Image segmentation variational method is good at processing the images with blurry and complicated contours, which is useful in quality identification of pathologic picture of onion. An adaptive Shannon wavelet precise integration method (WPIM) on digital image segmentation was proposed based on the image processing variational model to improve the processing speed and eliminate the artifacts of the images. First, taking full advantage of the interpolation property of the Shannon wavelet function, a multiscale Shannon wavelet interpolation scheme was constructed based on the homotopy perturbation method (HPM). The image pixels of the Burkholderia cepacia (ex-Burkholder) infected onions were taken as the collocation points of the WPIM. Then, with this scheme, the image segmentation model (C-V model) can be discretized into a system of nonlinear ODEs and solved by the half-analytical scheme combining the HPM and the precision integration method. At last, the numerical precision and efficiency of WPIM were discussed and compared with other common segmentation methods such as OSTU method and Sobel operator. The results show that the contour curve of the segmentation object obtained by the new method has many excellent properties such as closed and clear topological structure and the artifacts can be eliminated.
A Highly Efficient Shannon Wavelet Inverse Fourier Technique for Pricing European Options
