The Application Of Image Edge Detection Based On The Nonlinear Diffusion Filtering About Topological Gradient

The whole processing of an image is usually divided into several stages:filtering, segmentation, classification and finally recognition. Image filtering is the most important step before the effective analysis about image data. Whether it is successful or not, it will directly affect the following work. Image filtering is not only to remove noises and smoothening, but also to find its meaningful regions or its edges. Classical filtering methods can hardly satisfy the above requirements. The idea the Partial Differential Equations (PDE) been used in image processing can be traced back to the work of Gabor and Jain followed. But the substantial and original achievement in this field should own to the individual effort of Koenderink and Witkin who connected the convolution of original image with Gaussian kernel with solution of PDE. PDE algorithm is a fine method in image analysis and processing and can be used in many aspects, such as noise reduction, image enhancement and segmentation. In this paper, we mainly discuss the nonlinear diffusion filtering of images using the topological gradient approach to edges detection and use the relation between M-S function and numerical solution of partial differential equations, finally get the edge detection image. The outline of the dissertation as follows:In Chapter1, the research background and history and actuality of the nonlinear diffusion filtering of images using the topological gradient approach to edges detection are introduced. The significance and the main contents about the research are presented additionally.In Chapter2, we simply introduce three kinds of diffusion model including linear diffusion model, Perona and Malik model and the Weickert model and point out their advantages and disadvantages.In Chapter3, we derive an asymptotic expansion of the functional Jε inspired by the Mumford-Shah model at its minimum and obtain topological gradient formulation.In Chapter4, based on the Mumford-Shah model and the process to the asymptotic expansion, we define a new functional Jε,k and proof the τ convergence of Jε,k to the functional F In the end, we make conclusions about the whole dissertation and find the following research direction.