基于分形的数字图像修补算法

A new image inpainting algorithm based on fractal theory

针对传统图像修复方法中搜索范围局限于待修复图像源区域的问题,提出了一种新的基于分形的数字图像修复算法,首次将分形理论应用于图像修复领域,利用图像的自仿射性(或自相似性)对破损图像进行修复。首先,在图像的源区域中选取定义域块,经仿射变换后建立码本;然后,从码本中查找待修复块的最佳匹配块,同时为了加快查找速度,降低计算复杂度,采用了基于方差和内积的快速搜索算法来提高修复效率;最后,用查找得到的最佳匹配块对待修复块进行填补。提出了一种改进的优先值计算方法,在计算优先值时加大置信度的比重,从而可以加强搜索匹配过程中的约束,使得修复过程总体按照"剥洋葱"的顺序进行,同时兼顾线性结构的延伸。实验结果证明,与传统修复方法相比,本算法不仅提高了修复质量,同时也提高了修复效率。

Aiming at solving the problem in the traditional inpainting methods of which the searching scope is confined to the source region of the damaged image,a novel image inpainting algorithm based on fractal theory is proposed in this paper.For the first time the fractal theory is applied to the area of the image inpainting by utilizing self-affinity（or self-similarity） to restore the damaged image.Firstly,a codebook is built up with a set of domain blocks which are obtained after affine transform on the blocks in the source region.Then,the best-match block is chosen from the codebook,and in order to reduce the computational complexity and improve the inpainting efficiency,a fast searching technique based on variance and inner product is creatively utilized in this step.Lastly,the best-match block is used to restore the block to be inpainted.In addition,an improved method of calculating the priority value is proposed in this paper,which raises the proportion of the confidence term in order to strengthen the constraint during searching and to make the filling process proceed by the order of ＂onion-peel＂ and linear structures propagate into the target region simultaneously.The results show that this algorithm not only improves the inpainting quality,but also raises the inpainting efficiency compared with traditional inpainting methods.