Research On Image Processing Based On Anisotropic Diffusion Equations

Image processing has a wide range of applications in many important fields such as medical image processing, military target recognition, fingerprint automatic processing and aviation satellite images of the machine processing. As we know, image processing such as image denoising, image decomposition and image segmentation are the foundation of image analysis, and a better result of image processing often leads to a better result of image analysis. Therefore, the research on the image denoising, image decomposition and image segmentation has important practical significance and application value.Since 1990 s, image processing methods based on partial differential equation(PDE)have obtained a rapid development. As an important kind of partial differential equation,diffusion equations are widely used in image processing. The diffusion models often establish diffusion equations by combining the mechanism of diffusion and quantified image feature. By using partial differential equation based image processing methods,we propose a series of models based on nonlinear anisotropic diffusion equations to deal with image denoising, image decomposition and image segmentation. The main work is as follows:Firstly, based on characters of different noise types, we propose a new hybrid anisotropic diffusion equation model to deal with. The new model behaves like anisotropic diffusion to preserve little structures near the edges of image, and the new model behaves like isotropic diffusion to remove noise in interior regions. We prove the existence and uniqueness of the solution of the model by using fixed point theorem, and some properties such as long time behavior. In numerical aspects, the new model can be effciently implemented not only by the PMS scheme, but also by the AOS scheme. The experimental results show the new model can preserve edges in nonhomogeneous regions while it removes noise in homogeneous regions of image.Then we propose a two–phase image segmentation algorithm based on the forward and backward diffusion equation and discrete gray level set. In the first phase, we propose a nonconvex functional model to denoise the original image to obtain a smoothed version and more prominent image boundaries. In the second phase, a new functional based on gray level sets is firstly proposed, and then the associated discrete model based on the discrete gray level sets is discussed, which deduces the new segmentation algorithm to obtain the segmentation results. We calculate the energy directly on discrete gray level sets rather than solving a partial differential equations, which promotes effciency of the algorithm and deduces the complexity of our algorithm to O(N)(N is the number of pixels). The obtained numerical results of segmentation clearly outperform CV methods and provides significant effciency improvement when dealing with large-scale images.Finally, we propose an image decomposition model based on a system of degenerate and singular parabolic equations, which allows us to decompose the texture part from a large domain. The new equations consist of two diffusion equations with different diffusion terms(a p-Laplace term and a Total Variation term). As it possesses degeneracy and singularity, we need to regularize this system to discuss its properties. We define the entropy solutions to the system and prove the existence and uniqueness by regularization and some estimates. The numerical results illustrate that the new model has the ability to decompose the image into small scale texture information and large geometric scale image contour information, and obtain better decomposition results compared to TV model.