Riemann-Liouville分数阶图像增强算法及其电路实现

为了解决整数阶微分对图像纹理增强效果不明显及Grümwald-Letnikov（G-L）微分后会使RGB彩色图像边缘色彩失真的问题，提出了一种Riemann-Liouville（R-L）分数阶图像增强算法并讨论了该算法的电路实现.从R-L定义出发，推导出分数阶微分方程，构造了数字图像8个方向上的0~1阶分数阶微分模板并讨论了其数值运算规则，在此基础上构造并实现了数字图像的R-L分数阶微分电路，并在HSI空间对I分量进行分数阶微分实现彩色图像增强.实验结果表明，该算法能比较明显地增强图像的纹理和边缘细节，增强后的图像清晰度和对比度提高，图像视觉效果明显，具有非线性增强灰度图像和彩色图像的复杂纹理特征及边缘信息的独特优势和良好效果.

Riemann-Liouville fractional-order image enhancement algorithm and its circuit realization

In order to solve the problem that the integer-order differential has no obvious enhancement effect on image texture and the edge color distortion of RGB color images occurs after Grümwald-Letnikov(G-L) differential,a Riemann-Liouville(R-L) fractional-order image enhancment algorithm was proposed and its circuit realization was discussed.A R-L fractional-order differential equation was derived based on the R-L definition.The 0 to 1 order fractional-order differential template of digital image in eight directions was configurated,and its numerical operation rules were discussed.And thus,the R-L fractional differential circuit for digital image was established and realized.In addition,the fractional-order differential for the I componenet was conducted in HSI space to realize the enhacement of color image.The experimental results show that the proposed algorithm can enhance the image texture and edge details significantly,and the definition and contrast of the images after enhancement are improved.The images after enhancement show the obvious visual effect,exhibit the complex texture characteristics of both non-linear enhanced gray and color images,and have the unique advantage and good effect of edge information.