讨论了基于光滑函数的二维小波极大模边缘算子和小波过零点边缘算子及其特性。提出了多尺度二进小波变换过零点边缘聚焦算法。通过对不同尺度下小波变换的遥感影像进行复合、边缘提取和聚焦后结果进行比较，可以发现该算法适应影像空间尺度不确定性目标边缘提取。既可保证大尺度下的轮廓信息不失真，又能在边缘定位上保持很高的精度。

The zero-crossings and the maximum of the wacelet transform are very rffective for locating the edges of the image function.In this paper,we investigate the properties of the zero crossing and the maximum related the wavelet transform which are dericed from the first derivative or the second derivative of the smooth function respectively.Multiscale wavelet transform provides a pyramid hierarchie descriptive method of image features.Its main advantages are that both the algorithms involved do not create false generic features and the difference of edges derived from two near scale wavelet transforms is not larger than one pixel.Mallat discrete dyadic wavelet transform has the advantages.In multiscate wavelet transform,if a scale is bigger,the edge contour of image will be derived and the detail information be blurred or lost.If the scale is smaller,the details in inage can be detected,in the same time,finer noise in image will be also kept.The object scale changes in remote sensing image occur over a wide range and vary unpredictably over the image. It is difficult to select an adaptive scale before or in the wavelet transform.Inspired by the scale-space theorem and wide and wavelet transform,the arithmetic of focusing edge in dyadic wacelet transform is introduced as follows. 1)The image function f(x,y)is transformed by 2D Gaussian symmetric wavelet at dyadic scales,and subsets｛W2j f(x,y),0《j《n｝relatef the transform are stored.The edge features in subimage W2nf(x,y)(at scale j=n)are detected by zero-crossings of Gaussian symmetnc wavelet transtorm and the map related to the edge teatures is derived and stored. 2)A sprcial region around the edge related to W2jf(x,y)(j《n) is selected as a searching area.The edge features in subimage W2j-1f(x,y)are detected by zero-crossings of the same transform around searching area and a new efge map is derrved.The former edge map is updated by the new edge map. 3)j=j-1,if j=0 stop,else go to step 2. Experiments show that the arithmetic is effective to solve the problem,in which the object scale in image function is uncertain.The method is not only to eliminate fine scale noise and lovate edge accurately,but also to extract edge contour corrrctly at langer scale.