【作者】 谢爱敏；

【导师】 冯象初；

【作者基本信息】 西安电子科技大学 ， 计算数学， 2010， 硕士

【摘要】 数字图像修补问题是图像处理中的一个热点问题,主要是利用一定的数学模型针对有缺损的图像进行修复,或者从图像中去除指定的目标和文字,以达到特定的目的。本文首先介绍图像修补的研究背景、意义,以及现状;重点讨论了对于小块的缺损有良好修补效果的基于偏微分方程(PDE)的修补模型,包括BSCB模型,TV模型,Mumford-Shah-Euler模型和CDD模型;接着详细分析了Split Bregman迭代方法,介绍了两种Split Bregman迭代方法的运用。CDD模型是通过引入曲率项求解高阶偏微分方程来进行图像修补,在求解偏微分方程过程中,大量迭代运算导致修复速度非常缓慢。另一方面,Split Bregman方法具有迭代次数少、运算速度快和适于解决L1正则化问题等特点。本文把Split Bregman方法引入到CDD图像修补模型中,提出了一种基于Split Bregman迭代的CDD图像修补方法,取得了很好的效果。最后,介绍了适合于大块缺损的纹理合成的图像修补方法。重点研究了非参数性采样的纹理合成和基于优先权的纹理合成方法。更多还原

【Abstract】 Digital image inpainting,which is a hot issue in the field of image processing,is mainly used to inpaint damaged images or remove of objects or words in images with some mathematical models to achieve special goals.In this thesis, the background of the research, the significance and the present situation of image inpainting are firstly introduced. Then, we focus on some of PDE-based image inpainting models: BSCB model,TV inpainting, Mumford-Shah-Euler inpainting, CDD model,which have good inpainting effects for those damaged in some small blocks. Thereafter, we analyse Split Bregman method in detail and present its two applications.For using the curvature term in the process of image inpainting with CDD model, a large number of iterations to solve the high order PDEgreatly lowers the speed of inpainting.To speed up the algorithm, a Split Bregman method ,which is operated faster and good for solving L1 regularization problems, is introduced to the CDD model. The experiments show that our new algorithm is much faster and with better vision effects.Finally,this thesis introduces the inpainting models based on texture synthesis,which have good inpainting effect on large damaged blocks. Texture synthesis methods by non-parametric sampling and based on priority are studied respectively.更多还原