中文摘要：

由于人类识别图像特征涉及非线性的识别机制，提出基于改进二维LogButterworth滤波器的全方向边缘检测方法。该方法从频域角度出发，利用正反快速傅里叶变换来实现边缘检测工作。首先，将非线性Log函数引入Butter—worth滤波器，获得二维LogButterworth滤波器，当图像行列数不一致时，中心频率分布于椭圆之上，椭圆的长短轴之比与图像长宽比相等，进而给出以角度为变量滤波器表达式。其次，为方便滤波器参数的选取，对二维LogButterworth滤波器参数进行归一化等处理。再次，利用F—measure和PSNR（峰值信噪比）来衡量不同参数的边缘检测结果，确定最优的二维LogButterworth滤波器参数范围。然后，乘法次数和加法次数被用来分析本文方法的理论效率，同时以不同大小的图像作为试验数据来比较两种方法的检测耗时。最后，以伯克利图像分割数据库（BSDS）图像和高空间分辨率遥感图像为试验数据，对本文方法的边缘检测结果进行评价分析。结果表明：本文方法可以有效地应用于图像边缘检测。

英文摘要：

An omnidirectional edge detection algorithm based on two-dimensional Log Butterworth filter is proposed to satisfy the need of the nonlinear recognition mechanism. The edge detection using the proposed algorithm involves fast Fourier transform （FFT） and inverse fast Fourier transform （IFFT）. The two-dimensional Log Butterworth filter is developed by introducing the Log function into the band-pass butterworth filter. When the length and width of image is different, the centre frequency is located at an ellipse with the ratio of long axis to minor axis being equal to the length-width ratio of the original image. Thus, this filter can be expressed with a variable of angle. The parameters of the two-dimensional Log Butterworth filter are normalized to choose the parameters easily. Then F- measure and PSNR （peak signal to noise ratio） are introduced to determine the range of optimal parameters. Meanwhile, the numbers el multiplication and addition, and computation time are used to illustrate the efficiency of the proposed algorithm. Finally, detection results of the Berkeley segmentation dataset and benchmark （BSDS） images and high spatial resolution remote sensing images using the proposed algorithm are evaluated and analyzed. The experimental results show that the proposed algorithm can be used for edge detection efficiently.