MULTIGRID METHOD FOR A MODIFIED CURVATURE DRIVEN DIFFUSION MODEL FOR IMAGE INPAINTING

• 来源期刊: 计算数学(英文版)
• 关键词: Image inpainting Variational models Regularization Multilevel methods
• 年，卷（期）: 2008,（6）
• 页码范围: 856-875
• 页数: 20页
• 语种: 英文

摘要

Digital inpainting is a fundamental problem in image processing and many variational models for this problem have appeared recently in the literature. Among them are the very successfully Total Variation (TV) model [11] designed for local inpainting and its improved version for large scale inpainting: the Curvature-Driven Diffusion (CDD) model [10]. For the above two models, their associated Euler Lagrange equations are highly nonlinear par-tial differential equations. For the TV model there exists a relatively fast and easy to implement fixed point method, so adapting the multigrid method of [24] to here is immedi-ate. For the CDD model however, so far only the well known but usually very slow explicit time marching method has been reported and we explain why the implementation of a fixed point method for the CDD model is not straightforward. Consequently the multigrid method as in [Savage and Chen, Int. J. Comput. Math., 82 (2005), pp. 1001-1015] will not work here. This fact represents a strong limitation to the range of applications of this model since usually fast solutions are expected. In this paper, we introduce a modification designed to enable a fixed point method to work and to preserve the features of the orig-inal CDD model. As a result, a fast and efficient multigrid method is developed for the modified model. Numerical experiments are presented to show the very good performance of the fast algorithm.