Bound Of Step-Structure Edge Detection Of MAS Wavelet Transform Approach

Wavelet analysis is a newly arised subject that develops gradually on the basis of the wavelet transform. It is not only of the profound theoretical significance, but also of the extensive applications. Because wavelet transform is the basis of the wavelet analysis, discussing wavelet transform deeply is of theoretical significance and practical value. Wavelet analysis is the local transform of time and frequency. It is now widely used in the signal processing. Along with the improvement of wavelet theory, its application becomes more and more extensive. This thesis conducts the discussion both in theoretical and practical perspectives.In theoretical perspectives, based on that the continuous wavelet transform is the foundation of the reproducing kernel function of the image space, for the Cgau wavelet which is often used in edge detection and is of a good performance, this thesis gives the concrete forms of reproducing kernel function of wavelet transform image space. When the scale factors are fixed,we give some properties in the wavelet transform image space of Cgau,and further we give a theoretical foundation to the studies of general wavelet transform.In practical perspectives, based on the modular-angle-separated wavelet transform algorithm and the Canny algorithm, to solve the problem which modular-angle-separated wavelet transform doesn't solve well with the connection of edge and Canny algorithm is easy to obtain noise. A new edge detection method by using fusion technique is given in this paper.The method could well combine Canny algorithm with MAS wavelet transform. Good effect is achieved in the image edge detection of the bound of step-structure.The algorithm is simple and easy to implement. It used to remove weak edge by the method of threshold values in the process of edge detection , big and singular edge are reserved. Using double-threshold values, we could get more good effect. But double-threshold values method doesn't solve well how to get more valueable edge and how to delete noise, in order to reduce noise, some weak but long edge may be deleted if we can't obtain proper threshold value.To solve this problem, A new edge detection method based on the double-threshold values is given in this paper. It use the length of edge, good effect is achieved in the image edge detection.