Abstract In this paper, an image segmentation method based on subsethood measure theory of fuzzy set is proposed. Because of the subjective of human vision and the uncertainty of image structure, fuzzy techniques are used in image segmentation. Firstly, the subsethood measure theory of fuzzy set is introduced. Then the new criteria function of image segmentation threshold choosing is defined on the basis of fuzzy subsethood theory. Finally, the optimal method for choosing parameters of fuzzy membership is presented based on mutual information and Chaos theory. Experimental results show that the image thresholding segmentation method based on subsethood measure theory is feasible, and its segmentation performance is obviously better than that of thresholding method based on fuzzy entropy or similarity measure.
[1] Sezgin M, Sankur B. Survey over Image Thresholding Techniques and Quantitative Performance Evaluation. Journal of Electronic Image, 2004, 13(1): 145165 [2] Pal S K, King R R, Hashion A A. Automatic Graylevel Thresholding through Index of Fuzziness and Entropy. Pattern Recognition, 1983, 1(1): 141146 [3] Cheng H D, Lui Y M. Automatic Bandwidth Selection of Fuzzy Membership Functions. Information Science: An International Journal, 1997, 103(1): 121 [4] Zenzo S D, Cinque L, Levialdi S. Image Thresholding Using Fuzzy Entropies. IEEE Trans on System, Man and Cybernetics, 1998, 28(1): 1523 [5] Chaira T, Ray A K. Segmentation Using Fuzzy Divergence. Pattern Recognition Letters, 2003, 24(12): 18371844 [6] Liu X C. Entropy, Distance Measure and Similarity Measure of Fuzzy Sets and Their Relations. Fuzzy Sets and Systems, 1992, 52(3): 305318 [7] Fan Jiulun, Xie Weixin. Distance Measure and Induced Fuzzy Entropy. Fuzzy Sets and Systems, 1999, 104(2): 305314 [8] Kosko B. Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence. Englewood Cliffs, USA: PrenticeHall, 1992 [9] Kppen M, Nowack C H, Rsel G. FuzzySubsethood Based Color Image Processing // Proc of the 11th Scadina Vian Conference on Image Analysis. KangerLussnag, Denmark, 1999, Ⅰ: 195202 [10] Kunchva L I. Fuzzy Rough Sets: Application to Feature Selection. Fuzzy Sets and Systems, 1992, 51(2): 147153 [11] Fan Jiulun, Wu Chengmao. Subsethood Measures Applied to Clustering Validity Judgement. Fuzzy Systems and Mathematics, 2002,16(1): 8086 (in Chinese) (范九伦,吴成茂.用于聚类有效性判定的包含度公式.模糊系统与数学, 2002, 16(1): 8086) [12] Wu Chengmao, Fan Jiulun. Study on Evaluating Data Classifying Quality Based on Mutual Subsethood. Computer Science, 2005, 32(1): 159161 (in Chinese) (吴成茂,范九伦.基于互包含度的数据分类效果评价研究.计算机科学, 2005, 32(1): 159161) [13] Kosko B. Fuzzy Engineering. Englewood Cliffs, USA:Prentice Hall, 1997: 336361 [14] Sinha D, Dougherty E R. Fuzzification of Set Inclusion: Theory and Application. Fuzzy Sets and Systems, 1993, 55(1): 1542 [15] Young V R. Fuzzy Subsethood. Fuzzy Sets and Systems, 1996, 77(3): 371384 [16] Fan Jiulun, Xie Weixin, Pei Jihong. Subsethood Measure: New Definitions. Fuzzy Sets and Systems, 1999, 106(1): 201209 [17] Fan Jiulun. Some New Formulas of Similarity Measures. Journal of Xi’an Institute of Post and Telecommunications, 2002, 7(3): 6971 (in Chinese) (范九伦.若干新的贴近度公式.西安邮电学院学报, 2002, 7(3): 6971) [18] Fan Jiulun. Mutual Induced Relations between Similarity Measure and Subsethood Measure. Fuzzy Systems and Mathematics, 2003, 17(3): 2937 (in chinese) (范九伦.包含度和贴近度的相互诱导关系.模糊系统与数学, 2003, 17(3): 2937) [19] Xue Jinghao, Zhang Yujin, Lin Xinggang. Threshold Selection Using CrossEntropy and Fuzzy Divergence. Proc of SPIE, 1998, 3561: 152162 [20] Lü Qingwen, Chen Wufan. Image Segmentation Based on Mutual Information. Chinese Journal of Computers, 2006, 29(2): 297300 (in Chinese) (吕庆文,陈武凡. 基于互信息量的图像分割.计算机学报, 2006, 29(2): 297300)
2007, Vol. 20 
