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Research on Scale Selection in Image Edge Detection Methods Based on Wavelet Transform

The actual images are often contaminated by noise. Noise reduction is the first step to image processing. But the noise reduction and edge localization are contradictory, which makes edge detection is an ill-posed problem. In multi-scale edge detection using wavelet transform (WT), the scale selection is one key problem. In small scale, edges can be localized accurately, but are sensitive to noise, while in large scale, noise can be suppressed effectively, but edges may deviate from original location. Edges can be detected exactly only when scale selected is a good compromise of these two factors. In this paper, seven edge types are modeled and the scale selection is analyzed for each type. According to the analytical results, some important rules are given, which can guide the scale selection of WT and provide theoretical basis for edge detection and noise reduction. compromise of noise reduction and edge localization. In (11), the effective scales in multi-scale edge detection were discussed and the scale scopes were given, among which edges can localized. But in this study, the edge localization and noise reduction were not considered simultaneously. In order to solve the aforesaid problems, we analyze systematically the problem of scale selection in edge detection methods and give some useful rules to guide the scale selection, according to which, edges can be detected accurately and noise can be reduced effectively. First, seven edge types were modeled and edges were detected based on WT. Then the characteristics of each edge type and the relationships of edge localization and scale factor were analyzed. Finally some useful rules were deduced based on simulation results.