Abstract: Image inpainting is an important research branch in image processing. It is aimed to fill in the information for the damaged regions and to restore the integrity of the image by using the information around. There are many applications in protection of cultural relics, restoring aged or damaged photographs and films, text removal, and so on. This paper introduces the term[?up][0<p<1]instead of the total variation in the energy functional and obtains an improved model for Euler’s elastic inpainting model. Accordingly, the staircase effect due to the total variation is reduced effectively. In addition, Peak Signal to Noise Ratio（PSNR） and Structural Similarity index（SSIM） are used to evaluate the image inpainting quantitatively. Experiments and comparisons show that values of PSNR and SSIM acquired by the proposed model are much higher than the other models’. The inpainting effect is improved obviously. Compared with the traditional Euler’s elastic model, the effect of the new model is much better, which is consistent with the needs of human visual psychology.

Key words: image inpainting, calculus of variations, partial differential equations, Euler’s elastic model, numerical simulation

摘要： 数字图像修补技术是数字图像处理领域的一个重要分支，目的是利用待修补区域周围未损坏的信息对图像中的待修补区域进行信息填补，恢复破损图像的完整性，其应用领域主要有文物保护、对旧照片和老电影进行修复、对图像中遮挡文字的移除等。通过将能量泛函中的[?u]改为[?up][0<p<1]对传统的欧拉弹性修补模型进行了改进，克服了弹性项中所包含的全变分容易产生阶梯效应的弊端；采用峰值信噪比和结构相似性指标评定图像的修补效果。实验结果表明，该模型的峰值信噪比和结构相似性均远远大于其他几类已有模型，修补效果得到明显改善。相对于传统的欧拉弹性修补模型，该模型具有更好的修补性能，不仅能够满足人类视觉心理学的需要，而且在客观上得到了有效证实。

关键词: 图像修补, 变分法, 偏微分方程, 欧拉弹性模型, 数值仿真