The Study Of Wavelet Theory In Image Edge Detection

Image edge detection is an important technology in image pretreatment, being used abroad in the figure drawn out and veins analysed. In this article, the wavelet analysis, the ridgelet analysis and the curvelet analysis are discussed in the image edge detection.Multiresolution analysis is developed from the consonance analysis , it is based on the multiscale decomposition theory, and have time-frequency localization and multiscale decomposition characteristic. It can effectively analyze signal singularities, so the wavelet analysis can detect edges and restrain the noise. It had applied diffusely in the image procession. In the article, by the multiresolution analysis and wavelet analysis, the thrice Battle-Lemarie wavelet filter detects the edge, signal's singularities and edge structure are discussed in detail.Ridgelet transform is based on the conception and method of the neoteric consonance analysis, It developed from the wavelet analysis and group theory. The ridgelet can express the beeline singularities in the 2D or higher dimensions space. So in the great scale beeline detection, This method can get better effect than wavelet. In the article, the theories of radon transform and ridgelet transform are introduced briefly, and applied in the detection of the beeline figure in the image which is polluted by noise. The experiment indicates that: in the detection of large scale beeline, radon transform and ridgelet transform are better than wavelet transform in the noise.The theory of curvelet transform is based on the ridgelet transform, To the curve signal's singularities, the curvelet transform can express them sparsely. The curvelet combines the characters of ridgelet transform which expresses the beeline figure and the characters of wavelet transform which expresses the points figure. It well imposes the original superiority, processing the coefficient of curvelet by threshold , the better result can be gained than the general wavelet. In the article, the theory of curvelet is introduced in detail, and the edge detection is researched elementarily by the curvelet transform, The experiment shows that the curvelet transform is more predominant and more feasible than the wavelet transform in the edge detection.