一种基于分数阶导数的边缘检测算法

New approach for edge detection based on fractional derivative

传统的边缘检测算法多采用整数阶的一阶或二阶微分算子锐化,通过求取图像的一阶导数局部极大值或二阶导数过零点得到边缘点。本文将基于分数阶导数的边缘检测算子应用于图像边缘检测中,通过对含噪图像g(x)采用合适尺度函数的高斯滤波函数h(x)去噪处理,后对得到的图像f(x)采用阶数为q(q∈(1,2))的左右方向微分的合成分数阶导数算子提取边缘点。结果表明该方法在抗噪声干扰和提取更多边缘细节方面取得了很好的平衡,具有较好的边缘检测效果。

This paper presents a edge detection algorithm which uses a fractional—order differentiation against the traditional edge detection algorithms which often adopt the integer—order differentiation operators . Then make a further study of this fractional—order operator's characteristics in the edge detection in image processing, especially about the approach that introduces the fractional differentiation as an operator for edge detection. It proves that the algorithm can get a proper balance between the edge thinning and edge selectivity for edge detection, and greatly improves the quality of the image edge detection.