基于丰度反演及光谱变换的书画霉斑虚拟修复

古书画在保存过程中容易滋生霉斑病害，霉斑不仅影响书画的外观，还会对纸质文物造成不可逆转的永久性破坏。为了给霉斑清洗提供直观参考，提出基于丰度反演及光谱变换的书画霉斑提取与虚拟修复方法。选取与霉斑区域光谱曲线存在明显差异的450～600 nm之间244个波段作为特征波段，通过连续最大角凸锥端元提取与灰度分割，提取霉斑区域。再对高光谱影像进行主成分变换，选取包含信息量最大的前三主成分合成影像，利用Criminisi算法对霉斑区域进行修复，再将修复后的影像进行主成分逆变换，完成高光谱影像的虚拟修复。以中国近现代画家倪田的《捕鱼图》为例进行了研究，发现修复后的霉斑区域与画体融入性较好，边界自然平滑，均方根误差值普遍变小。研究结果可为书画霉斑清洗提供直观的修复依据，具有较强的实用性。

Virtual restoration of mildew stains on calligraphy and paintings based on abundance inversion and spectral transformation

During the preservation process of ancient calligraphy and paintings, mildew spots are easy to breed mildew stains not only affect the appearances of works, but also cause irreversible and permanent damage to paper cultural relics. In order to provide an intuitive reference for the cleaning of mildew stains on calligraphy and paintings, we proposed a method of stained area extraction and virtual restoration based on hyperspectral imaging. The 244 bands between 450~600 nm significantly different from the stained area spectral curve were selected as the characteristic bands, which were used to extract the stained area by the sequential maximum angle convex cone and gray-scale segmentation algorithm. Next, the hyperspectral image was transformed by the principal component analysis. The first three principal components were selected to synthesize a pseudo color image, which was restored virtually by typical algorithm of Criminisi. Then, inverse principal component transformation was performed on the restored image to complete the virtual restoration of the hyperspectral image. Taking a painting by Ni Tian as an example, we found that the restored stained area was better integrated with the painting body, the boundary was naturally smooth, and the root mean square error value generally became smaller. The research results could provide an intuitive restoration basis for the cleaning of mildew stains on calligraphy and paintings, and have strong practicability.