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

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