Wavelet Multi-Scale Algorithm for Image Processing and Edge Detection

This article discusses image processing and edge detection based on the wavelet multi-scale algorithm, implemented using the MATLAB programming language. The algorithm employs a fractal transformation approach that decomposes images into wavelet functions at multiple scales, enabling comprehensive image processing and analysis. Wavelet transform serves as a powerful tool widely applied in signal processing and image analysis domains. This article introduces the fundamental principles and core concepts of wavelet multi-scale algorithms, supplemented with practical code demonstrations to illustrate MATLAB implementation techniques for image processing and edge detection. We will systematically elaborate each algorithmic step while providing concrete examples to facilitate readers' understanding and practical application. Key implementation aspects include: utilizing MATLAB's wavelet toolbox functions (e.g., wavedec2 for 2D wavelet decomposition, wrcoef2 for coefficient reconstruction) to achieve multi-scale decomposition; applying edge detection operators to wavelet coefficients at different scales; and combining thresholding techniques for noise-robust edge localization. The concluding section explores application scenarios and future research directions for wavelet multi-scale algorithms in computer vision and medical imaging.