Estimating the complexity of objects in images

V. B. Bokshanskiy; Бокшанский В. Б.; V. A. Kulin; Кулин В. А.; G. S. Finiakin; Финякин Г. С.; A. S. Kharlamov; Харламов А. С.; A. A. Shatskiy; Шацкий А. А.

doi:10.31857/S0132347424050036

Estimating the complexity of objects in images

Authors: Bokshanskiy V.B.¹, Kulin V.A.¹, Finiakin G.S.¹^,2, Kharlamov A.S.³, Shatskiy A.A.¹
Affiliations:
1. Bauman Moscow State Technical University
2. National Research University “Moscow Power Engineering Institute”
3. Moscow State Technical University of Civil Aviation
Issue: No 5 (2024)
Pages: 31-41
Section: COMPUTER GRAFICS AND VISUALIZATION
URL: https://medjrf.com/0132-3474/article/view/683330
DOI: https://doi.org/10.31857/S0132347424050036
EDN: https://elibrary.ru/OLZNYI
ID: 683330

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Abstract
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About the authors
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Abstract

A new method for estimating the complexity of geometric shapes (spots) is proposed, taking into account the internal structure of the spots, and not only their external contour. The task of calculating the degree of complexity of objects is divided into components: segmentation of spots and estimation of the complexity of isolated spots. The new method has a relatively low computational complexity compared to the alternative methods considered in the work. Using the new method, an algorithm based on parallel computing of the CUDA programming language for graphics accelerators (video cards) was created, which further increases the performance of our method. A qualitative and quantitative analysis of existing (alternative) methods has been carried out, their advantages and disadvantages in comparison with our method and with each other have been revealed. The algorithm implemented on the basis of the new method has been tested on both artificial and real digital images.

Keywords

Hu invariants, image complexity, image compression, image contour, image segmentation, contour selection, image classification, statistical moments of images, computational complexity

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About the authors

V. B. Bokshanskiy

Bauman Moscow State Technical University

Email: shatskiyalex@gmail.com
Russian Federation, Moscow

V. A. Kulin

Bauman Moscow State Technical University

Email: shatskiyalex@gmail.com
Russian Federation, Moscow

G. S. Finiakin

Bauman Moscow State Technical University; National Research University “Moscow Power Engineering Institute”

Email: shatskiyalex@gmail.com
Russian Federation, Moscow; Moscow

A. S. Kharlamov

Moscow State Technical University of Civil Aviation

Email: shatskiyalex@gmail.com
Russian Federation, Moscow

A. A. Shatskiy

Bauman Moscow State Technical University

Author for correspondence.
Email: shatskiyalex@gmail.com
Russian Federation, Moscow

References

https://ru.wikipedia.org/wiki/WMAP/
https://en.wikipedia.org/wiki/Planck_(spacecraft)
Hu M.K. Visual pattern recognition by moment invariants, IRE Trans. Info. Theory, 1962. V. IT-8, P. 179–187 (1962).
Doerr F.J.S., Florence, A.J. A micro-xrt image analysis and machine learning methodology for the characterisation of multi-particulate capsule formulations, Int. J. Pharm., 2020. V. 2.
Kornilov A.S., Safonov I.V. An overview of watershed algorithm implementations in open source libraries, J. Imaging, 2018. V. 4. No. 10. P. 123.
Shaiduk A.M., Ostanin S.A. Quantitative estimation of shape comlexity in medical images // Zh. Radioelektron. 2013. V. 2.
Rothganger M., Melnik A., Ritter H. Shape complexity estimation using VAE. ArXiv:2304.02766, 2023.
Gilchrist J. Parallel data compression with bzip2, Proceedings of the 16th IASTED International Conference on Parallel and Distributed Computing and Systems, 2004. V. 16. P. 559–564.
Shannon C.E. A mathematical theory of communication. Bell Syst. Techn. J., 1948. V 27, No. 3. P. 379–423.

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2. Fig. 1. Image brightness intensity.

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3. Fig. 2. Grayscale images (left) and segmentation of the same images into individual segments (combined into spots) highlighted in different colors (right).

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4. Fig. 3. Sorting image spots by decreasing complexity level and highlighting the main spot with a green frame. The output of the top-5 spots of the image is shown, ranked first by the value of the Max_i number at the | kiHui | max value, and then by the spot brightness. On the right is a table of spot characteristics: spot number, Max_i number at the maximum value | kiHui | max, spot brightness Etot, spot area Stot and value | kiHui | max.

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5. Fig. 4. Scheme of the architecture of the neural network – variational autoencoder, example of tracing a test binary image and assessing its degree of complexity.

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6. Fig. 5. Test images used to compare complexity estimation methods for invariance to some of the affine transformations and to additive noise: apple (left), bird (center), and fly (right).

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7. Fig. 6. Stability under noise exposure obtained by different methods.

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8. Fig. 7. An example of a test image of a fly with noise implementation at RMS = 64(y. e.). For binary images, whose brightness values are either 0 or 255 (at 8-bit coding depth), adding noise with RMS = 64 is not a factor, as a result of which the original geometric shapes cannot be visually recognized.