Abstract: The fractional differential approach can strengthen and extract textural features of two dimensional digital images; therefore, the digital image feature can be enhanced and extracted more easily. In order to improve the accuracy of image matching，based on fractional differential theory, an improved Scale Invariant Feature Transform (SIFT) matching algorithm was proposed. Combining the Gauss filter with the fractional differential filter to enhance the feature of image, more extrema and keypoints could be detected. Compared with the original SIFT, the simulation results show that the proposed algorithm can detect more key points, and improves the accuracy of image matching.

Key words: fractional differential, image enhancement, Scale Invariant Feature Transform (SIFT) algorithm, image matching, feature keypoint

摘要： 利用分数阶微积分运算处理图像信息，有利于强化和提取图像的纹理细节，使图像得到增强，更有利于对图像特征的提取。为了提高图像匹配的正确性，用基于分数阶微积分图像处理方法，提出了改进的尺度不变特征变换(SIFT)匹配算法，将高斯滤波和分数阶微分滤波相结合,用分数阶微分对图像特征进行强化，检测出更加稳定的尺度空间极值点，然后筛选出更多和更准确的匹配特征点，最后进行图像匹配。实验表明，在SIFT中引入分数阶微积分的应用，能够得到更多的特征关键点，提高图像匹配的正确性。

关键词: 分数阶微分, 图像增强, 尺度不变特征变换算法, 图像匹配, 特征关键点