基于G-L分数阶微分的图像边缘检测

Image Edge Detection Based on G-L Fractional Differential

传统的基于整数阶微分的图像边缘检测算子,存在对噪声敏感、抗干扰能力差,提取图像边缘信息简单等缺点。分数阶微分能加强信号的高频成分,同时对信号的中低频成分进行非线性保留。本文根据分数阶微分的G-L定义,推导出分数阶微分的差分表达式,构造5×5大小的分数阶微分算子模板,并采用Sobel算子、Prewitt算子和Laplacian算子进行图像边缘检测的仿真实验。仿真实验结果表明,相比整数阶微分算子,分数阶微分算子抗噪声性能强,能有效保留图像平滑区域中的纹理细节信息,图像边缘检测结果的信息也更为丰富。

Traditional image edge detection algorithm based on integer order differential is sensitive to noise, and the image edge detection results are often simple. The fractional differential can enhance the high frequency and keep the middle and the low frequency of the image signal. The paper infers the difference expression of the G-L fractional differential, and designs a 5 - 5 size template. The image edge detection experiments are made with the Sobel, the Prewitt, the Laplacian, and the G-L fractional differential algorithm. The results show that the fractional differential algorithm is not sensitive to noise, and can keep the image texture detail of the smoothing region and get more information of the image edge.