Abstract: 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.

Key words: Robust principal component analysis(RPCA),Low rank image,Edge detection,Membership function,Fuzzy property plane