The edge of an image is one of the important features in image analysis and processing. The edge often corresponds to the sharp variation points of intensities that carry most of the image information. In practice, the implementation of edge detection is often performed by some multiscale operators. Wavelet transform is closely related to multiscale edge detection. This paper suggests a regularization method for determining scales for wavelet transform adaptively for each site in image plane. An energy function was introduced to obtain a set of optimal scales by minimizing this function. The multiscale wavelet transform filter was derived from this energy function. The maxima of wavelet transform modulus at these scales acquired from the local site of the image were detected to form the edge map. Experiments for real image shows that both step and differ edges can be detected by this method.