基于RPCA的图像模糊边缘检测算法  

Fuzzy Edge Detection Algorithm Based on RPCA

作　　者：李姗姗[1] 陈莉[1] 张永新[1,2] 袁娅婷 LI Shan-shan;CHEN Li;ZHANG Yong-xin;YUAN Ya-ting(School of Information Science and Technology,Northwest University, Xi＇an 710127 ,China;School of Land and Tourism,Luoyang Normal University, Luoyang, Henan 471022, China)

机构地区：[1]西北大学信息科学与技术学院,西安710127 [2]洛阳师范学院国土与旅游学院,河南洛阳471022

出　　处：《计算机科学》2018年第5期273-279,290,共8页Computer Science

基　　金：国家科技支撑计划项目(2013BAH49F02);国家自然科学基金(61502219);中国博士后科学基金(2015M582697)资助

摘　　要：针对传统边缘检测方法未能在抗噪性能与边缘检测精度之间取得较好的权衡的问题,利用鲁棒主成分分析模型良好的矩阵恢复能力与图像模糊边缘检测算法较佳的边缘检测性能,提出一种基于RPCA的图像模糊边缘检测算法,将图像的边缘检测问题转化为图像主成分的边缘检测问题。该算法对含噪图像进行RPCA分解,得到对应的稀疏图像和低秩图像,再用一种基于阈值的隶属函数将低秩图像转化至等效的模糊特征平面,并在该特征平面上进行模糊增强运算,最后进行空域转化及边缘提取等操作得到最终的边缘图像。实验结果表明,该算法提高了边缘定位的精度,对不同类型、不同强度的噪声均具有较好的抑制能力,适用于对实时性要求不高的图像处理。The traditional edge detection methods fail to achieve a good compromise between the anti-noise performance and the edge detection accuracy.Aiming at this problem,utilizing the effective matrix recovery capability of the robust principal component analysis model and the superior edge detection performance of fuzzy edge detection algorithm,combining the robust principal component analysis model with the fuzzy edge detection algorithm,this paper proposed a fuzzy edge detection algorithm based on robust principal component analysis,which formulates the problem of image edge detection as the edge detection of the image principal component.The steps of this approach can be summarized as follows.Firstly,the noisy image is decomposed into a sparse image and a low rank image by RPCA.Secondly,in order to extract the fuzzy property plane from the spatial domain for the low rank image,a threshold-based membership function is defined.Thirdly,image enhancement is performed in the fuzzy domain by using fuzzy enhancement operator.Finally,the modified spatial domain is obtained and the edge detection is excuted by using min or max operators.The experiment results demonstrate that the new approach can effectively suppress the different types and different intensity of noise and improve the accuracy of edge localization,which is suitable for low level image processing with lower demand in real-time.

关 键 词：鲁棒主成分分析 低秩图像 边缘检测 隶属函数 模糊特征平面 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]