Application of Fractals to Detect Breast Cancer

Datta, Debabrata; Sathish, Shakeela

doi:10.1088/1742-6596/1377/1/012030

Cited by 5 publications

(3 citation statements)

References 2 publications

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“…A fractal is scale-invariant and self-affine, and an indicator called fractal dimension is used to quantify its complexity. Fractal analysis is successfully used in natural sciences [17][18][19], engineering technologies [20,21], medicine [22][23][24], meteorology [25], finance [26] and other fields [27]. In the 1980s, Grassberger introduced the concept of a multifractal.…”

Section: Introductionmentioning

confidence: 99%

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

Zagretdinov,

Ziganshin,

Izmailova

et al. 2024

Fractal Fract

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In this paper, the possibility of using monofractal and multifractal analysis of acoustic signals of pipelines to detect leaks is considered. An experimental stand has been created to study the fractal characteristics of acoustic signals of pipelines with “slit” type defects. During the experiments, defects of the “slit” type pipeline with dimensions of 2 mm, 8 mm, and 20 mm were modeled. Detrended fluctuation analysis (DFA) and the multifractal detrended fluctuation analysis (MF-DFA) were used. As a result of the experimental studies, it was found that the occurrence of leakage leads to the occurrence of anticorrelated vibrations in a pipeline with multifractal properties. The analyses of acoustic signals by DFA and MF-DFA methods make it possible to reliably determine the leakage. The Hurst exponent and the width of the multifractal spectrum can serve as indicators of the occurrence of leaks in pipelines.

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Section: Introductionmentioning

confidence: 99%

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

Zagretdinov,

Ziganshin,

Izmailova

et al. 2024

Fractal Fract

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“…Recently, fractal theory has been widely used in practical engineering to study the laws governing various complex, irregular and chaotic processes. Fractal methods are used in industries such as medicine (for analyzing data to detect cancer cells) [14][15][16], finance (to determine trends in securities charts) [17], meteorology [18], engineering [19][20][21][22], and other fields [23,24]. Monofractal models cannot always provide a complete description of patterns, especially when attempting to capture subtle spatial and temporal variations that are governed by natural laws.…”

Section: Introductionmentioning

confidence: 99%

Detection of Gate Valve Leaks through the Analysis Fractal Characteristics of Acoustic Signal

Zagretdinov,

Ziganshin,

Izmailova

et al. 2024

Fractal Fract

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This paper considers the possibility of using monofractal and multifractal analysis of acoustic signals to detect water leaks through gate valves. Detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MF-DFA) were used. Experimental studies were conducted on a ½-inch nominal diameter wedge valve, which was fitted to a ¾-inch nominal diameter steel pipeline. The water leak was simulated by opening the valve. The resulting leakage rates for different valve opening conditions were 5.3, 10.5, 14, 16.8, and 20 L per minute (L/min). The Hurst exponent for acoustic signals in a hermetically sealed valve is at the same level as a deterministic signal, while the width of the multifractal spectrum closely matches that of a monofractal process. When a leak occurs, turbulent flow pulsations appear, and with small leak sizes, the acoustic signals become anticorrelated with a high degree of multifractality. As the leakage increases, the Hurst exponent also increases and the width of the multifractal spectrum decreases. The main contributor to the multifractal structure of leak signals is small, noise-like fluctuations. The analysis of acoustic signals using the DFA and MF-DFA methods enables determining the extent of water leakage through a non-sealed gate valve. The results of the experimental studies are in agreement with the numerical simulations. Using the Ansys Fluent software (v. 19.2), the frequencies of flow vortices at different positions of gate valve were calculated. The k-ω SST turbulence model was employed for calculations. The calculations were conducted in a transient formulation of the problem. It was found that as the leakage decreases, the areas with a higher turbulence eddy frequency increase. An increase in the frequency of turbulent fluctuations leads to enhanced energy dissipation. Some of the energy from ordered processes is converted into the energy of disordered processes.

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“…Furthermore, biomedical image, i.e. magnetic resonance image (MRI) [1] [7], ultrasound, X-ray, and computerized tomography (CT) scan segmentation is a challenging task with the existence of speckle noise, its poor luminance and indistinctive contrast [8] which cause difficulties in identifying the edges [9][10] [11] [12].…”

Section: Introductionmentioning

confidence: 99%

Mini Kirsch Edge Detection and Its Sharpening Effect

Sia¹,

Swee²,

Yahya³

et al. 2021

IJEEI

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In computer vision, edge detection is a crucial step in identifying the objects' boundaries in an image. The existing edge detection methods function in either spatial domain or frequency domain, fail to outline the high continuity boundaries of the objects. In this work, we modified four-directional mini Kirsch edge detection kernels which enable full directional edge detection. We also introduced the novel involvement of the proposed method in image sharpening by adding the resulting edge map onto the original input image to enhance the edge details in the image. From the edge detection performance tests, our proposed method acquired the highest true edge pixels and true nonedge pixels detection, yielding the highest accuracy among all the comparing methods. Moreover, the sharpening effect offered by our proposed framework could achieve a more favorable visual appearance with a competitive score of peak signal-to-noise ratio and structural similarity index value compared to the most widely used unsharp masking and Laplacian of Gaussian sharpening methods. The edges of the sharpened image are further enhanced could potentially contribute to better boundary tracking and higher segmentation accuracy.

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Application of Fractals to Detect Breast Cancer

Cited by 5 publications

References 2 publications

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

Detection of Gate Valve Leaks through the Analysis Fractal Characteristics of Acoustic Signal

Mini Kirsch Edge Detection and Its Sharpening Effect

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