Abstract: The irreversible risk of the digital inpainting work of Tang dynasty tomb murals is greatly reduced. According to the thought of inpainting the whole cartoon first and then the local texture in artificial inpainting of Tang dynasty tomb murals, this paper proposes a new method based on morphological component analysis (MCA) for the inpainting of Tang dynasty tomb murals. Firstly, according to the characteristics of Tang dynasty tomb murals, the improved MCA method has been used to decompose the image into two parts: cartoon part and texture part; then, according to the complexity and degree of texture and cartoon, the simplified total variation (TV) algorithm and the K-singular value decomposition (K-SVD) algorithm are used to inpaint the image. The experimental results show that the algorithm can take into account the effect of the texture and structure, and improve the inpainting accuracy of the cracks in the Tang dynasty tomb murals.

Key words: Tang dynasty tomb murals, morphological component analysis (MCA), image inpainting, total variation (TV) algorithm, K-singular value decomposition (K-SVD)

摘要： 壁画数字化修复工作极大降低了手工修复时带来的不可逆的风险。根据唐墓室壁画人工修复时先整体结构、后局部纹理的思路，提出一种基于形态学成分分析（morphological component analysis，MCA）分解的唐墓室壁画修复算法。首先结合唐墓室壁画的特点，采用改进的MCA方法进行图像分解，得到结构部分和纹理部分；然后根据图像分解后纹理和结构的复杂程度与稀疏程度，分别采用简化的全变分（total variation，TV）算法和K奇异值分解（K-singular value decomposition，K-SVD）算法进行修复。实验结果表明，该算法可兼顾纹理与结构的修复效果，唐墓室壁画中的裂缝现象的破损修复精度得到提高。

关键词: 唐代墓室壁画, 形态学成分分析（MCA）, 图像修复, 全变分（TV）算法, K奇异值分解（K-SVD）