Image Filtering Based On Partial Differnetial Equations

Limited to the hardware, environment and human factors, images are often suffered from noise in acquisition, transmission or conversion processing, which usually degrades the visual quality of the images. To reduce noise and improve image quality, for better meeting the following image processing and application requirements, image filtering has become an important part of image preprocessing. As the anisotropic diffusion technique can simultaneously eliminate noise and preserve edges, partial differential filtering theory based on anisotropic diffusion has been thoroughly studied and widely used. In this thesis, the anisotropic diffusion model and improved diffusion models in application of image filtering field are investigated. The main work and contributions include the following aspects:1. Based on explaining the basic theory of anisotropic diffusion equation, analyzing its diffusion mechanism and the existing advantages and disadvantages. Meanwhile, the selective anisotropic diffusion equation, robust anisotropic diffusion and fourth-order partial differential equations are introduced. In particular, three kinds of typical error norm of robust anisotropic diffusion: Lorenzian, Huber and Tukey are deeply analyzed. And the performances of the three are compared.2. For the existing diffusion filtering equation mainly consider the diffusion equation itself, and without comprehensive considering the characteristics of the image information. This paper analyzes the characteristics of image local gray variance, an adaptive anisotropic diffusion equation based on image local features is proposed. In addition, the iteration number has a very large impact for filtering effect. If the number is small, the noise reduction is not ideal, whereas the edges detail of the image is lost. Introduced a Q matrix theory, and use it to determine the iteration number of the proposed adaptive anisotropic diffusion equation.3. In low SNR images filtering, the gradient in the original anisotropic diffusion discriminate between edges and noise is not ideal. We can map the input space to a higher order feature space, and then discriminate between edges and noise in the feature space. Based on the careful analysis of kernel anisotropic diffusion, according to Mercer theory, we proposed a composite kernel anisotropic diffusion for image filtering by integrating the global property of linear kernel and the local property of radial basis function (RBF) kernel. The algorithm can solve the strong noise of the image filtering problems.