Abstract: Starting from the enhanced ability of fractional differential to image details, the paper analyzes the mechanism of fractional differential, then constructs an approximate sixteen directions fractional differential template according to vector synthesis theorem and fractional differential difference function deduced by fractional calculus G-L definition, and uses the template to enhance retinal vascular image. The experimental results show, in response to those retinal vascular images which have rich textural detail information, fractional differential outperforms integral differential operation to extract the textural detail information in smooth region without too much gray scale change.

Key words: fractional differential, image enhancement, retinal vascular, vector synthesis, cover module

摘要： 从分数阶微分对图像纹理细节的增强能力出发，对分数阶微分的机理进行分析，根据分数阶微积分的G-L定义推导出的差分公式与向量合成定理构建了近似的16方向分数阶微分模板，并将其应用于视网膜血管图像增强中。实验结果表明，对于纹理细节信息丰富的视网膜血管图像而言，分数阶微分对灰度变化不大的平坦区域中的纹理细节信息的提取效果明显优于整数阶微分运算。

关键词: 分数阶微分, 图像增强, 视网膜血管, 向量合成, 掩模模板