Multifractal Scaling of Singularity Spectra of Digital Mueller-matrix Images of Biological Tissues: Fundamental and Applied Aspects

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Oleksandr Ushenko 1 Oleksandr Saleha 2 Yuriy Ushenko 3,* Ivan Gordey 3 Oleksandra Litvinenko 4

1. Research Institute of Zhejiang University-Taizhou, Taizhou, China

2. Optics and Publishing Department, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine

3. Computer Science Department, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine

4. Bucovinian State Medical University, Chernivtsi, Ukraine

* Corresponding author.


Received: 13 Oct. 2023 / Revised: 16 Nov. 2023 / Accepted: 24 Dec. 2023 / Published: 8 Apr. 2024

Index Terms

Mueller matrix, biological tissue, optical anisotropy, birefringence, fractal, singularity spectrum, wavelet transform, diagnostics, trauma, spleen


The fundamental component of the work contains a summary of the theoretical foundations of the algorithms of the scale-self-similar approach for the analysis of digital Mueller-matrix images of birefringent architectonics of biological tissues. The theoretical consideration of multifractal analysis and determination of singularity spectra of fractal dimensions of coordinate distributions of matrix elements (Mueller-matrix images - MMI) of biological tissue preparations is based on the method of maxima of amplitude modules of the wavelet transform (WTMM). The applied part of the work is devoted to the comparison of diagnostic capabilities for determining the prescription of mechanical brain injury using algorithms of statistical (central statistical moments of the 1st - 4th orders), fractal (approximating curves to logarithmic dependences of power spectra) and multifractal (WTMM) analysis of MMI linear birefringence of fibrillar networks of neurons of nervous tissue. Excellent (~95%) accuracy of differential diagnosis of the prescription of mechanical injury has been achieved.

Cite This Paper

Oleksandr Ushenko, Oleksandr Saleha, Yurii Ushenko, Ivan Gordey, Oleksandra Litvinenko, "Multifractal Scaling of Singularity Spectra of Digital Mueller-matrix Images of Biological Tissues: Fundamental and Applied Aspects", International Journal of Image, Graphics and Signal Processing(IJIGSP), Vol.16, No.2, pp. 29-42, 2024. DOI:10.5815/ijigsp.2024.02.03


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