Pyramidal fractal dimension for high resolution images.

Area of Science:

• Image analysis
• Computational geometry
• Digital imaging

Background:

• Fractal analysis (FA) is crucial for quantifying complex patterns in digital images.
• Current FA methods can be slow and less accurate for high-resolution images, limiting real-time applications.
• Efficient FA for binary images has paved the way for new approaches.

Purpose of the Study:

• To introduce and evaluate three novel pyramidal methods for fractal dimension (D) estimation in digital images.
• To compare the performance of these new methods against standard FA techniques.
• To assess the accuracy, computation time, and scalability of different FA methods for high-resolution images.

Main Methods:

• Development of three pyramidal methods: pyramid triangular prism (PTPM), pyramid gradient (PGM), and pyramid differences (PDM).
• Evaluation using artificial fractal images generated by three models, with sizes up to 8192x8192 pixels.
• Comparison with five standard fractal dimension estimation techniques.

Main Results:

• All pyramidal methods (PMs) yielded reasonable D values across different fractal generator models and image sizes.
• PMs demonstrated superior accuracy and computation time compared to standard methods for images >= 1024x1024 pixels.
• PDM and PGM were the fastest, followed by PTPM, with standard methods being significantly slower.

Conclusions:

• The new pyramidal methods offer high-quality fractal dimension estimation with short computation times.
• PMs are well-suited for fast fractal analysis of high-resolution images, outperforming standard techniques, especially for large datasets.
• These methods are eligible for applications requiring immediate and reliable fractal analysis outcomes.