Image Space Of Gauss Wavelet Transform And Character Image Edge Detection

Wavelet analysis is a newly arisen 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.On one side, based on that the continuous wavelet transform is the foundation of the reproducing kernel function of the image space, for for the Gauss 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. And when fixes the scale factors and translational factors, the paper gives isometry and Inversion formula respectively and further lays a theoretical foundation to the studies of general wavelet transform.On the other hand, in the image edge detection, the bounds of step-structure and dirac-structure are distinguished by using modular-angle-separated wavelet transform and combining with scale-independent algorithm, thus obtaining the bound of the step-structure The threshold value of the peak value is chosen to filter the points at which the wavelet transform coefficients are very small in scale-independent algorithm. However, the singularity of the edge in a image is not uniform, the faintness edge will be filtered with the non-uniform of gray-scale and noise, etc when taking the same threshold from the transformed whole image. To solve this problem, the improved adaptive threshold method is presented and the fixed threshold method is substituted. Good effect is achieved in the edge detection of character image. The algorithm is simple and easy to realize.