Based On The Nonlocal Method Research On Image Segmentation And Image Denoising

Image processing based on partial differential equations (PDE) is a new research field full of a number of challenges. There are more advantages than traditional methods in this field, so it has attracted a lot of scholars’attention. In this paper, the main content is to study some related problems of image segmentation, image denoising and related algorithms by using partial differential equations method.Most of models based on PDE always include L1norm result in slow computational speed. They often require strict boundary conditions. Besides, the calculation process is easy to fall into local minimum if initial value is selected improperly, so it is very meaningful to study the numerical algorithms of PDEs. In this paper, some common numerical methods is firstly introduced, then the popular Split-Bregman algorithm whose computational speed is very fast is studied deeply. Meanwhile, the main advantages of this algorithm are analysed.On the basis above, image segmentation is firstly researched. Aiming at CV model, segmentation results between level set method and Split-Bregman method is compared by experiments. Replacing the TV iterm with Non-local TV iterm, the standard CV model is improved based on non-local ideas; then, the local binary fitting model is researched deeply, and a fuzzy kernel model based on fuzzy region competition is proposed according to the ideology of fuzzy clustering algorithm. Combining with the fuzzy kernel model’s characteristics, the traditional Heaviside function is improved and a new weight function is proposed. The improved model includes a fuzzy kernel model and a penalty model, and the Split-Bregman algorithm is applied to solve this model. The experiments show that the improved model proposed in this paper has more accurate segmentation results and faster convergence rate.Finally, image denoising is studied. The classical total variation model is firstly researched, and the Split-Bregman algorithm is applied to solve this model. Some related experimental results show that the Split-Bregman algorithm can accelarate the computation speed effectively. Then the non-local TV model is deeply studied which establishs similarity weighting function by using lots of redundant information in images. This model is solved by using two different fast iterative algorithms include Chambolle and Split-Bregman. As the experimental results indicate, the images processed by this model have a higher PSNR.