Several Image Processing Methods Based On PDE And Numerical Solution

Image processing is the basis of computer vision, and is also an important component of image understanding. Along with the improving and popularization of electron and computer technique, especially the vigorous development of computer multimedia and information technique, digital image processing has come into nearly every field including people's normal life. Image processing technique has been widely used in science engineering, such as vision communication, robot guiding, medical diagnosis, remote sensing and chronometer observation, etc.Among all the methods of image processing, nonlinear method, especially image processing based on PDE, for one thing, it attracts too much attention because of its better veracity compared to linear processing method, for another, this method could also deal with some feature on image like gradient and geometrical curvature directly, which is easy for flexible describing with various mathematical models, therefore, it has become an important method in image processing in present.However, comparing to traditional linear method, main problem of PDE method is large quantity of computation, and slow computation speed. In this paper, based on completely summarizing the classical models based on PDE and their numerical algorithm, aiming at some factors that restrict the computation speed in the level set segmentation model based on PDE, such as unitary level set initial method, unsuitability between local fast algorithm and global model, improve the level set segmentation, present a fast level set segmentation based on multigrid and adaptive initial signed distance function. Define signed distance function by signed distance between image surface and threshold surface. This method makes the definition of signed distance function related to image, by which make it could choose shape adaptively, and makes attribute to decrease iteration time and accelerate computation speed; Synchronously, multigrid is introduced to decrease the quantity of computation by relax algorithm; Finally, combined with global segmentation model based on Mumford-Shah model, which make the new model not only as universal as origin global model but also have less computation cost. Numerical experiment has been used to prove the validity of the new model.