基于 G-L 分数阶微分的图像边缘检测

摘要

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 fre -quency 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 dif-ferential algorithm .The results show that the fractional differential algorithm is not sensitive to noise , and can keep the image tex-ture detail of the smoothing region and get more information of the image edge .%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。