Multiscale analysis of digital images in terms of entropy – complexity using the shearlet transform

Krasnyakov I.V.
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This paper presents a method for digital image analysis based on the combined use of the Fast Finite Shearlet Transform and statistically significant measures of information entropy and complexity. The proposed approach is aimed at studying spatial structures of various nature, including regular, stochastic, and multiscale systems, and enables the identification of their organizational patterns without the need for preliminary segmentation or model training.

The method is based on constructing local probability distributions derived from shearlet decomposition coefficients, which capture both the scale and directional properties of images. Using these distributions, the normalized Shannon entropy and statistical complexity — defined via divergence from the uniform distribution — are computed. This allows transitioning from the analysis of individual coefficients to a more robust characterization of structural properties in the entropy – complexity space.

The method has been tested on a range of synthetic and real-world data. In particular, the transition from ordered to chaotic systems has been investigated, demonstrating the sensitivity of the proposed measures to the degradation of regular structures. Using fractal objects (such as the Sierpinski triangle) as an example, it is shown that statistical complexity reaches its maximum at characteristic scales of self-similarity. Application of the method to images of the Martian surface demonstrates its potential for remote sensing and geomorphological analysis.

Special attention is given to noise robustness. It is shown that even weak noise leads to an increase in entropy and a decrease in complexity, allowing these measures to be used as indicators of structural degradation.

The obtained results indicate that the entropy – complexity framework based on the shearlet transform can serve as a universal tool for multiscale image analysis. The proposed approach exhibits high sensitivity to structural features and can be applied across a wide range of tasks, including texture analysis, natural image processing, and medical diagnostics.

Keywords: shearlet-transform, entropy – complexity, multiscale analysis, structure analysis, image analysis
Citation in English: Krasnyakov I.V. Multiscale analysis of digital images in terms of entropy – complexity using the shearlet transform // Computer Research and Modeling, 2026, vol. 18, no. 5, pp. 1093-1120
Citation in English: Krasnyakov I.V. Multiscale analysis of digital images in terms of entropy – complexity using the shearlet transform // Computer Research and Modeling, 2026, vol. 18, no. 5, pp. 1093-1120
DOI: 10.20537/2076-7633-2026-18-5-1093-1120
URL: http://crm-en.ics.org.ru/journal/article/3772/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Krasnyakov I.V.

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