中文摘要：

灰度图像放大时，插值的平滑作用会退化图像的高频部分，致使放大图像的边缘变得模糊．本文提出了一种基于离散边缘曲线光顺连续性恢复的灰度图像放大算法，算法包括两个步骤，第一步是使用能量优化方法，根据一定的准则从离散的边缘曲线数据恢复出连续而光顺的边缘曲线；第二步是基于这些曲线对图像实施插值计算．使用本文方法得到的放大图像边缘清晰光顺．文中络出了放大实例，实验结果证明了本文方法的有效性．

英文摘要：

When gray images are magnified, the smoothing effect of interpolation may degrade the high frequency components and make edges become blurred. A magnification algorithm for gray images, based on fairing and continuous restoration of edge curves was presented in this paper. Two stages were included in this algorithm ： the first stage was the restoration of continuous and fairness curve from digitized edge data, using energy optimization method, under given rules; the second is to interpolate the image, based on the curve obtained in the last step. Using this algorithm, the edges of the magnified image kept sharp and smooth. Examples were given in this paper, the results showed the validity of this algorithm.