Journal of Radio Electronics. eISSN 1684-1719. 2024. ¹9

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DOI: https://doi.org/10.30898/1684-1719.2024.9.5

 

 

 

ON THE CALCULATION OF THE MINKOWSKI DIMENSION
FOR GRAYSCALE IMAGES

 

A.I. Shaposhnikov

 

Tomsk middle school No. 70
634034, Tomsk, Nakhimov st., 3/1.

 

The paper was received May 15, 2024.

 

Abstract. In the article the result of the statistical experiment is presented. The purpose of the experiment is inspection of the correctness of the algorithm for determining the value and accuracy of Minkowski dimension for grayscale images. For arbitrary image from internet the sample population is constructed. Then for every element of this sample population the Minkowski dimension is calculated by the box counting method. Then for this sample population the mean and standard deviation are defined. Although the box counting method singly has a slow accuracy but in combine with this statistical approximation the Minkowski dimension with the better precision is get. In this article for inspection of the correctness two sample populations are constructed. The first sample population is generated by shifts the image down and the second sample population is generated by shifts image left. Two different sample populations have the little differ means and standard deviation but the Wilcoxon test rejects the hypothesis about the including these sample populations to different general populations. Such result allows make algorithm for more précised the set's Minkowski dimension.

Key words: Minkowsky dimension, sample population, sample mean, sample standard deviation, Wilcoxon signed-rank test.

Corresponding author: Shaposhnikov Albert Igorevich, albertelena@mail.ru

References

1. Crownover R.M. Introduction to Fractals and Chaos – ISBN 5-901095-03

2. Sheluhin O.I., Magomedova D.I. Analysis of methods for calculating the fractal dimension of color and grayscale images High-Tech in Earth Space Research. 2017; 9(6): 6—16.

3. Kalaida V.T., Shaposhnikov A.I. Obtaining the statistical parameters for the estimation of the fractal dimension: Computer program. Registration certificate number – Ò. 2022666440.

4. Kalaida V.T., Shaposhnikov A.I. Estimation of the fractal dimensions of images // Radiophysics, Photonics and the Study of the Properties of Matter : Abstracts of the II Russian Scientific Conference (Omsk, 2022, October 5–7). Omsk : ONIIP, 2022. P. 137–138.

5. Software and hardware system for monitoring and control of the optical-physical state of the atmosphere: Part 1: Panoramic optical station / V. P. Galileyskii, A. I. Elizarov, D. V. Kokarev [et al.] // Proceedings of SPIE - The International Society for Optical Engineering : 27, Moscow, 05–09 èþëÿ 2021 ãîäà. – Moscow, 2021. – P. 119168K. – https://doi.org/10.1117/12.2603231. – EDN VMZBKB.

6. Shaposhnikov A.I. Digital description of a set during computer processing. Collection of proceedings of the IX International Scientific and Practical Conference. Tomsk; 2021: 276–277.

7. PVSM Calculation of Minkowski fractal dimension for a flat image. 20114, Access address: https://www.pvsm.ru/matematika/52344.

8. Kalaida V.T., Shaposhnikov A.I. Variation the fractal dimensions of object images under equiaffine transformations // Materials III Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii «Dorozhnoe stroitel’stvo i ego inzhenernoe obespechenie» [Proceedings of the III International scientific conference «Road construction and its engineering provision»] Compiled by Sobolevskaya S. N., Zhukovskiy E. M. Minsk, BNTU Publ., 2022, pp. 65-68.

9. The Minkowski dimensions of images with shifts// The data: – URL: https://drive.google.com/drive/folders/1nsp2xuLtlJ2AV7q83m2UWvrkB0g4qqX5?usp=sharing

10. 2018.01.08__08_03_14.334.jpg_FractalDimensionLeft280Cutted2023_08_08. txt // The data with the right shifts: – URL: https://drive.google.com/file/d/1xNwTBYnlt6xix5m9emShhyNIndkdaY2q/view?usp=drive_link

11. 2018.01.08__08_13_14.516.jpg_FractalDimensionLeft280Cutted2023_08_08. txt // The data with the right shifts: – URL: https://drive.google.com/file/d/1yUcmNM1ZtR_qCP7fREVls3o1N8cvA92I/view?usp=drive_link

12. 2018.01.08__11_47_58.987.jpg_FractalDimensionLeft280Cutted2023_08_08. txt // The data with the right shifts: – URL: https://drive.google.com/file/d/1whHfxxHEzUyyeKqACLCV6_jJcOg4cgvw/view?usp=drive_link

13. 2018.01.08__08_03_14.334.jpg_FractalDimDown280Cutted2023_08_08. txt // The data with the down shifts: – URL: https://drive.google.com/file/d/17GgQYnibYulwXOjixuNP3v1TENvvw5EG/view?usp=drive_link

14. 2018.01.08__08_13_14.516.jpg_FractalDimDown280Cutted2023_08_08. txt // The data with the down shifts: – URL: https://drive.google.com/file/d/1AJ3vcwM9-rCnaE0TaaVgonvSORi_Wdqt/view?usp=drive_link

15. 2018.01.08__11_47_58.987.jpg_FractalDimDown280Cutted2023_08_08. txt // The data with the down shifts: – URL: https://drive.google.com/file/d/1LhV9rUEDbPX0uTanljcVaVgfxMzTGmFt/view?usp=drive_link

16. Mandelbrot B. The fractal geometry of nature. Moscow: Institute of Computer Research. 2002:–605.

17. Minkowski. Bouligand dimension. Wikipedia. Free Encyclopedia: https://en.wikipedia.org/wiki/Minkowski_Bouligand_dimension  (accessed 04.07.2022).

18. Monitoring of the atmosphere and underlying surface. Panoramic optical station TomSky 2022. Access address: https://sky.iao.ru/gallery/2015.07.01__00_15_41.225.jpg

19. Frederic Moisy Boxcount. Access address: https://www.mathworks.com/matlabcentral/fileexchange/13063-boxcount (accessed 04.07.2022).

20. Blaginin A.L., Sajfulin E.R., Sarkisova A.Yu. From the experience of organizing automated data collection at tomsk university. Big Data and problems of society. Proc. of the International Conference. Kirov, May 19–20, 2022. Tomsk: Tomsk State University. pp. 34–46.

21. Kalaida V.T., Shaposhnikov A.I. The modification of algorithms for the estimation of the fractal dimension for cloud’s images // Computational Technologies. 2024. Ò. 29. ¹ 1. Ñ. 86-92. https://doi.org/10.25743/ICT.2024.29.1.008.

 

For citation:

Shaposhnikov A.I On the calculation of the Minkowski dimension for grayscale images. // Journal of Radio Electronics. – 2024. – ¹. 9. https://doi.org/10.30898/1684-1719.2024.9.5 |