Partial Differential Equations-based Image Repair

Digital image inpainting is an important part of image processing. With the development of computer technology, image Processing has been more and More popular in the last two decades. There are three kinds of basic research methods, Which are based on probability and statistics, wavelets and PDEs respectively. Image Processing based on PDEs has achieved great development in the last two decades, because of its strong adaptability, the anisotropy diffusion characteristic and the property of keeping the edge and texture details simultaneously. Its research areas include: image segmentation, image denoising , deblurring , image decomposition , image inpainting and Image reconstruction et al. This thesis focuses on the study of image inpainting based on PDEs and their applications. The main contributions include the following aspects. Firstly, we studied several previous inpainting methods. focus on Curvature-Driven Diffusions model (CDD) and Total Variation model(TV), we carry out research on the advantages and disadvantages about these image inpainting models. Secondly, we proposed an fast inpainting method based on the tensor diffuse model. It is two to three orders of magnitude faster than TV model while producing comparable results. Thirdly, against the traditional variational model beyond repair patch flow-like images of linear structures, we developed a novel method for flow-like images of linear structures based on the tensor diffuse. Through the introduction of local structures direction, we set up new inpainting model at local coordinate system, the diffuse along coherence direction to repair the fracture characteristics.In conclusion, we studied the digital image inpainting techniques and achieved some valuable results. However, digital image inpainting is still a potential research field which is worthy of further study.