Higuchi dimension of digital images

Area of Science:

• Image Analysis
• Fractal Geometry
• Signal Processing

Background:

• Traditional methods for 2D fractal dimension calculation (e.g., Box Counting, Fourier analysis) have limitations.
• These methods typically require analysis of the entire image, restricting the assessment of specific regions or directional properties.

Purpose of the Study:

• To propose a novel method for calculating fractal dimensions in 2D digital images.
• To overcome the limitations of existing methods by enabling region-specific and direction-dependent analyses.

Main Methods:

• 2D images are transformed into 1D signals suitable for time series analysis.
• Higuchi's algorithm is applied to calculate the Higuchi dimension of these 1D signals.
• The proposed method is validated and compared against the Fourier dimension method.

Main Results:

• The new method successfully calculates fractal dimensions for regions of interest independently of the whole image.
• Directional dependencies in fractal dimension can be evaluated, allowing for both direction-dependent and independent analyses.
• The method provides reliable fractal dimension values and demonstrates effective treatment of regions of interest.

Conclusions:

• The proposed technique offers a flexible and powerful approach to fractal dimension analysis in 2D images.
• It overcomes key limitations of existing methods, enabling detailed analysis of image structures.
• The methodology is adaptable to various 1D signal analysis techniques beyond Higuchi's algorithm.