| 引用本文: | 陈永,陶美风,陈锦.块核范数的RPCA分解与熵权类稀疏的壁画修复[J].哈尔滨工业大学学报,2021,53(8):72.DOI:10.11918/202101038 |
| CHEN Yong,TAO Meifeng,CHEN Jin.Mural inpainting based on RPCA decomposition of block nuclear norm and entropy weighted clustering sparse representation[J].Journal of Harbin Institute of Technology,2021,53(8):72.DOI:10.11918/202101038 |
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| 摘要: |
| 针对图像修复过程中,颜色纹理光学属性分离不彻底,以及在稀疏表示图像修复时字典设计单一,导致壁画图像修复结果易出现结构不连贯和模糊效应等问题,提出了一种基于块核范数的鲁棒主成分分析(robust principal component analysis,RPCA)分解与熵权类稀疏的壁画修复方法。首先,采用提出的基于块核范数的RPCA图像分解算法,将壁画图像分解为结构层和纹理层,利用块核范数进行纹理矫正操作,克服了RPCA结构纹理分离不完全的问题。然后,提出熵加权k-means方法对结构层图像进行聚类,构建得到稀疏子类字典,并通过奇异值分解和分裂Bregman迭代优化的类稀疏修复方法,完成结构层图像的重构。最后,利用双三次插值算法实现对纹理层图像的修复,将修复后的结构层和纹理层进行融合,完成破损壁画的修复。通过对真实敦煌壁画数字化修复,实验结果表明,该算法能够有效地保护壁画图像的边缘和纹理等重要特征信息,无论从视觉效果还是从峰值信噪比等定量评价方面,提出的方法修复效果均优于比较算法,且修复执行效率更高。 |
| 关键词: 图像重构 壁画修复 RPCA分解 块核范数 类稀疏表示 |
| DOI：10.11918/202101038 |
| 分类号:TP391.4 |
| 文献标识码:A |
| 基金项目:教育部人文社会科学研究青年基金(19YJC760012)；兰州交通大学天佑创新团队(TY202003)；甘肃省人文社会科学一般项目(20ZC11) |
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| Mural inpainting based on RPCA decomposition of block nuclear norm and entropy weighted clustering sparse representation |
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CHEN Yong1,2,TAO Meifeng1,CHEN Jin1
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(1.School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China; 2.Gansu Provincial Engineering Research Center for Artificial Intelligence and Graphics & Image Processing, Lanzhou 730070, China)
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| Abstract: |
| In the process of image restoration, in order to solve the problems of incomplete separation of color and texture optical properties and single dictionary design in image inpainting of sparse representation, which leads to the structural incoherence and blurring effect of mural image inpainting results, a mural inpainting method based on robust principal component analysis (RPCA) decomposition of block nuclear norm and entropy weighted clustering sparse representation was proposed. First, the proposed RPCA image decomposition algorithm based on block nuclear norm was used to decompose the mural image into a structure layer and a texture layer, and the block nuclear norm was used to perform texture correction operations, which could overcome the problem of incomplete separation of structure and texture by RPCA. Then, the entropy weighted k-means method was proposed to cluster the structure layer image and construct sparse sub-cluster dictionaries, and the reconstruction of the structure layer image was completed by sparse value decomposition and split Bregman iterative optimization method. Finally, the image of texture layer was repaired by using the bicubic interpolation algorithm, and the repaired structure layer and texture layer were fused to complete the repair of the damaged murals. Experimental results of digital restoration on the real Dunhuang murals show that the proposed method could effectively protect the edges, textures, and other important features in the mural image. In terms of visual quality and quantitative evaluation such as peak signal-to-noise ratio (PSNR), the proposed method had better performance than the comparison algorithms, and the restoration efficiency was higher. |
| Key words: image reconstruction mural inpainting RPCA decomposition block nuclear norm clustering sparse representation |
