The zero-crossings and the maximum of the wavelet transform are very effective 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 derived from the first derivative or the second derivative of the smooth function respectively. Multiscale wavelet transform provides a pyramid hierarchic 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 multiscale 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 image 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 unpredictable scale changes in remote sensing image as mentioned above

and based on zero crossings of 2D multiscale wavelet transform

the arithmetic of focusing edge in dyadic wavelet transform is introduced as follows. 1) The image function f（x

y）is transformed by 2D Gaussian symmetric wavelet at dyadic scales

and subsets {W 2jf（x

y）

0≤j≤n} related the transform are stored. The edge features in subimage W 2nf（x

y）（at scale j=n） are detected by zero-crossings of Gaussian symmetric wavelet transform and the map related to the edge features is derived and stored. 2) A special region around the edge related to W 2jf（x

y）（j≤n） is selected as a searching area. The edge features in subimage W 2 j-1f（x

y） are detected by zero-crossings of the same transform around searching area and a new edge map is derived. 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 locate edge accurately

but also to extract edge contour correctly at larger scale.