一种基于分数阶次微积分模板的新型边缘检测方法

何春; 叶永强; 姜斌; 周鑫

doi:10.3724/SP.J.1004.2012.00776

一种基于分数阶次微积分模板的新型边缘检测方法

doi: 10.3724/SP.J.1004.2012.00776

1.
南京航空航天大学自动化学院南京 210016

详细信息

通讯作者:
叶永强, 南京航空航天大学自动化学院教授. 2004 年在南洋理工大学电气与电子工程学院获博士学位. 主要研究方向为电力电子系统及控制, 应用控制理论, 图像处理.

计量
- 文章访问数: 2259
- HTML全文浏览量: 80
- PDF下载量: 1509
- 被引次数: 0
出版历程
- 收稿日期: 2011-05-20
- 修回日期: 2011-12-20
- 刊出日期: 2012-05-20

A Novel Edge Detection Method Based on Fractional-order Calculus Mask

1.
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016

摘要

摘要: 利用分数阶次微分和分数阶次积分组成复合导数, 在复合导数基础上提出了一种边缘检测新算子. 为实现分数阶次微分, 推导出一种新的复数模板. 通过检测一维曲线, 验证了复合导数可以近似模拟一阶导数并具有抑制噪声的能力. 二维图像的检测结果表明, 新算子在无噪声干扰情况下可以精确、有效地完成边缘检测任务; 在有噪声情况下可以有效地抑制噪声干扰. 最后, 对新算子进行了定量分析并与 Canny 算子进行比较. 结果表明新算子具有低定位错误率的优势.
- 图像处理 /
- 边缘检测 /
- 分数阶次微积分 /
- 抗噪性 /
- 定量分析
Abstract: In this paper, a new edge detection operator based on a composite derivative is proposed, which is realized by the combination of fractional differentiation and integration. The new complex edge-detection mask is also deduced for the implementation of fractional differentiation. The abilities of the compound derivative in terms of approximate simulation of first-order derivative and suppression of noise are demonstrated through one-dimensional examples. The experimental results of two-dimensional examples indicate that without the contamination of noise, the new operator can accurately detect the edge, while with the noise contamination, the new operator can effectively suppress the noise. Finally, quantitative analysis of the new operator is given. The results of the comparison between the new operator and Canny operator show that the new operator has the advantage of a low mispositioning rate.
- Image processing /
- edge detection /
- fractional differentiation and integration /
- noise immunity /
- quantitative analysis

HTML全文

参考文献(1)

[1]

Dong Hong-Yan. Research on Some Techniques in Edge Detection [Ph.D. dissertation], National University of Defense Technology, China, 2008 (董鸿燕. 边缘检测的若干技术研究 [博士学位论文], 国防科学技术大学, 中国, 2008)[2] Yang Zhu-Zhong, Zhou Ji-Liu, Huang Mei, Yan Xiang-Yu. Fractional differential for edge extraction. Computer Engineering and Application, 2007, 43(35): 15-18 (杨柱中, 周激流, 黄梅, 晏祥玉. 用分数阶微分提取图像边缘. 计算机工程与应用, 2007, 43(35): 15-18)[3] Gonzalez R C, Woods R E. Digital Image Processing. New Jersey: Prentice-Hall, 2008. 703-728[4] Shih F Y. Image Processing and Pattern Recognition: Fundamentals and Techniques. New Jersey: John Wiley Sons, 2010. 53-58[5] John C. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8(6): 679-698[6] Zhang Y, Rockett P I. The Bayesian operating point of the Canny edge detector. IEEE Transactions on Image Processing, 2006, 15(11): 3409-3416[7] Mcilhagga W. The Canny edge detector revisited. International Journal of Computer Vision, 2011, 91(3): 251-261[8] Torre V, Poggio T A. On edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8(2): 147-163[9] Engheta N. On the role of fractional calculus in electromagnetic theory. IEEE Antennas and Propagation Magazine, 1997, 39(4): 35-46[10] Li Wen, Zhao Hui-Min. Rational function approximation for fractional order differential and integral operators. Acta Automatica Sinica, 2011, 37(8): 999-1005 (李文, 赵慧敏. 一种分数阶微积分算子的有理函数逼近方法. 自动化学报, 2011, 37(8): 999-1005)[11] Leu J S, Papamarcou A. On estimating the spectral exponent of fractional Brownian motion. IEEE Transactions on Information Theory, 1995, 41(1): 233-244[12] Benmalek M, Charef A. Digital fractional order operators for R-wave detection in electrocardiogram signal. IET Signal Processing, 2009, 3(5): 381-391[13] Li H S, Luo Y, Chen Y Q. A fractional order proportional and derivative (FOPD) motion controller: tuning rule and experiments. IEEE Transactions on Control Systems Technology, 2010, 18(2): 516-520[14] Mathieu B, Melchior P, Oustaloup A, Ceyral Ch. Fractional differentiation for edge detection. Signal Processing, 2003, 83(11): 2421-2432[15] Pu Y F, Zhou J L. A novel approach for multi-scale texture segmentation based on fractional differential. International Journal of Computer Mathematics, 2011, 88(1): 58-78[16] Lu Yang. Fractional Differential Applied to the Study of Edge Detection [Master dissertation], Dalian Jiaotong University, China, 2010 (卢洋. 分数阶微分应用于图像边缘检测的研究[硕士学位论文], 大连交通大学, 中国, 2010)[17] Gao C B, Zhou J L, Hu J R, Lang F N. Edge detection of colour image based on quaternion fractional differential. IET Image Processing, 2011, 5(3): 261-272[18] Ye Y Q, Tayebi A, Liu X P. All-pass filtering in iterative learning control. Automatica, 2009, 45(1): 257-264[19] Xue Li-Xia. Research on Remote Sensing Image Fuzzy Edge Detection Based on Object Cloud [Ph.D. dissertation], Southwest Jiongtong University, China, 2007 (薛丽霞. 基于对象云的遥感图像模糊边缘检测研究 [博士学位论文], 西南交通大学, 中国, 2007)[20] Li Xue. Performance Evaluation in Edge Detection Algorithm of Gray Image [Master dissertation], Shenyang University of Technology, China, 2007 (李雪. 灰度图像边缘检测算法的性能评价 [硕士学位论文], 沈阳工业大学, 中国, 2007)[21] Abdou I E, Pratt W K. Quantitative design and evaluation of enhancement/thresholding edge detectors. Proceedings of the IEEE, 1979, 67(5): 753-763

施引文献

资源附件(0)

访问统计