Multilevel Image Thresholding Based on 2D Histogram and Maximum Tsallis Entropy— A Differential Evolution Approach

Multilevel thresholding amounts to segmenting a gray-level image into several distinct regions. This paper presents a 2D histogram based multilevel thresholding approach to improve the separation between objects. Recent studies indicate that the results obtained with 2D histogram oriented approaches are superior to those obtained with 1D histogram based techniques in the context of bi-level thresholding. Here, a method to incorporate 2D histogram related information for generalized multilevel thresholding is proposed using the maximum Tsallis entropy. Differential evolution (DE), a simple yet efficient evolutionary algorithm of current interest, is employed to improve the computational efficiency of the proposed method. The performance of DE is investigated extensively through comparison with other well-known nature inspired global optimization techniques such as genetic algorithm, particle swarm optimization, artificial bee colony, and simulated annealing. In addition, the outcome of the proposed method is evaluated using a well known benchmark-the Berkley segmentation data set (BSDS300) with 300 distinct images.

[1]  Mehmet Sezgin,et al.  A new dichotomization technique to multilevel thresholding devoted to inspection applications , 2000, Pattern Recognit. Lett..

[2]  Amir Nakib,et al.  Image histogram thresholding based on multiobjective optimization , 2007, Signal Process..

[3]  R. Kayalvizhi,et al.  PSO-Based Tsallis Thresholding Selection Procedure for Image Segmentation , 2010 .

[4]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[5]  Josef Kittler,et al.  Minimum error thresholding , 1986, Pattern Recognit..

[6]  Patrick Siarry,et al.  A comparative study of various meta-heuristic techniques applied to the multilevel thresholding problem , 2010, Eng. Appl. Artif. Intell..

[7]  Márcio Portes de Albuquerque,et al.  Image thresholding using Tsallis entropy , 2004, Pattern Recognit. Lett..

[8]  Y. Zhang,et al.  A REVIEW ON IMAGE SEGMENTATION TECHNIQUES WITH REMOTE SENSING PERSPECTIVE , 2010 .

[9]  Nikhil R. Pal,et al.  On minimum cross-entropy thresholding , 1996, Pattern Recognit..

[10]  Tang Xu-dong,et al.  Multi-threshold image segmentation based on two-dimensional Tsallis , 2010, 2010 3rd International Conference on Computer Science and Information Technology.

[11]  Pau-Choo Chung,et al.  A Fast Algorithm for Multilevel Thresholding , 2001, J. Inf. Sci. Eng..

[12]  W. Eric L. Grimson,et al.  Mutual information in coupled multi-shape model for medical image segmentation , 2004, Medical Image Anal..

[13]  Chih-Chin Lai,et al.  A Hybrid Approach Using Gaussian Smoothing and Genetic Algorithm for Multilevel Thresholding , 2004, Int. J. Hybrid Intell. Syst..

[14]  Aly A. Farag,et al.  Threshold selection based on histogram modeling , 1992, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics.

[15]  Andrew K. C. Wong,et al.  A gray-level threshold selection method based on maximum entropy principle , 1989, IEEE Trans. Syst. Man Cybern..

[16]  Xavier Cufí,et al.  Yet Another Survey on Image Segmentation: Region and Boundary Information Integration , 2002, ECCV.

[17]  Marina Meila,et al.  Comparing clusterings: an axiomatic view , 2005, ICML.

[18]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[19]  Paul L. Rosin.  Unimodal thresholding , 2001, Pattern Recognit..

[20]  R. Kayalvizhi,et al.  Modified bacterial foraging algorithm based multilevel thresholding for image segmentation , 2011, Eng. Appl. Artif. Intell..

[21]  Bülent Sankur,et al.  Survey over image thresholding techniques and quantitative performance evaluation , 2004, J. Electronic Imaging.

[22]  Ge Yu,et al.  An Efficient Iterative Optimization Algorithm for Image Thresholding , 2004, CIS.

[23]  Hui Zhang,et al.  Image segmentation evaluation: A survey of unsupervised methods , 2008, Comput. Vis. Image Underst..

[24]  P.K Sahoo,et al.  A survey of thresholding techniques , 1988, Comput. Vis. Graph. Image Process..

[25]  King-Sun Fu,et al.  A survey on image segmentation , 1981, Pattern Recognit..

[26]  Shu-Kai S. Fan,et al.  Optimal multi-thresholding using a hybrid optimization approach , 2005, Pattern Recognit. Lett..

[27]  Qingmao Hu,et al.  On minimum variance thresholding , 2006, Pattern Recognit. Lett..

[28]  Allen Y. Yang,et al.  Unsupervised segmentation of natural images via lossy data compression , 2008, Comput. Vis. Image Underst..

[29]  Jan Havrda,et al.  Quantification method of classification processes. Concept of structural a-entropy , 1967, Kybernetika.

[30]  A. D. Brink.  Thresholding of digital images using two-dimensional entropies , 1992, Pattern Recognit..

[31]  Gurdial Arora,et al.  A thresholding method based on two-dimensional Renyi's entropy , 2004, Pattern Recognit..

[32]  Ming-Huwi Horng,et al.  Multilevel Image Thresholding Selection Using the Artificial Bee Colony Algorithm , 2010, AICI.

[33]  Ahmed S. Abutaleb,et al.  Automatic thresholding of gray-level pictures using two-dimensional entropy , 1989, Comput. Vis. Graph. Image Process..

[34]  Peng-Yeng Yin,et al.  Multilevel minimum cross entropy threshold selection based on particle swarm optimization , 2007, Appl. Math. Comput..

[35]  Ge Yu,et al.  An efficient iterative algorithm for image thresholding , 2008, Pattern Recognit. Lett..

[36]  Amitava Chatterjee,et al.  A hybrid cooperative-comprehensive learning based PSO algorithm for image segmentation using multilevel thresholding , 2008, Expert Syst. Appl..

[37]  Martial Hebert,et al.  Toward Objective Evaluation of Image Segmentation Algorithms , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[38]  Max Mignotte,et al.  Segmentation by Fusion of Histogram-Based $K$-Means Clusters in Different Color Spaces , 2008, IEEE Transactions on Image Processing.

[39]  Lorenzo Bruzzone,et al.  Image thresholding based on the EM algorithm and the generalized Gaussian distribution , 2007, Pattern Recognit..

[40]  Wenbing Tao,et al.  Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm , 2003, Pattern Recognit. Lett..

[41]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[42]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[43]  Peng-Yeng Yin,et al.  A fast scheme for optimal thresholding using genetic algorithms , 1999, Signal Process..

[44]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[45]  H. D. Cheng,et al.  Thresholding using two-dimensional histogram and fuzzy entropy principle , 2000, IEEE Trans. Image Process..

[46]  Pierre Soille,et al.  Local Mutual Information for Dissimilarity-Based Image Segmentation , 2014, Journal of Mathematical Imaging and Vision.

[47]  H. R. Keshavan,et al.  An optimal multiple threshold scheme for image segmentation , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[48]  Martial Hebert,et al.  A Measure for Objective Evaluation of Image Segmentation Algorithms , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops.

[49]  Prasanna K. Sahoo,et al.  Image thresholding using two-dimensional Tsallis-Havrda-Charvát entropy , 2006, Pattern Recognit. Lett..

[50]  Sankar K. Pal,et al.  A review on image segmentation techniques , 1993, Pattern Recognit..

[51]  Martial Hebert,et al.  A Comparison of Image Segmentation Algorithms , 2005 .

[52]  Constantino Tsallis,et al.  I. Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Status , 2001 .

[53]  Michael W. Berns,et al.  Digital Image Processing and Analysis , 1986 .

[54]  Swagatam Das,et al.  A Differential Evolution Based Approach for Multilevel Image Segmentation Using Minimum Cross Entropy Thresholding , 2011, SEMCCO.

[55]  Patrick Siarry,et al.  A multilevel automatic thresholding method based on a genetic algorithm for a fast image segmentation , 2008, Comput. Vis. Image Underst..

[56]  Andrew K. C. Wong,et al.  A new method for gray-level picture thresholding using the entropy of the histogram , 1985, Comput. Vis. Graph. Image Process..

[57]  Athanasios V. Vasilakos,et al.  On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[58]  N. Pavesic,et al.  Gray level thresholding using the Havrda and Charvat entropy , 2000, 2000 10th Mediterranean Electrotechnical Conference. Information Technology and Electrotechnology for the Mediterranean Countries. Proceedings. MeleCon 2000 (Cat. No.00CH37099).

[59]  Ling-Hwei Chen,et al.  A fast iterative scheme for multilevel thresholding methods , 1997, Signal Process..

[60]  Ahmed S. Abutableb.  Automatic thresholding of gray-level pictures using two-dimensional entropy , 1989 .

[61]  Shu-Kai S. Fan,et al.  A multi-level thresholding approach using a hybrid optimal estimation algorithm , 2007, Pattern Recognit. Lett..

[62]  Jitendra Malik,et al.  A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[63]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[64]  Korris Fu-Lai Chung,et al.  A novel image thresholding method based on Parzen window estimate , 2008, Pattern Recognit..

[65]  H. D. Cheng,et al.  Threshold selection based on fuzzy c-partition entropy approach , 1998, Pattern Recognit..

[66]  Thierry Pun,et al.  Entropic thresholding, a new approach , 1981 .

[67]  Prasanna K. Sahoo,et al.  Threshold selection using Renyi's entropy , 1997, Pattern Recognit..