基于二维 Log Butterworth滤波器的全方向边缘检测的频域实现方法

›› 2013, Vol. 42 ›› Issue (5): 682-690.

基于二维 Log Butterworth滤波器的全方向边缘检测的频域实现方法

王珂¹,肖鹏峰²,冯学智³,吴桂平⁴,李晖⁵

1. 河海大学地球科学与工程学院
2. 南京大学
3. 南京大学城市与资源学系
4. 中国科学院南京地理与湖泊研究所
5. 南京大学地理信息科学系

收稿日期:2012-09-13 修回日期:2013-12-04 出版日期:2013-10-20 发布日期:2014-01-23
通讯作者: 王珂 E-mail:wangke_A@hotmail.com
基金资助:
国家863计划;国家自然科学基金;中国博士后科学基金

Omnidirectional Edge Detection Based on Two-dimensional Log Butterworth Filters in Frequency Domain

1.
2. Nanjing Institute of Geography & Limnology, Chinese Academy of Sciences

Received:2012-09-13 Revised:2013-12-04 Online:2013-10-20 Published:2014-01-23

摘要/Abstract

摘要： 由于人类识别图像特征涉及非线性的识别机制，本文提出了基于改进二维Log Butterworth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Butterworth滤波器，获得二维Log Butterworth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优化选取，本文对二维 Log Butterworth滤波器参数进行归一化等处理；再次，本文利用F-measure和PSNR (峰值信噪比)值来衡量不同参数下的边缘检测结果，确定最优的二维 Log Butterworth滤波器参数范围；然后，为了分析本文方法的边缘检测效率，对比了本文方法与空域算子（Canny算子）的乘法次数和加法次数，同时以不同大小的图像作为实验数据来比较两种方法的边缘检测耗时；最后，以BSDS（伯克利图像分割数据库）图像和高空间分辨率遥感图像为实验数据，对本文方法的边缘检测结果进行了评价分析。结果表明：本文方法可以有效地应用于图像边缘检测。

关键词: Log Butterworth滤波器, 全方向边缘检测, 频域, 乘法和加法次数

Abstract: In this paper, an improved algorithm of omnidirectional edge detection based on two-dimension Log Butterworth filter is proposed to satisfy the need of the nonlinear recognition mechanism in the image processing. The edge detection using the proposed algorithm involves Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) in frequency domain. The two-dimension Log Butterworth filter is proposed by introducing the Log function into the 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. In order to obtain the optimal parameters range, the parameters of the two-dimension Log Butterworth filter are normalized. Then F-measure and PSNR (Peak Signal to Noise Ratio) are introduced into the determination of the range of optimal parameters. Meanwhile, the numbers of multiplication and addition, and computation time for edge detection with different size of image are used to compare the efficiency of the proposed algorithm and a traditional edge detector (Canny detector). Finally, edge detections of BSDS (The Berkeley Segmentation Dataset and Benchmark) images and high spatial resolution remotely sensed imageries using the proposed algorithm are evaluated and analyzed. The results of evaluation and analysis show that the proposed algorithm can be used to detect edges from images efficiently.

Key words: Log Butterworth filter, omnidirectional edge detection, frequency domain, the number of multiplications and additions

中图分类号:

TP751.1

王珂肖鹏峰冯学智吴桂平李晖. 基于二维 Log Butterworth滤波器的全方向边缘检测的频域实现方法[J]. , 2013, 42(5): 682-690.

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