New improved 1-2-order fractional differential edge detection model based on Riemann-Liouville integral

doi:10.11772/j.issn.1001-9081.2016.01.0227

Journal of Computer Applications ›› 2016, Vol. 36 ›› Issue (1): 227-232.DOI: 10.11772/j.issn.1001-9081.2016.01.0227

Previous Articles Next Articles

New improved 1-2-order fractional differential edge detection model based on Riemann-Liouville integral

WANG Chengxiao¹, HUANG Huixian¹, YANG Hui¹, XU Jianmin²

1. College of Information Engineering, Xiangtan University, Xiangtan Hunan 411105, China;
2. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou Guangdong 510200, China

Received:2015-07-06 Revised:2015-09-28 Online:2016-01-09 Published:2016-01-10
Supported by:
This work is partially supported by the National Natural Science Foundation of China (61174184) and the Major Science and Technology Project of Guangdong Province (2012A010800007).

基于Riemann-Liouville改进的1~2阶分数阶边缘提取新模型

王程啸¹, 黄辉先¹, 杨辉¹, 徐建闽²

1. 湘潭大学信息工程学院, 湖南湘潭 411105;
2. 华南理工大学土木工程与交通学院, 广州 510200

通讯作者: 王程啸(1991-),男,湖南衡阳人,硕士研究生,主要研究方向:数字图像处理、智能控制、优化算法
作者简介:黄辉先(1957-),男,湖南益阳人,教授,博士,主要研究方向:智能控制、复杂建模与非线性控制、智能控制与城市智能交通系统、优化算法;杨辉(1991-),男,湖南衡阳人,硕士研究生,主要研究方向:数字图像处理、智能控制;徐建闽(1960-),男,山东招远人,教授,博士,主要研究方向:交通信息工程及控制、控制理论、控制工程。
基金资助:
国家自然科学基金资助项目(61174184);广东省重大科技项目(2012A010800007)。

Abstract

Abstract: Focusing on the issues of failing to pinpoint the edge information accurately and lacking texture detail of image by using integer order differential or 0-1-order fractional differential mask operators in digital image processing, a new 1-2-order edge detection operator based on Laplacian operator was proposed. Deduced from the definition of Riemann-Liouville (R-L),the 1-2-order fractional differential had the advantage in enhancing high-frequency signal and reinforcing medium frequency signal. The simulation results demonstrate that the proposed operator can take an higher recognition rate on the subjective recognition, and it's better at extracting the edge information, especially for the image with rich texture detail in the smooth region with little change of gray scale. Objectively, the integrated location error rate is 7.41% which is less than that of integer order differential operators (a minimum of 10.36%) and 0-1-order differential operator (a minimum of 9.97%). Quantitative indicators show the new fractional operator can effectively improve the positioning accuracy of the edge, and the proposed operator is particularly suitable for edge detection with high frequency information.

Key words: edge information, texture detail, fractional differentiation, mask operator, location error

摘要： 针对数字图像的处理中采用整数步长与0~1阶分数阶微分的掩模算子未能精确定位边缘信息、缺少图像的纹理细节的问题,在Laplacian算子的基础上提出了一种新的边缘检测掩模算子。该算法从Riemann-Liouville(R-L)定义出发,推出1~2阶分数阶微分在中频信号的增强效果优于0~1阶分数阶微分并显著提升了高频信号,最终得到精确的检测效果。仿真结果表明:提出的算子能更好地提取边缘信息,尤其对灰度变化不大的平滑区域中纹理细节丰富的图像,该算子检测到的信息优于现有0~1阶微分算子,针对主观识别有更高的准确率;客观上采用扫描法的定位误差统计,该算子的综合定位误差率为7.41%,低于整数阶微分算子(最低为10.36%)与0~1阶微分算子(最低为9.97%),有效提高了边缘定位精度。该算子尤其适用于具有较高频信息的图像边缘检测中。

关键词: 边缘信息, 纹理细节, 分数阶微分, 掩模算子, 定位误差

CLC Number:

TP391.9

WANG Chengxiao, HUANG Huixian, YANG Hui, XU Jianmin. New improved 1-2-order fractional differential edge detection model based on Riemann-Liouville integral[J]. Journal of Computer Applications, 2016, 36(1): 227-232.

王程啸, 黄辉先, 杨辉, 徐建闽. 基于Riemann-Liouville改进的1~2阶分数阶边缘提取新模型[J]. 计算机应用, 2016, 36(1): 227-232.

References

[1] GONZALEZ R C, WOODS R E. Digital image processing [M]. Beijing: Publishing House of Electronics Industry, 2006: 98-105.
[2] 张俊,韦志辉.一种分数阶的多尺度变换模型和交替投影图像去噪算法[J].应用数学建模,2011,35(5):2516-2528.(ZHANG J, WEI Z H. A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising [J]. Applied mathematical modeling, 2011, 35(5): 2516-2528.)
[3] 蒲亦非.将分数阶微分演算引入数字图像处理[J].四川大学学报(工程科学版),2007,39(3):125-128.(PU Y F. Application of fractional differential approach to digital image processing [J]. Journal of Sichuan university (engineering science edition), 2007, 39(3): 125-128.)
[4] 王波.滤波算法在图像增强中的应用研究[J].计算机仿真,2013,30(3):364-367.(WANG B. Application of bilateral filtering algorithm in image enhancement [J]. Computer simulation, 2013, 30(3): 364-367.)
[5] 汪成亮,乔鹤松,陈娟娟.基于纹理复杂度的自适应分数阶微分算法[J].计算机工程,2012,38(7):177-178.(WANG C L, QIAO H S, CHEN J J. Adaptive fractional differential algorithm based on texture complexity [J]. Computer engineering, 2012, 38(7): 177-178.)
[6] GAN Z, YANG H. Texture enhancement though multiscale mask based on RL fractional differential [C]// Proceedings of the 2010 International Conference on Information Networking and Automation. Piscataway, NJ: IEEE, 2010: 333-337.
[7] 杨柱中,周激流,晏祥玉,等.基于分数阶微分的图像增强[J].计算机辅助设计与图形学学报,2008,20(3):343-348.(YANG Z Z, ZHOU J L, YAN X Y, et al. Image enhancement based on fractional differentials [J]. Journal of computer-aided design & computer graphics, 2008, 20(3): 343-348.)
[8] PU Y, ZHOU J. A novel approach for multi-scale texture segmentation based on fractional differential [J]. International journal of computer mathematics, 2011, 88(1): 58-78.
[9] 张志宝,沈怀荣,路振民,等.基于分数阶微分的遥感图像边缘检测方法[J].现代电子技术,2014,37(20):99-102.(ZHANG Z B, SHEN H R, LU Z M, et al. Method on remote sensing image edge detection based on fractional order differential [J]. Modern electronics technique, 2014, 37(20): 99-102.)
[10] 何春,叶永强,姜斌,等.一种基于分数阶次微积分模板的新型边缘检测方法[J].自动化学报,2012,38(5):776-787.(HE C, YE Y Q, JIANG B, et al. A novel edge detection method based on fractional-order calculus mask [J]. Acta automatica sinica, 2012, 38(5): 776-787.)
[11] 甘志凤,杨红雨.基于R-L分数阶微分梯度算子的边沿检测[J].计算机工程与设计,2010,31(21):4342-4645.(GAN Z F, YANG H Y. Edge detection based on R-L fractional-order differential gradient operator [J]. Computer engineering and design, 2010, 31(21): 4342-4645.)
[12] CAFAGNA D. Fractional calculus: a mathematical tool from the past for present engineers [J]. IEEE industrial electronics magazine, 2007, 1(2): 35-40.
[13] 蒋伟,陈辉.基于分数阶微分和Sobel算子的边缘检测新模型[J].计算机工程与应用,2012,48(4):182-185.(JIANG W, CHEN H. New edge detection model based on fractional differential and Sobel operator [J]. Computer engineering and applications, 2012, 48(4): 182-185.)
[14] 苑玮琦,李雪.一种边缘检测效果评价方法的研究[J].微计算机信息,2007,23(11):304-306.(YUAN W Q, LI X. Study on evaluating results of edge detectors [J]. Microcomputer information, 2007, 23(11): 304-306.)

New improved 1-2-order fractional differential edge detection model based on Riemann-Liouville integral

基于Riemann-Liouville改进的1~2阶分数阶边缘提取新模型

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 6

Recommended Articles

Metrics

[1]	GAO Leifu, LI Chao. Improvement of adaptive generalized total variation model for image denoising [J]. Journal of Computer Applications, 2016, 36(6): 1699-1703.
[2]	CHEN Zhenzhen, QING Linbo, HE Xiaohai, WANG Yun. Wavelet domain distributed depth map video coding based on non-uniform quantization [J]. Journal of Computer Applications, 2016, 36(4): 1080-1084.
[3]	JIANG Wei LI Xiaolong YANG Yongqing ZHANG Heng. New image denoising method based on rational-order differential [J]. Journal of Computer Applications, 2014, 34(3): 801-805.
[4]	HU Xuegang LI Yu. Improved image poisson denoising model based on fractional variation [J]. Journal of Computer Applications, 2013, 33(04): 1100-1102.
[5]	JIANG Wei DING Zhi-quan LIU Ya-wei. New image edge detection model based on fractional-order partial differention [J]. Journal of Computer Applications, 2012, 32(10): 2848-2850.
[6]	CHEN Shi-qiang ZHOU Xu WANG Jun-Feng TANG Hui. Location error eliminating approach for network delay measurement based on network driver interface specification [J]. Journal of Computer Applications, 2012, 32(07): 1787-1790.