基于Riemann-Liouville改进的1~2阶分数阶边缘提取新模型

doi:10.11772/j.issn.1001-9081.2016.01.0227

计算机应用 ›› 2016, Vol. 36 ›› Issue (1): 227-232.DOI: 10.11772/j.issn.1001-9081.2016.01.0227

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

收稿日期:2015-07-06 修回日期:2015-09-28 出版日期:2016-01-10 发布日期:2016-01-09
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)。

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:2016-01-10 Published:2016-01-09
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).

摘要/Abstract

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

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

中图分类号:

TP391.9

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.

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.

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基于Riemann-Liouville改进的1~2阶分数阶边缘提取新模型

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

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