Rough-Fuzzy Collaborative Multi-level Image Thresholding: A Differential Evolution Approach

In this article, a granular computing based multi-level gray image thresholding algorithm is presented. An image is divided into spatial blocks called granules, and the classes of gray levels are represented using a fuzzy-rough collaborative approach, where the measure of roughness of a rough set is also modified from the classical definition of rough sets. This measure for each rough set is minimized simultaneously to obtain the optimal thresholds. Tchebycheff decomposition approach is employed to transform this multi-objective optimization problem to a single objective optimization problem. Differential Evolution (DE), one of the most efficient evolutionary optimizers of current interest, is used to optimize this single objective function, thus reducing the execution time. Superiority of the proposed method is presented by comparing it with some popular image thresholding techniques. MSSIM index and Probabilistic Rand Index (PRI) are used for quantitative comparison on the Berkley Image Segmentation Data Set (BSDS300).

[1]  Didier Dubois,et al.  Putting Rough Sets and Fuzzy Sets Together , 1992, Intelligent Decision Support.

[2]  Yan Xu,et al.  Image decomposition based ultrasound image segmentation by using fuzzy clustering , 2009, 2009 IEEE Symposium on Industrial Electronics & Applications.

[3]  Yu-Jin Zhang,et al.  Ridler and Calvard's, Kittler and Illingworth's and Otsu's methods for image thresholding , 2012, Pattern Recognit. Lett..

[4]  Kohtaro Kohtaro The Tsallis entropy and the Shannon entropy of a universal probability , 2008, 2008 IEEE International Symposium on Information Theory.

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

[6]  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.

[7]  Feng Feng,et al.  Generalized Rough Fuzzy Sets Based on Soft Sets , 2009, 2009 International Workshop on Intelligent Systems and Applications.

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

[9]  D. Arar,et al.  A fast technique for gray level image thresholding and quantization based on the entropy maximization , 2008, 2008 5th International Multi-Conference on Systems, Signals and Devices.

[10]  Anders Eriksson,et al.  Image Segmentation Using Minimal Graph Cuts , 2006 .

[11]  Kalyanmoy Deb,et al.  A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization , 2002, Evolutionary Computation.

[12]  Humberto Bustince,et al.  Image thresholding using restricted equivalence functions and maximizing the measures of similarity , 2007, Fuzzy Sets Syst..

[13]  Swagatam Das,et al.  Multi-level image segmentation based on fuzzy - Tsallis entropy and differential evolution , 2013, 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

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

[15]  Qinghua Hu,et al.  On Robust Fuzzy Rough Set Models , 2012, IEEE Transactions on Fuzzy Systems.

[16]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[17]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[18]  Qinghua Hu,et al.  Communication Between Information Systems Using Fuzzy Rough Sets , 2013, IEEE Transactions on Fuzzy Systems.

[19]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[20]  Xin Meng,et al.  A fast region-based image segmentation based on least square method , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[21]  Mario Beauchemin,et al.  Image thresholding based on semivariance , 2013, Pattern Recognit. Lett..

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

[23]  Hamid R. Tizhoosh,et al.  Image thresholding using type II fuzzy sets , 2005, Pattern Recognit..

[24]  Witold Pedrycz,et al.  Granular computing: an introduction , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[25]  Sankar K. Pal,et al.  Granular computing, rough entropy and object extraction , 2005, Pattern Recognit. Lett..

[26]  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).

[27]  Zhiguo Cao,et al.  Entropic image thresholding based on GLGM histogram , 2014, Pattern Recognit. Lett..

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

[29]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

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

[31]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[32]  Ying-Tung Hsiao,et al.  A contour based image segmentation algorithm using morphological edge detection , 2005, 2005 IEEE International Conference on Systems, Man and Cybernetics.

[33]  Masoumeh Bourjandi Image Segmentation Using Thresholding by Local Fuzzy Entropy-Based Competitive Fuzzy Edge Detection , 2009, 2009 Second International Conference on Computer and Electrical Engineering.

[34]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[35]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.