Multi-level thresholding with a decomposition-based multi-objective evolutionary algorithm for segmenting natural and medical images

Display Omitted A novel bi-objective formulation of multi-level thresholding entropy functions.Application of evolutionary multi-objective optimization for threshoding.Extensive comparative study among MOEAs on the segmentation problem.Well known dataset and performance evolutions are used for performance assessments. The objective of multilevel thresholding is to segmenting a gray-level image into several distinct homogeneous regions. This paper presents an alternative approach for unsupervised segmentation of natural and medical images to improve the separation between objects in the framework of multi-objective optimization. In contrast to the existing single-objective optimization and entropy-based methods, a multi-objective framework is adopted by combining two objectives based on the Minimum Cross Entropy (MCE) and Renyi Entropy (RE). One of the most competitive Multi-Objective Evolutionary Algorithms (MOEAs) of current interest, called MOEA/D-DE (Decomposition based MOEA with Differential Evolution) is then applied to determine the set of Pareto optimal solutions for these two objectives. The threshold values for multi-level segmentations are obtained from the approximated Pareto Fronts (PFs) generated by MOEA/D-DE. The performance of MOEA/D-DE is also investigated extensively through comparison with other popular nature-inspired single-objective and multi-objective optimizers. Moreover, outcome of the proposed method is evaluated by comparing against the results of other well cited algorithms both qualitatively and quantitatively on test-suites comprising well-known natural and medical test images in order to showcase the efficiency of the proposed algorithm.

[1]  Wei Liu,et al.  Fuzzy entropy based optimal thresholding using bat algorithm , 2015, Appl. Soft Comput..

[2]  Swagatam Das,et al.  Hyper-spectral image segmentation using Rényi entropy based multi-level thresholding aided with differential evolution , 2016, Expert Syst. Appl..

[3]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

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

[5]  Shang Gao,et al.  An improved scheme for minimum cross entropy threshold selection based on genetic algorithm , 2011, Knowl. Based Syst..

[6]  Solomon Kullback,et al.  Information Theory and Statistics , 1970, The Mathematical Gazette.

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

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

[9]  Ashish Kumar Bhandari,et al.  Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur's, Otsu and Tsallis functions , 2015, Expert Syst. Appl..

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

[11]  Chun-hung Li,et al.  Minimum cross entropy thresholding , 1993, Pattern Recognit..

[12]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[14]  Millie Pant,et al.  Multi-level image thresholding by synergetic differential evolution , 2014, Appl. Soft Comput..

[15]  Brian B. Avants,et al.  The Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) , 2015, IEEE Transactions on Medical Imaging.

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

[17]  Weiyu Yu,et al.  Multi-level threshold selection based on artificial bee colony algorithm and maximum entropy for image segmentation , 2012, Int. J. Comput. Appl. Technol..

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

[19]  Swagatam Das,et al.  A multilevel color image thresholding scheme based on minimum cross entropy and differential evolution , 2015, Pattern Recognit. Lett..

[20]  Aizhu Zhang,et al.  A novel hybrid algorithm of gravitational search algorithm with genetic algorithm for multi-level thresholding , 2016, Appl. Soft Comput..

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

[22]  Prasanta K. Panigrahi,et al.  Multilevel thresholding for image segmentation through a fast statistical recursive algorithm , 2006, Pattern Recognit. Lett..

[23]  Ujjwal Maulik,et al.  New quantum inspired meta-heuristic techniques for multi-level colour image thresholding , 2016, Appl. Soft Comput..

[24]  P. Siarry,et al.  Non-supervised image segmentation based on multiobjective optimization , 2008, Pattern Recognit. Lett..

[25]  C. H. Li,et al.  An iterative algorithm for minimum cross entropy thresholding , 1998, Pattern Recognit. Lett..

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

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

[28]  Amir Nakib,et al.  Fractional differentiation and non-Pareto multiobjective optimization for image thresholding , 2009, Eng. Appl. Artif. Intell..

[29]  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).

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

[31]  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..

[32]  Ujjwal Maulik,et al.  Unsupervised Pixel Classification in Satellite Imagery Using Multiobjective Fuzzy Clustering Combined With SVM Classifier , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Ashish Kumar Bhandari,et al.  Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur's entropy , 2014, Expert Syst. Appl..

[34]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

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

[36]  Ming-Huwi Horng,et al.  Multilevel minimum cross entropy threshold selection based on the firefly algorithm , 2011, Expert Syst. Appl..

[37]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

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

[39]  Bijaya K. Panigrahi,et al.  Tsallis entropy based optimal multilevel thresholding using cuckoo search algorithm , 2013, Swarm Evol. Comput..

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

[41]  Ujjwal Maulik,et al.  Multiobjective Genetic Clustering for Pixel Classification in Remote Sensing Imagery , 2007, IEEE Transactions on Geoscience and Remote Sensing.

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

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

[44]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[45]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[46]  Qingfu Zhang,et al.  The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances , 2009, 2009 IEEE Congress on Evolutionary Computation.

[47]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

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

[49]  Ming-Huwi Horng,et al.  Multilevel thresholding selection based on the artificial bee colony algorithm for image segmentation , 2011, Expert Syst. Appl..

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

[51]  Swagatam Das,et al.  Multilevel Image Thresholding Based on 2D Histogram and Maximum Tsallis Entropy— A Differential Evolution Approach , 2013, IEEE Transactions on Image Processing.

[52]  Sheli Sinha Chaudhuri,et al.  A Differential Evolutionary Multilevel Segmentation of Near Infra-Red Images Using Renyi’s Entropy , 2013 .

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

[54]  Bahriye Akay,et al.  A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding , 2013, Appl. Soft Comput..

[55]  Scott T. Acton,et al.  Learning automata for image segmentation , 2016, Pattern Recognit. Lett..