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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.