Method Of Partial Differential Equations-based Image To Enlarge

The technology to get a larger size of the image by using a smaller one is what we called Digital Image Magnification. As the rapid progress of computer technology, Digital Image Magnification has become an important component of Image Processing, It has wide applications in the domain of industry, iatrology, avigation and military affairs. It plays a predominant role in social and economic development.In this thesis, we analyzed the common methods of the Digital Image Magnification. There are usually two steps in these methods: Interpolation and Post-processing. First, we discussed the current work of Interpolation and the theories of several interpolation methods. Then we summarized the artifacts introduced into the interpolated images: the blurred and jagged contours. After that we studied several Post-processing models based on PDE of Anisotropic Diffusion, including Directional Diffusion and Self-Snake model. Results show that they have good effect in smoothing the contours. But the effects of Post-processing are still subject to the restrictions of the Interpolation.Based on the above analysis, we deeply studied another Image Magnification method: Total Variation model, which is propounded by T. Chen et al. This method transformed Image Magnification into Image Inpainting. Results show that it can maintain the sharpness and the fairing of the contours without any Post-processing measures. This is the outstanding features of this method.At the end of this thesis, we extend the TV model to the magnification of color images. We suggested to adopt Chromaticity - Brightness TV model. In this model, color images are represented as two images: Chromaticity and Brightness. To magnify the chromaticity part, we used Non_Flat Images TV Model. But to the Brightness part, we used the ordinary TV model. We found out that the results of this method is better than magnify the three component of color image independently. It can be proved to be a simple and effective way of Color Image Magnification.