ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
374 
A TROUS WAVELET DECOMPOSITION APPLIED TO DETECTING IMAGE EDGE 
Xiaodong ZHANG 1 Deren LI 1 
(National Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan 
University, 129 Luoyu Road, Wuhan, China 
E_mail: xdzhanq@hpQ1 wtusm.edu.cn) 
Key words: Wavelet decomposition ; Detecting image edge ; A trous wavelet decomposition 
ABSTRACT 
An image edge can be defined as a difference of image features in a local image region, its appearance is like as a mutation of 
different image gray-level or texture structures or image colors. Image edges are very important to human being and in computer 
machine vision field, because the image edges can transfer the most information of an image. Detecting image edge is considered 
as a key step in many complicated processing methods such as image segmentation, image recognition, and feature extraction. 
Detecting edge is an unsolved problem in the image process field. Hitherto, many methods of detecting image edges have been 
developed, but almost every method has its restriction in application of image processing. In this paper, disadvantages and 
advantages of some classic methods for image edge detection are thoroughly discussed. Base on the analysis of the classic 
methods, a new a trous wavelet decomposition algorithm is applied to detecting image edge in the paper, characteristics of the 
algorithm are discussed in detail. The £ trous decomposition is one of discrete wavelet transform algorithms, from the a trous wavelet 
decomposition theory a detecting image edge method is derived. According to the a trous wavelet decomposition theory, an image 
can be decomposed into some wavelet planes of increasing scales, and the wavelet planes have the same number of pixels as the 
original image. That is very important to some applications, for example image fusion and image classification. Therefore, an 
algorithm of detecting image edge is derived from the a trous wavelet decomposition. The algorithm is suitable for computer program, 
and can execute efficiently. We use the method, classic Sobel, and Robert algorithms to process one SPOT image. From the 
process results, we can find that the main edges detected by our a trous wavelet decomposition method are better than those 
processed by classic Sobel, and Robert methods. We also note that the new algorithm of detecting image edge can gain more tiny 
fine edge information than the other two classic methods. In addition, when the original image is stained by noise, the detecting 
image edge algorithm developed on the a trous wavelet decomposition almost is not disturbed, on the contrary, the classic Sobel, 
and Robert algorithms are sensitive to noise. 
In order to test robust and flexibility, in practice, we also have employed the algorithm of detecting image edge developed in this 
paper to produce a binary image. The experiment results are shown the algorithm is satisfactory. Therefore, we think that the 
algorithm is super to the other two traditional methods in many aspects, especially when it is applied to those original images which 
are stained by noise. 
However, besides the advantages of the new method of detecting image edge, we also find out some shortcomings, for example the 
contrast of result image is weaker, so that the detected image edges is not more evident, etc. Those disadvantages need to further 
research for improving the result. 
1. Introduction 
Image edge can be defined as the difference of image 
features in a local region. Its appearance is the mutation of 
image gray or texture structure or color. The image edge is 
very important to both human being and machine vision 
because it can describe the shape of a region, define local 
feature and convey most information in an image. Detecting 
image edges is considered as a key step in many 
complicated processing methods such as image 
segmentation, image recognition and feature extraction. 
There are some classic operators which are used to detect 
image edges, like gradient, Laplace, LOG, Sobel, Prewitt and 
Robert operators etc. Gradient operator looks like a high 
pass filter, but it only sharps image edges. Some 
experiments have proved that the methods based on the 
difference are not effective to detect complicated image 
edges; The Sobel method is a weighted average operator, it 
contributes weight to the center pixel in order to enhance the 
edges; Robert operator is sensitive to noise, therefore it is 
seldom used it in the dense point region; The Laplace