Research on Edge Shift in Case of Multi-scale Edge Detection
对多尺度边缘检测中边缘位移的研究

One of the main tasks in multi-scale edge detection is to seek the best compromising between removing noise and remaining fine edges. At present, many adaptive multi-scale edge detection algorithms have been developed. But there is one problem in these methods in that some detected edge points are moved actually from their exact positions. In order to obtain edge points as exactly as possible, in this paper, a new adaptive multi-scale edge detection method is developed, in which the edge positions are kept invariant to the most in the case of large scale. Moreover, firstly, it is proved that, within an apt scale range, with a special class of wavelet basis, the positions of edge points based on zero crossing of two order derivatives won't be changed after wavelet transform even with ordinary edge detection operator; secondly, according to the property of multi-scale analysis and the relation between differentiating and integration operation in which a wavelet function is taken as a kernel function, a multi-scale self-adaptive multi-scale edge detection algorithm was put forward in which the local maximum scale in that the positions of local edge points won't be changed is developed; finally, two group of experiments are carried out with different kinds of wavelet basis. The experiments show that, under the restriction that the specific edges should be kept as good as possible, the positions of edge will not be changed in large-scale case.