Application of Wavelet Modulus Maximum Principle in Image Edge Extraction and Signal Singularity Detection

The wavelet modulus maximum principle is an effective method widely used in image edge extraction and signal singularity detection. This approach leverages wavelet transform theory by identifying local maxima points in signals or images to capture critical features and edge information. In practical implementation, this involves calculating wavelet coefficients across multiple scales, then applying modulus maxima detection algorithms to identify points where the wavelet transform modulus reaches local maxima while preserving phase consistency across scales. For edge detection in images, the Canny-like algorithm enhanced with wavelet modulus maxima can be implemented by first performing 2D wavelet decomposition using functions like wavedec2() in MATLAB, then applying thresholding to modulus maxima chains to distinguish true edges from noise. In signal processing, modulus maxima detection helps identify singularities through functions such as findpeaks() combined with continuous wavelet transform (cwt) analysis. This methodology has achieved significant breakthroughs in computer vision, image processing, and signal processing domains, enabling more precise localization and analysis of image edges and signal discontinuities. Mastering the application of wavelet modulus maximum principle is crucial for developing robust algorithms that enhance understanding and processing of image and signal data, particularly in multi-resolution analysis frameworks.