Traditional Edge Detection Operators: Algorithmic Differences and Comparative Analysis

This paper first introduces the definition of edges and provides detailed explanations of traditional edge detection operators such as Sobel and Canny operators, comparing their algorithmic differences, advantages and disadvantages with implementation insights. The Sobel operator typically employs 3x3 convolution kernels for gradient approximation in horizontal and vertical directions, while the Canny algorithm involves multi-stage processing including Gaussian smoothing, gradient calculation, non-maximum suppression, and hysteresis thresholding. The paper then introduces wavelet concepts, fundamental principles of wavelet transform, and their application domains. Additionally, it explores the advantages and limitations of wavelet-based edge detection, discussing improved methods and techniques such as multi-scale edge detection using wavelets and wavelet domain threshold processing. Multi-scale edge detection leverages wavelet transform's ability to capture features at different resolutions, while threshold processing in wavelet domain involves coefficient modification for noise reduction. Finally, the paper summarizes the main content and discusses future research directions and development trends in wavelet-based edge detection, including potential optimizations in wavelet function selection and computational efficiency improvements.