Abstract: Generally, fractional differential mask doesn’t have flexibility, because it is not filtered with the changes of images’ local information, once it is decided. To remedy the limitations of fractional differential mask, this paper puts forward one way of the enhancement of fractional differential image based on the local feature. The relation between Laplace mask and fractional differential mask based on the 3×3 symmetric fractional differential masks is found out. The fractional differential mask is obtained using the weighted Laplace mask. Based on the relation between local mean and standard deviation, a new method of image enhancement is obtained by improving weighted Laplace mask. This method can execute filter according to the local image feature. It is called as the local feature based image enhancement of fractional differential. Compared with other image enhancement algorithms, the experiments show that the visual results of the way of the enhancement of fractional differential image based on the local feature are the best.

Key words: fractional differential, image enhancement, Laplace mask, mean value, standard deviation

摘要： 一般情况下分数阶微分模板一经确定，再用其进行滤波时并不随图像的局部信息而变化，它不具有灵活性。针对分数阶微分模板滤波的这种局限性，提出了一种基于局部特征的分数阶微分图像增强的方法。在3×3对称分数阶微分模板的基础上找出与拉普拉斯模板的关系，从而得到加权的拉普拉斯模板表示的分数阶微分模板；根据图像的局部均值与标准差的关系对加权的拉普拉斯模板进一步改进，得到基于局部特征的分数阶微分图像增强的方法，它使分数阶图像增强模板能够根据局部特征灵活地进行滤波。将其与其他的图像增强算法比较，实验证明基于局部特征的分数阶微分图像增强算法能获得更好效果。

关键词: 分数阶微分, 图像增强, 拉普拉斯模板, 均值, 标准差