An Image Zooming Method Based On Partial Differential Equations

The use of PDEs in image processing is a new research topic. Its mathematical model can represent image accurately and can solve many complicated problems. On the other hand image processing has been concerned extensively. Compared with other approaches, variational PDEs method has remarkable advantages in both theory and computation, and it can profoundly benefit from the existing wealth of literature on numerical analysis on PDEsImage zooming is one of the essential topics in image processing. In this paper mainly we study the image zooming by using of PDEs method.At present we have found many works on the application in image enlarging of PDEs model by virtue of isotropic diffusion. Because of the property of the model, the image enlarged could not keep the detail information and the edge. However, as we iterate move, some important message deviate from the image after amplifying, it will make the image fuzzy.This paper has put forward the idea of predict-correct and derives a new kind of algorithm on image zooming. According to the physical meaning of PDEs, it regards the gray level of the image as the temperature of a plane object, takes some kind of interpolation results of original image as the initial value of the anisotropic diffusion equation, then solves the equation by way of numerical method and then takes the solution as the prediction value. To replace the pixel value by the original image at the pixel corresponding to the original image. We obtain an new image, which would be considered as the corrector. Then it will amplify the image by using of the method regarding the corrector value as the initial value after keeping the edge, detail of an image and keeping the stability in a long time. That is to say, how much time does this algorithm iterate, it can amplify the image after keeping some information of an image and can't be fuzzy still.Furthermore we have carried out the experiments, the results show that this method can keep the edges, details and the algorithm is stability.