Modification of Two-Dimensional Entropic Thresholding Method and Its Fast Iterative Algorithm
WU Cheng-Mao1,2,TIAN Xiao-Ping1,2,TAN Tie-Niu2
1.College of Electronics Engineering,Xian University of Posts and Telecommunications,Xian 710121 2.National Laboratory of Pattern Recognition,Institute of Automation Chinese Academy of Sciences,Beijing 100080
Abstract A modified method for two-dimensional entropic thresholding method and its fast iterative algorithm are proposed. Aiming at the disadvantage of high computational complexity of the classical two-dimensional entropic thresholding and its recursive algorithm, the two-variables probability distribution of two dimensional histogram is firstly modified and a new two-dimensional entropic thresholding method is obtained. Then, the fast iterative algorithm for the new modified two-dimensional entropic thresholding method is educed on the assumption that the modified two-variables probability distribution of two-dimensional histogram is continuous and differentiable. Experimental results show that the modified two-dimensional entropic thresholding method and its fast iterative algorithm are feasible, and the computational time of the fast iterative algorithm is much less than that of its recursive algorithm to a certain extent.
[1] Pal N R, Pal S K. A Review on Image Segmentation Techniques. Pattern Recognition Letters, 1993, 26(9): 1277-1294 [2] Sezgin M, Sankur B. Survey over Image Thresholding Techniques and Quantitative Performance Evaluation. Journal of Electronic Image, 2004, 13(1): 146-165 [3] Pun T. A New Method for Gray-Level Picture Thresholding Using the Entropy of the Histogram. Signal Processing, 1980, 2(2): 223-237 [4] Pun T. Entropic Thresholding: A New Approach. Computer Vision, Graphics, and Image Processing, 1981, 16(2): 210-239 [5] Kapur J N, Sajoo P K, Wong A K C. A New Method for Gray-Level Picture Thresholding Using the Entropy of the Histogram. Computer Vision, Graphics, and Image Processing, 1985, 20(3): 273-285 [6] Pal N R, Pal S K. Entropic Thresholding. Signal Processing, 1989, 16(2): 97-108 [7] Pal N R, Pal S K, Pal R, et al. Entropy: A New Definition and Its Applications. IEEE Trans on System, Man and Cybernetics, 1991, 21(5): 1260-1270 [8] Chang C I, Chen K, Wang J, et al. A Relative Entropy-Based Approach to Image Thresholding. Pattern Recognition, 1994, 27(9): 1275-1289 [9] Sahoo P K, Wilins C, Yenger J. Threshold Selection Using Renyis Entropy. Pattern Recognition, 1997, 30(1): 71-84 [10] Paveic P, Ribaric S. Gray Level Thresholding Using the Havrda and Charvat Entropy // Proc of the 10th Mediterranean Electrotechnical Conference. Limassol, Cyprus, 2000, Ⅱ: 631-634 [11]de Albuquerque M P, Esquef I A, Gesualdi M A R. Image Thresholding Using Tsallis Entropy. Pattern Recognition Letters, 2004, 25(9): 1059-1065 [12]Abutaleb A S. Automatic Thresholding of Gray-Level Pictures Using Two-Dimensional Entropy. Computer Vision, Graphics, and Image Processing, 1989, 47(1): 22-32 [13]Brink A D. Thresholding of Digital Images Using Two-Dimensional Entropies. Pattern Recognition, 1992, 25(8): 803-808 [14]Chen W T, Wen C H, Yang C W. A Fast Two-Dimensional Entropic Thresholding Algorithm. Pattern Recognition, 1994, 27(7): 885-893 [15]Gong Jian, Li Liyuan, Chen Wenan. Fast Recursive Algorithm for Two-Dimensional Thresholding. Pattern Recognition, 1998, 31(3): 295-300 [16]Reddi S S, Rudin S F, Keshavan H R. An Optimal Multilevel Threshold Scheme for Image Segmentation. IEEE Trans on System, Man and Cybernetics, 1984, 14(4): 661-665 [17]Morii F. An Image Thresholding Method Using a Minimum Weighted Squared-Distortion Criterion. Pattern Recognition, 1995, 28(7): 1063-1075 [18]Wang Haojun, Mao Baixin, Bi Duyan, et al. A Study of Image Segmentation for Silver Grains in In-Situ Hybridization. Chinese Journal of Image and Graphics, 1999, 4(6): 454-457 (in Chinese) (王浩军,毛柏鑫,毕笃彦,等.原位分子杂交图象中银粒的分割方法研究.中国图象图形学报, 1999, 4(6): 454-457) [19]Wu Yiquan, Wu Wenyi, Pan Zhe. A Fast Iterative Algorithm for Image Segmentation Based on 2D Maximum Between-Cluster Variance. Chinese Journal of Stereology and Image Analysis, 2007, 12(3): 216-220 (in Chinese) (吴一全,吴文怡,潘 喆.二维最大类间方差阈值分割的快速迭代算法.中国体视学与图象分析, 2007, 12(3): 216-220) [20] Li C H, Tam P K S. An Iterative Algorithm for Minimum Cross-Entropy Thresholding. Pattern Recognition Letter, 1998, 19(8): 771-776
2010, Vol. 23 
