针对噪声图像边缘模糊、边缘检测困难的问题,提出了一种结合分数阶微分的噪声图像非下采样contourlet变换 (NSCT)域边缘检测方法。该方法首先对图像进行NSCT分解,对低频子带的轮廓进行针对性提取;其次对于边缘细节和噪声较多的各方向高频子带,利用NSCT域的多尺度积和方向分数阶微分矩阵对高频系数进行阈值去噪与信息增强;最后将NSCT域各频域和方向的尺度图像进行融合,得到完整的边缘图像。对不同类型的原始图像和噪声图像进行实验,本文方法检测到的平均连续边缘像素比分别为0.931和0.861,相比Canny算子、分数阶微分检测方法和现有的多尺度域边缘检测方法,本文方法具有更好的边缘检测效果。随着图像噪声水平的增加,本文方法得到的平均连续边缘像素比较高,抗噪性强,边缘准确、完整、连续。

To overcome the edge blurring and the difficulty in edge detection of noisy images, a method for edge detection of noisy images in nonsubsampled contourlet transform (NSCT) domain is proposed based on fractional differentiation. This method first decomposes the image by NSCT, and then extracts the contours of the low-frequency sub-bands. Second, for the high-frequency sub-bands in various directions with more edge details and noise, the proposed method uses the multi-scale product of the NSCT domain and the direction fractional differential matrix to perform threshold denoising and enhance information on high-frequency coefficients. Finally, the scale images of each frequency domain and direction in the NSCT domain are fused to obtain a complete edge image. Experiments are carried out on different types of original and noisy images, and the average continuous edge pixel ratio obtained by the proposed method is 0.931 and 0.861, respectively. Compared with Canny operator, fractional differential detection method, and existing multiscale domain edge detection methods, this method has better edge detection effect. With the increase of the image noise level, we can obtain a high average continuous edge pixel ratio, strong anti-noise, and accurate, complete and continuous edges by the proposed method.