Image Processing Based On Partial Differential Equations

Image processing is an interdisciplinary topic , which is connected to photology ,electronics, mathematics, imaging and computer techniques. There are lots of important applications about image processing in many scientific areas and engineering fields. In the current stage, image processing approaches can be divided mainly into three classes, i.e, stochastic modeling, wavelets theory, and partial differential equations (PDEs). It is a new research field to use partial differential equations in image processing .In this field, there are a number of theoretical and practical questions that waited to be studied and solved. Many of the PDEs have been used in image processing and computer vision .And it has attracted a lot of mathematicians' attention. The main advantages of image processing based on PDE can obtain better image quality and a certain stability. Flexible and diverse Numerical program is helpful to image processing. In this paper, we mainly do image processing with PDEs. As we know the work of Perona and Malik on anisotropic diffusion has been one of the most influential papers in the area .They proposed replacing Gaussian smoothing, equivalent to isotropic diffusion by means of the heat flow ,with a selective diffusion that preserves edges .Their work opened many theoretical and practical questions that continue to occupy the PDE image processing community .This is the basis of our work..In this paper, we mainly discuss image fusion and image denoising. We inevitably bring to the noise. As we know, it is mainly because of the random pulse transmission, optical instruments, atmospheric attenuation, weather, the reasons for the observed moment, and so. This paper proposes a new method for fused image. We will combine image fusion and image denoising .the Numerical program of partial differential equations is so flexible and diverse that it will make full use in the image denoising .then we do image defusion after or before denoising. As a comparison, the new method of this paper has a good effect .For the second part, we also made a new fusion method to rich texture images. The image is decomposed into texture and structure parts .Then we use Laplacian operator in the structure of image and use the largest variance method in the texture of the image .Then we get the composite image by fused images A and B.