一种新的分数阶微分的图像边缘检测算子  

New fractional order differential based image edge detection operator

作　　者：王斌[1] 蒲亦非[2] 周激流[2] 

机构地区：[1]四川大学电子信息学院,成都610064 [2]四川大学计算机学院,成都610064

出　　处：《计算机应用研究》2012年第8期3160-3162,3184,共4页Application Research of Computers

基　　金：国家自然科学基金资助项目(60972131);国家教育部回国人员科研启动基金资助项目(20111139);四川省科技支撑计划基金资助项目(2011GZ0201);四川大学计算机学院杰出青年教师基金资助项目

摘　　要：为了提取出更加精确和细微的边缘信息,同时为了具有更好的抗噪性能,提出了一种新的分数阶微分梯度算子。根据Riemann-Liouville分数阶微积分定义,推导出了非整数步长的分数阶微分方程,并采用拉格朗日插值方法确定非整数步长像素点的灰度值,进而构造出八个方向的微分掩模,实现了图像边缘检测。实验表明,该方法更好地利用了图像的自相关性,比传统的边缘检测算子能更好地提取图像边缘细节,且对噪声具有更好的鲁棒性。To extract more accurate and subtle edge information, and also to obtain better anti-noise capability, this paper proposed a new fractional order differential based image edge detection operator. It derived the fractional order differential equation based on non-integer step according to the Riemann-Liouville definition, and used the method of Lagrange interpolation polynomial to get the gray value of non-integer step pixel. It constructed eight directions fractional order differential mask to realize image edge detection. The experimental results show that this method used more advantage of image autocorrelation so it can extract more detail edge information than the classic method of edge detection, also it has a better anti-noise capability.

关 键 词：边缘检测 非整数步长 Riemann-Liouville分数阶微分 拉格朗日插值 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]