The Construction Of Dyadic Wavelet And Its Edge Detection Algorithm

The edge detection plays an important role in image processing.It is widely used in many aspects of production and life,such as fault detection of mechanical components,medical image analysis and pattern recognition.However,the image is very easy to be interfered by noise in the process of acquisition and storage,which makes the edge lines unclear,discontinuous or incorrect when extracting the edge of the noisy image.The result is that the accuracy of image edge detection is greatly reduced.Therefore,in the current research of image edge detection,how to consider both the de-noising ability of edge detection algorithm and the quality of edge extraction is a hot research content.Considering the advantages of dyadic wavelet and mathematical morphology in image processing,this paper mainly studies two image edge detection algorithms which combine two different properties of dyadic wavelet and mathematical morphology.The specific research is as follows:Firstly,a dyadic wavelet with non orthogonality,symmetry,finite frequency spectrum and almost everywhere smooth is constructed by Shannon function.Then,the related properties of the dyadic wavelet are discussed,and the integral expression and inversion formula of the dyadic wavelet are given.A new nonlinear threshold function is constructed by using the dyadic wavelet function and applied to image denoising.The new threshold function is more effective in the process of image noise removal.Next,from the two aspects of structural elements and morphological operation properties,the morphological edge detection algorithm is analyzed and improved,and then a edge extraction algorithm is obtained by combining mathematical morphology theory with threshold function de-noising.Compared with the single morphological edge detection,the edge of the image extracted by the new edge detection algorithm based on the fusion of the two algorithms has a great improvement,not only the image edge detected is more clear and less noise,but also the continuity of the edge lines and the accuracy of the position have a better improvement.Secondly,by analyzing the existing dyadic lifting scheme and combining withthe condition of vanishing moment,a new lifting scheme is proposed to improve the order of vanishing moment of dyadic wavelet filter.Based on the B-spline dyadic wavelet filter,a new dyadic wavelet filter is realized by using the new lifting scheme proposed in this paper,which has 4 order vanishing moment,tight support and symmetry.The simulation results show that when the order of vanishing moment of the filter increases gradually,the effect of edge detection of dyadic wavelet image is improved,but there is still noise.Considering that various morphological operations can effectively remove noise,the improved mathematical morphological edge detection operator is combined with the dyadic wavelet filter with high-order vanishing moment to achieve a more significant edge detection,which also provides a new way for image processing.