基于法矢量雅可比的总广义变差图像修复模型

A Total Generalized Variation Model for Image Inpainting Using the Jacobian of Normal

图像修复是图像处理领域的基础问题,变分方法是实现图像修复的主要方法之一。经典的一阶变分模型存在阶梯效应,不能有效修复大破损区域。二阶变分模型为克服上述问题做出了改进,但修复后的图像会出现破损区域对比度降低、边界模糊现象。以经典二阶总广义变差模型(Total Generalized Variation,TGV)为基础,提出了一种基于法矢量雅可比的总广义变差模型(Total Generalized Variation Model with Jacobian of Normal,TGVJN)以修复更多破损图像区域信息。该模型通过引入一系列辅助变量、拉格朗日乘子和惩罚参数设计相应的交替方向乘子算法。实验结果表明,本文模型在保持对比度和边缘方面有明显优势,同时能够有效修复大尺度破损图像,缩小边界模糊区域。

Image inpainting is a basic problem in the field of computer vision and image processing,which is to repair the lost or damaged areas with the existing information in the original image.The smoothing feature of the first-order variational model is remarkable,but the staircase effect occurs during the process of inpainting.Variational models with second-order regularizers make efforts on overcoming these problems,but the contrast of the damaged area is reduced and the boundary is fuzzy after inpainting.Based on the classical second-order Total Generalized Variation model,a Total Generalized Variation model using Jacobian of Normal(TGVJN)is proposed to restore more image information.The proposed model introduces Auxiliary variables,Lagrangian multipliers and penalty parameters to design the corresponding Alternating Direction Method of Multipliers(ADMM).Experiment results demonstrate that the proposed model has superior advantages in edge and contrast preserving,and repairs the large-scale damaged image effectively as well as reduces the fuzzy boundary region.