二维分数阶泰勒级数算法在边缘检测中应用

Application of two-dimensional fractional order Taylor series algorithm in edge detection

为避免传统的整数阶微分算子存在边缘出现断点、边缘细节信息泄露等问题,提出构建基于二维分数阶泰勒级数权矩阵滤波的Sobel算子。推广整数阶边缘检测模型,将分数阶微分的维数扩至二维;对分数阶微分的阶次进行选择,构建基于二维分数阶泰勒级数权矩阵;以分数阶权矩阵为基础,对整数阶Sobel算子进行分数阶滤波,设计分数阶权矩阵滤波器,检测图像边缘。实验结果表明,对细节信息较多的图像边缘得到有效提取,能够检测出更多的边缘细节。该算法能有效提取细节信息较多的图像边缘信息,获得满意的边缘检测效果。

The traditional integer order differential operator has the problems of edge break point and edge detailed information leaking,so the Sobel operator based on the two-dimensional fractional order Taylor series weighted matrix filter was proposed.The integer order variational edge extraction optical flow models were generalized,and the dimension of the fractional differential was expanded to two dimensions.The order of fractional order differential was chosen,and a two-dimensional fractional order Taylor series weight matrix was constructed.The fractional order weighted matrix filter was designed to detect the edge of the image based on the fractional weight matrices and the integer order Sobel operator was fractionaled filterly.Experimental results show that the image edges with more detailed information were extracted effectively and more edge details were detected.The algorithm can effectively extract the image edge information with more details and obtain the satisfactory edge detection effect.