多尺度边缘检测的任务之一是寻求噪声平滑与保持细节边缘的折中,现已出现了许多自适应多尺度边缘检测方法,但使用多尺度的边缘检测方法常常使得边缘发生位移.为了使得在大尺度下求取的边缘位置不变,提出了一种根据局部图象特点,在最大尺度下求取保持图象边缘点位置不变的多尺度自适应边缘检测方法,并首先证明了对于绝大多数边缘点,如果使用恰当的小波基,那么,对于常规边缘检测算子,在大尺度下,也能准确定位;然后,利用以小波函数为核函数的积分运算与求导数之间的关系以及小波分析的多尺度特性给出了一种自适应的、保持位置不变的图象边缘检测方法,最后用实验进行了验证.

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.