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.