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On estimating the local entropy of an image in a sliding window
V.V. Sergeyev 1,2, A.Y. Bavrina 1,3, I.D. Zaitsev 1, M.Y. Lazutov 1, D.A. Shapiro 1

1 Samara National Research University,
443086, Samara, Russia, Moskovskoye Shosse 34;
2 Image Processing Systems Institute, NRC «Kurchatov Institute»,
443001, Samara, Russia, Molodogvardeyskaya 151;
3 JSC «Samara-Informsputnik»,
443080, Samara, Russia, Karl Marx ave. 192, off. 717

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DOI: 10.18287/2412-6179-CO-1509

Pages: 714-725.

Full text of article: Russian language.

Abstract:
The paper considers a number of issues related to the calculation of the local entropy in a sliding window for image processing tasks. A new algorithm for entropy estimation is proposed, which has several times lower computational complexity than the known ones. The algorithm is based on the approximate representation of the histogram in the form of a truncated series expansion over some system of orthogonal basis functions, recursive calculation of the coefficients of this expansion in a sliding window and subsequent recalculation of the coefficients into the entropy estimate. Questions of an orthogonal basis selection for representing the local histogram as a truncated series are considered and the appropriateness of using the Haar basis is shown. A technique of constructing hierarchical approximator, which realizes fast recalculation of histogram decomposition coefficients into entropy value, is described. The theoretical statements of the paper are verified by experiments on the Earth remote sensing images.

Keywords:
image processing, local feature generation, sliding window, local histogram, entropy estimation, basis function decomposition, recursive processing, hierarchical approximation, estimation error, computational complexity.

Citation:
Sergeyev VV, Bavrina AY, Zaitsev ID, Lazutov MY, Shapiro DA. On estimating the local entropy of an image in a sliding window. Computer Optics 2024; 48(5): 714-725. DOI: 10.18287/2412-6179-CO-1509.

Acknowledgements:
This work was financially supported by the Russian Science Foundation under project No. 23-11-20013 (Sections 1-3, 8) and the RF Ministry of Science and the State assignment of NRC "Kurchatov Institute" (Sections 4-7).

References:
  1. Yaroslavsky LP. Introduction to digital image processing [In Russian]. Moscow: "Sovetskoe Radio" Publisher; 1979.
  2. Pratt WK. Digital image processing. New York: Willey; 1978. ISBN: 0471018880.
  3. Gashnikov MV, Glumov NI, Ilyasova NY, Myasnikov VV, Popov SB, Sergeyev VV, Soifer VA, Khramov AG, Chernov AV, Chernov VM, Chicheva MA, Fursov VA. Computer image processing methods [In Russian]. Moscow: "Fizmatlit" Publisher; 2003. ISBN: 5-9221-0270-2.
  4. Gonzalez RC, Woods RE. Digital image processing. London: Pearson; 2018. ISBN: 978-0-13-335672-4.
  5. Shapiro L, Stockman J. Computer vision [In Russian]. Moscow: Binom, Knowledge Laboratory; 2006. ISBN: 5-94774-384-1.
  6. Schowengerdt RA. Remote sensing: models and methods for image processing. Academic Press; 2006. ISBN: 978-0123694072.
  7. Wei Y, Tao L. Efficient histogram-based sliding window. IEEE Computer Society Conf on Computer Vision and Pattern Recognition 2010: 3003-3010. DOI: 10.1109/CVPR.2010.5540049.
  8. Velichko A, Belyaev M, Wagner MP, Taravat A. Entropy approximation by machine learning regression: application for irregularity evaluation of images in Remote Sensing. Remote Sens 2022; 14(23): 5983. DOI: 10.3390/rs14235983.
  9. Huang TS, Yang GY, Tang GY. A fast two-dimensional median filtering algorithm. IEEE Trans Acoust Speech Signal Process 1979; ASSP-27(1): 13-18. DOI: 10.1109/TASSP.1979.1163188.
  10. Huang TS, Eklund JO, Nussbaumer GJ, et al. Fast algorithms in digital image processing [In Russian]. Moscow: “Radio i Svyaz” Publisher; 1984.
  11. Chentsov NN. Estimation of unknown distribution density from observations [In Russian]. Report USSR Academy of Sciences 1962; 147(1): 45-48.
  12. Kass M, Solomon J. Smoothed local histogram filters. ACM Trans Graph 2010; 29(426): 100. DOI: 10.1145/1778765.1778837.
  13. Ventzel ES. Probability theory [In Russian]. Moscow: “Nauka” Publisher; 1969.
  14. Shannon K. Works on information theory and cybernetics [In Russian]. Moscow: Publishing House of Foreign Literature; 1963.
  15. Oppenheim A, Schafer R. Digital signal processing [In Russian]. Moscow: “Tehnosphera” Publisher; 2012. ISBN: 978-5-94836-329-5.
  16. Zalmanzon LA. Fourier, Haar, Walsh transforms and their application in control, communications and other areas [In Russian]. Moscow: “Nauka” Publisher; 1989. ISBN: 5-02-014094-5.
  17. Dedus FF, Kulikova LI, Pankratov AN, Tetuev RK. Classical orthogonal bases in problems of analytical description and processing of information signals [In Russian]. Moscow: VMKMGU Publisher; 2004.
  18. Shvedov AS. Approximation of functions using neural networks and fuzzy systems [In Russian]. Problems of Control 2018; 1: 21-29.
  19. Sergeev VV, Myasnikov VV. Algorithm for fast implementation of the Gabor filter [In Russian]. Avtometria 1999; 6: 51-55..

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