Fractal Dimension and Wavelet Transform-Based Region Matching Method

This document presents a region matching method based on fractal dimension and wavelet transform, implemented using MATLAB. This approach facilitates enhanced data understanding and analysis, particularly in image processing and pattern recognition domains. Fractal dimension enables quantitative measurement of object complexity and irregularity, while wavelet transform captures local features and detailed information within images. By combining these two methodologies, we achieve comprehensive data processing and research capabilities. MATLAB serves as a powerful software platform providing extensive built-in functions and toolboxes that streamline implementation and validation of this region matching approach. Key implementations include: - Computing fractal dimension using box-counting algorithms via MATLAB's image processing functions - Applying multi-scale wavelet decomposition using wavedec2() for 2D signal analysis - Implementing feature extraction through wavelet coefficient analysis at different resolution levels - Developing matching algorithms that combine fractal metrics with wavelet-based texture descriptors The integration of these techniques enables more profound data analysis and research outcomes, contributing to advancements in related technical fields. The MATLAB implementation allows for parameter customization, performance optimization, and experimental validation through script-based development and visualization tools.