VARIATIONAL METHOD FOR IMAGE INPAINTING AND ITS IMPLEMENTATION
Qiu Jun1, Hu Xiao2,3, Wang Hanquan4
1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China;
2. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China;
3. The Seventh High School of Panzhihua City, Panzhihua 617005, Sichuan, China;
4. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
Image inpainting is one of the most important part in digital image processing. It aims to fill in missing parts of damaged or degraded images based on the information around. In this paper, we discuss how to do image inpainting with variational methods and how to implement it in computers. We mainly investigate the general way on how to build partial differential equations based on variational methods and how to solve subsequent models. The key idea of variational methods for image inpainting is turning the inpainting problem into a functional minimization problem with constraints. To solve this minimization problem, we first apply the Lagrangian multiplier and solve a free functional minimization problem instead. The solution of the latter one satisfies Euler-Lagrangian equation. We next construct a continuous gradient flow and discretize it with finite difference method in order to find the steady state solution of the gradient flow, which is in fact the solution of related Euler-Lagrangian equation. We finally use the numerical solution as the approximation of inpainted image.
. VARIATIONAL METHOD FOR IMAGE INPAINTING AND ITS IMPLEMENTATION[J]. Journal of Numerical Methods and Computer Applicat, 2016, 37(4): 273-286.
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