application of these variations to the analysis of real and synthesized images are demonstrated. Recommendations concerning the use of two-dimensional Kronrod variations for solution of image filtering and reconstruction problems are given.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. G. Vitushkin, About Multidimentional Variations (Gostekhizdat, Moscow, 1955) [in Russian].

    Google Scholar 

  2. P. A. Chochia and O. P. Miliukova, “Two-dimensional variation and image decomposition,” in Proc. 6th Int. Workshop Image Processing and Computer Optics (DIP-97), Proc. SPIE 3346, 329–339 (1998).

    Google Scholar 

  3. A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Nauka, Moscow, 1979; Wiley, New York, 1977).

    Google Scholar 

  4. B. R. Hunt, “Bayesian method in nonlinear digital image restoration,” IEEE Trans. Comput. 26, 219–229 (1977).

    Article  MATH  Google Scholar 

  5. O. P. Milyukova, “On justification of image model,” in Optical Information Science and Technology (OIST-97), Proc. SPIE, 3348, 283–289 (1997).

    Google Scholar 

  6. A. S. Kronrod, “About functions of two variables,” Usp. Mat. Nauk 5(1(35), 24–134 (1955) [in Russian].

    MathSciNet  Google Scholar 

  7. J. S. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena (Topics in Applied Physics) (Springer-Verlag, 1975), Vol. 9, pp. 255–280.

    Chapter  Google Scholar 

  8. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern. Anal. Mach. Intell. 12, 629–639 (1990).

    Article  Google Scholar 

  9. P. A. Chochia, “Image smoothing under preservation of contours,” in Image Encoding and Processing (Nauka, Moscow, 1988), pp. 87–98 [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © O.P. Milyukova, P.A. Chochia, 2012, published in Informatsionnye Protsessy, 2012, Vol. 12, No. 4, pp. 362–371.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Milyukova, O.P., Chochia, P.A. On estimation of the image complexity by two-dimensional variations. J. Commun. Technol. Electron. 58, 628–635 (2013). https://doi.org/10.1134/S1064226913060181

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064226913060181

Keywords

Navigation