分数阶微分掩模及其滤波器的构造

Construction of Fractional Derivation Masks and Corresponding Filter

基于整数阶微分定义的一阶图像增强模板在处理图像时会产生宽边缘,而二阶模板会同时增强纹理和噪声.为了避免整数阶微分模板所产生的副作用,根据分数阶微积分的Riemann-Liouville定义分析和推导了数字图像的1～2阶分数阶微分掩模,构造了基于该定义的1～2阶分数阶微分滤波器.仿真实验表明,该滤波器不仅可以保留平滑区域的低频轮廓信息,还可以非线性地增强图像中的高频边缘和高频的纹理信息,对于纹理信息的意义相对重要的图像而言,该滤波器具有独特的优势和良好的效果.

Both the one-order and the two-order image enhancement masks based on integral-order calculus are insufficient in image processing because the former may cause wide edges and the latter may enhance the texture and the noise.In order to avoid these side effects,the 1~2-order fractional derivation masks of digital images are analyzed and deduced according to the Riemann-Liouville definition of fractional calculus,and the corresponding filter is constructed.Simulation results indicate that the constructed filter can not only maintain the low-frequency contour information in the smooth region but also nonlinearly enhance the high-frequency edges and the texture information in images,and that it has unique advantage and excellent visual effect for the treatment of images whose texture information is of great importance.