Abstract:An edge detection method based on rough fuzzy set is presented which combines advantages of rough sets that can handle vagueness and C-Set that can provide multi-granularity. An edge expression is proposed by the definition of rough operation and operation. Granularity w and structure similarity ε are introduced for better edge detection. The experimental results show that the image edge detection algorithm performs well.
[1] Canny J.A Computational Approach to Edge Detection.IEEE Trans on Pattern Analysis,1986,8(6): 679-698 [2] Mallat S,Hwang W L.Singularity Detection and Processing with Wavelets.IEEE Trans on Information Theory,1992,38(2): 617-643 [3] Smith S M,Brady J M.SUSAN-A New Approach to Low Level Image Processing.International Journal of Computer Vision,1997,23(1): 45-78 [4] Bao P,Zhang Lei,Wu Xiaolin.Canny Edge Detection Enhancement by Scale Multiplication.IEEE Trans on Pattern Analysis and Machine Intelligence,2005,27(9): 1485-1490 [5] Lindeberg T.Edge Detection and Ridge Detection with Automatic Scale Selection.International Journal of Computer Vision,1998,30(2): 117-154 [6] Sun Wei,Xia Liangzheng,Pan Hong.A New Edge Detection Algorithm Based on Fuzzy Partition.Journal of Image and Graphics,2004,9(3): 18-22 (in Chinese) (孙 伟,夏良正,潘 泓.一种基于模糊划分的边缘检测算法.中国图象图形学报,2004,9(3): 18-22) [7] Kuo Y H,Lee C S.A New Fuzzy Edge Detection Method for Image Enhancement // Proc of the 6th IEEE International Conference on Fuzzy System.Barcelona,Spain,1997: 1069-1074 [8] Yang Xibei,Lin T Y,Yang Jingyu,et al.Combination of Interval-Valued Fuzzy Set and Soft Set.Computers and Mathematics with Applications,2009,58(3): 521-527 [9] Bustince H,Barrenechea E,Fernandez J P.Interval-Valued Fuzzy Sets Constructed from Matrices: Application to Edge Detection.Fuzzy Sets and Systems,2009,160(13): 1819-1840 [10] Liu Ruiling.Algorithm of Image Edge Detection Based on Rough Set and Edge Information Measure.Computer and Modernization,2009,(10): 92-94 (in Chinese) (刘瑞玲.基于粗糙集和边缘信息测度的图像边缘检测算法.计算机与现代化,2009,(10): 92-94) [11] Petrosino A,Salvi G.Rough Fuzzy Set Based Scale Space Transforms and Their Use in Image Analysis.International Journal of Approximate Reasoning,2006,41(2): 212-228 [12] Petrosino A,Ferone A.Rough Fuzzy Set-Based Image Compression.Fuzzy Sets and Systems,2009,160(10): 1485-1506 [13] Mushrif M M,Ray A K.Color Image Segmentation: Rough-Set Theoretic Approach.Pattern Recognition Letters,2008,29(4): 483-493 [14] Dong Ying,Xiang Bingren,Wang Teng,et al.Rough Set-Based SAR Analysis: An Inductive Method.Expert Systems with Applications,2010,37(7): 5032-5039 [15] Pawlak Z.Rough Sets.International Journal of Computer and Information Science,1982,11(5): 241-356 [16] Zadeh L A.Fuzzy Sets.Information and Control,1965,8(3): 338-353 [17] Otsu N.A Threshold Selection Method from Gray-Level Histograms.IEEE Trans on Systems,Man and Cybernetics,1979,9(1): 62-66 [18] Liu Jianzhuang,Su Wenqing.The Automatic Thresholding of Gray-Level Picture via Two-Dimensional Otsu Method.Acta Automatica Sinica,1993,19(1): 101-105 (in Chinese) (刘健庄,粟文青.灰度图像的二维Otsu自动阈值分割法.自动化学报,1993,19(1): 101-105) [19] Wang Zhou,Bovik A C,Sheikh H R.Image Quality Assessment: From Error Visibility to Structural Similarity.IEEE Trans on Image Processing,2004,13(4): 600-612 [20] Zhang T Y,Suen C Y.A Fast Parallel Algorithm for Thinning Digital Patterns.Communications of ACM,1984,27(3) :236-239 [21] Che Wujun,Yang Xunnian,Wang Guozhao.A Dynamic Approach to Skeletonization.Journal of Software,2003,14(4): 818-823 (in Chinese) (车武军,杨勋年,汪国昭.动态骨架算法.软件学报,2003,14(4): 818-823) [22] Xu Xiangyang,Song Enmin,Jin Lianghai.Characteristic Analysis of Threshold Based on Otsu Criterion.Acta Electronica Sinica,2009,37(12): 2716-2719 (in Chinese) (许向阳,宋恩民,金良海.Otsu准则的阈值性质分析.电子学报,2009,37(12): 2716-2719) [23] Wang Dan,Wu Mengda.Binary Fuzzy Rough Set Model Based on Triangle Modulus and Its Application to Image Processing // Proc of the 8th IEEE International Conference on Cognitive Informatics.Hong Kong,China,2009: 249-255 [24] Wang Dan,Wu Mengda,Liu Yinshan.A New Mathematical Morphological Algorithm Based on Rough Sets and Its Application to Detecting Image Edge.Journal of Engineering Graphics,2007,28(2): 109-113 (in Chinese) (王 丹,吴孟达,刘银山.一种新的基于粗糙集的数学形态学算法及其在图像边缘检测中的应用.工程图学学报,2007,28(2): 109-113)