Elsevier

Neurocomputing

Volume 240, 31 May 2017, Pages 152-174
Neurocomputing

Modified firefly algorithm based multilevel thresholding for color image segmentation

https://doi.org/10.1016/j.neucom.2017.02.040Get rights and content

Highlights

  • A modified firefly algorithm (MFA) is proposed.

  • MFA algorithm is used for multilevel color image thresholding segmentation.

  • Kapur's entropy, minimum cross entropy and between-class variance are used as objective functions.

  • MFA algorithm is an effective multilevel thresholding method for color image segmentation.

Abstract

In this paper, a modified firefly algorithm (MFA) is proposed to find the optimal multilevel threshold values for color image. Kapur's entropy, minimum cross entropy and between-class variance method is used as the objective functions. To test and analyze the performance of the MFA algorithm, the presented method are tested on ten test color image and the results are compared with basic firefly algorithm (FA), Brownian search based firefly algorithm (BFA) and Lévy search based firefly algorithm (LFA). The experimental results show that the presented MFA algorithm outperforms all the other algorithms in term of the optimal threshold value, objective function, PSNR, SSIM value and convergence. In MFA algorithm, chaotic map is used to the initialization of firefly population, which can enhance the diversification. In addition, global search method of particle swarm optimization (PSO) algorithm is introduced into the movement phase of fireflies. Compared with the other methods, the MFA algorithm is an effective method for multilevel color image thresholding segmentation.

Introduction

Image segmentation is a critical preprocessing step in computer vision and pattern recognition. Basically, it is the technique of partitioning an image into different regions or objects and extracting the meaningful and interested objects. More precisely, image segmentation is the process of dividing an image into several non-overlapping regions, based on gray scale, color, texture, shape, size or position of image. Each of the pixels in the same region has some similar characteristic or computed property, but the pixels of adjacent regions has significantly different characteristic [1]. Now image segmentation methods have been widely used in various fields of applications.

Over the years, many scholars and researchers have done a lot of work in image segmentation. Nowadays there are several methods and algorithms for image segmentation. Image segmentation methods can be divided into four types: (1) histogram-thresholding-based methods; (2) clustering-based methods; (3) texture analysis-based methods; (4) region based split and merging methods [2], and thresholding is a simple and most widely used method for image segmentation. Thresholding techniques can be classified into two different types: bi-level and multilevel thresholding. If the objects are clearly distinguished from the background of an image by a single threshold value, it is termed as bi-level thresholding; while dividing an image into several different segments by multiple threshold values is known as multilevel thresholding. Over the years, multilevel thresholding techniques play an important role in image analysis and many scholars and researchers have done a lot of work on it.

Over the years numerous thresholding techniques have been reported in the related literatures [3]. In 1979, Otsu [4] presented a thresholding technique that obtains optimal threshold values by maximizing the between-class varianc. In 1985, Tsai [5] proposed a robust technique for gray image thresholding by using the moment-preserving principle. Kapur et al. [6] used the entropy of the histogram to find optimal thresholds called Kapur entropy method and the technique has been widely used for image thresholding segmentation problem. Minimum cross entropy method is used to minimizing the cross entropy between the original image and its segmented image to find optimal thresholding [7].These techniques can be easily extended to multilevel thresholding segmentation. However the computational time will quickly increase when extend to multilevel thresholding since they exhaustively search the optimal threshold values to optimize the objective functions.

Optimization is a term used to find the optimal solutions of a problem for satisfying certain constraint conditions [8]. The process of searching optimal threshold values of a given image is considered as a constrained optimization problem. Therefore, to solve the problems of computational inefficiency of conventional thresholding techniques, swarm intelligence (SI) algorithms are used extensively for multilevel thresholding problem to search optimal threshold values using different objective function. Over the years, many swarm intelligence algorithms and their improved algorithms have been used for multilevel thresholding such as genetic algorithm (GA) [9], [10], particle swarm optimization (PSO) [11], [12], [13], [14], artificial bee colony (ABC) algorithm [15], [16], [17], [18], differential evolution (DE) algorithm [19], [20], [21], cuckoo search (CS) algorithm [22], [23], Glowworm swarm optimization (GSO) algorithm [24], [25] and Bat algorithm (BA) [26], [27]. Swarm intelligence algorithm has become increasingly popular in recent years that refer to the collective behavior of nature or artificial system. The term was first introduced by Beni and Wang in the paper of Swarm Intelligence in Cellular Robotic Systems [28]. The behavior of the individuals is very simple, but when they work together they exhibit coordinated behavior that lead the swarms to find good solution.

In 2008, Yang proposed firefly algorithm (FA), a novel swarm intelligence algorithm, mimicking the glow behavior of fireflies in nature [29]. The algorithm belongs to stochastic algorithm and many simulation results in the related literatures reveals that the FA algorithm has better performance in relation to other swarm intelligence techniques. Since its inception, FA algorithm has been used in several applications and complex optimization problems [30], [31], [32], [33], [34], and it also has been used for multilevel thresholding segmentation problem.

In 2010, Horng and Jiang [35] proposed a new multilevel maximum entropy thresholding algorithm based on the firefly algorithm (FA) and the results show that the proposed algorithm has better performance for multilevel thresholding. After that, in 2011, Hassanzadeh et al. [36] incorporated maximum variance Intra-cluster with firefly algorithm for multilevel thresholding segmentation. Horng and Liou [37] presented a new multilevel thresholding algorithm called the firefly-based minimum cross entropy thresholding (FF-based MCET) algorithm. The simulation results demonstrate that the FF-based MCET algorithm is superior to particle swarm optimization (PSO), quantum particle swarm optimization (QPSO) and honey bee mating optimization (HBMO) algorithm based on minimum cross entropy method. In addition, Brajevic and Tuba [38] applied firefly algorithm to multilevel image thresholding and used Kapur's entropy and between-class variance as objective functions. The experimental results show that firefly algorithm has superior performance and robustness.

Color images contains more information than gray images, therefore multilevel color image thresholding segmentation techniques have been drawn much attention during recent years. Recently, firefly algorithm (FA) has been also used for color image multilevel thresholding segmentation problem. Rajinikanth and Couceiro [39] proposed new multilevel thresholding method using Brownian search based firefly algorithm (BFA), Lévy search based firefly algorithm (LFA), and firefly algorithm (FA) based on between-class variance method for color image segmentation and the performance of FA, LFA and BFA algorithm are compared in terms of the optimal values, objective value, PSNR, SSIM and CPU time. The results show that the convergence time of both LFA and FA seem better than BFA and the objective function values obtained with the BFA are superior.

Kapur's entropy, minimum cross entropy and between-class variance techniques are often used in thresholding segmentation and can be easily extended to multilevel thresholding. They are very efficient for bi-level thresholding, but are very time consuming when the number of thresholds grows exponentially. So many swarm intelligence algorithms based on Kapur's entropy minimum cross entropy and between-class variance are used for multilevel thresholding problem. In 2011, Sathya and Kayalvizhi [40] proposed a new multilevel thresholding method using modified bacterial foraging (MBF) algorithm based on Kapur's entropy and between-class variance. After that, in 2013, two swarm intelligence algorithms, particle swarm optimization (PSO) and artificial bee colony (ABC), have been used for multilevel thresholding. Kapur's entropy and between-class variance have been investigated as objective functions [41]. In 2014, Bhandari et al. [42] presented two new multilevel thresholding methods using Kapur's entropy which are based on cuckoo search (CS) algorithm and wind driven optimization (WDO). Recently, a modified artificial bee colony (MABC) algorithm using and between-class variance has been proposed to find the optimal multilevel thresholds [43]. For minimum cross entropy, the researcher Yin [44] presented an efficient method using particle swarm optimization algorithm based on minimum cross entropy to search optimal threshold values for multilevel thresholding. After that Horng [45] proposed a new multilevel minimum cross entropy thresholding method based on honey bee mating optimization (HBMO) algorithm and the results are validated that the presented method is efficient for multilevel thresholding segmentation problem. Recently, Sarkar et al. [46] proposed a novel thresholding method for color image segmentation using minimum cross entropy based on differential evolution.

In order to improve the performance of the standard FA algorithm and obtain an efficient method for multilevel color image thresholding segmentation, a modified firefly algorithm (MFA) based color image segmentation using Kapur's entropy, minimum cross entropy and between-class variance is proposed in this paper. Any meta-heuristic algorithm has two important components: exploitation and exploration, or intensification and diversification [47]. Intensification means to search around the current best solutions are found, while diversification means to explore the search space on the global scale. The standard FA use random distribution in the initialization phase of fireflies, the chaotic map is used to enhance diversification and avoid trap into local optima in MFA algorithm. In the movement phase of standard FA, each firefly do local search and do not memorize any history of global best in each iteration process that causes they miss their best situations. So, the new movement equation is inspired by particle swarm optimization (PSO) algorithm in this paper. The performance of MFA algorithm using Kapur's entropy, minimum cross entropy and between-class variance for multilevel color image thresholding segmentation is measured in terms of optimal thresholding values, objective functions, peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM), in comparison with other algorithms such as FA, BFA and LFA algorithm, and draw the convergence curves of best objective functions.

The rest of this paper is organized as follows. Kapur's entropy, minimum cross entropy and between-class variance method is reviewed in Section 2. Section 3 describes the standard firefly algorithm and modified firefly algorithm. In Section 4, the experimental results of the modified FA for multilevel color image thresholding segmentation using Kapur's entropy, minimum cross entropy and between-class variance method are shown and followed by a comparison between FA, BFA and LFA algorithm. Finally, the conclusion and analysis is drawn in Section 5.

Section snippets

Problem assessment of multilevel thresholding

The process of searching optimal thresholding values of a given image is considered as a constrained optimization problem.

For bi-level thresholding, the problem is to find an optimal value T*. If the image intensity Ii, j is less than the value T*, the pixel in an image is replaced with a black pixel or a white pixel if the image intensity is greater than that constant T*, the expression can be stated as follows: g(x,y)={1iff(x,y)>T*0iff(x,y)<T*

The problem can be extended to multilevel

Firefly algorithm

A brief description of the basic firefly algorithm and the modified firefly algorithm is presented in the following subsections.

Experiment setup

In computer science, mathematics, and management science, optimization is the process of selecting a best solution from some set of available alternatives. In other words, optimization is the method of computing the value of function and finding the optimal results by maximizing and minimizing an objective function within a given domain. So the objective functions play an important role in optimization problem. In this paper, Kapur's entropy, minimum cross entropy (MCE) and between-class

Conclusion

In this paper, a new multilevel thresholding method for color image segmentation based on modified firefly algorithm (MFA) is proposed. Three different objective functions, Kapur's entropy, minimum cross entropy and between-class variance are used. The proposed method is used to search the optimal threshold values for the ten test color images for m=4,5,6 and 7. In order to verify the efficiency and effectiveness of the MFA algorithm, optimal threshold value, objective function, PSNR and SSIM

Acknowledgments

This work was supported by the National Nature Science Foundation of China (No. 51204077) and the Nature Science Foundation of Kunming University of Science and Technology (No. 2014-9-x-8).

Lifang He received the B.S. degree in Electronics and Communications Engineering from the Kunming University of Science and Technology, China in 2002, the Ph.D. degrees in Mineral processing equipment automation from the Kunming University of Science and Technology, China in 2014. Since 2005 she has been with the Kunming University of Science and Technology, where she is currently an associate professor in the Department of Information Engineering. Her current research interest includes image

References (56)

  • S. Agrawal et al.

    Tsallis entropy based optimal multilevel thresholding using cuckoo search algorithm

    Swarm Evol. Comput.

    (2013)
  • YeZ.W. et al.

    Fuzzy entropy based optimal thresholding using bat algorithm

    Appl. Soft Comput.

    (2015)
  • L.F.F. Miguel et al.

    Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms

    Expert Syst. Appl.

    (2012)
  • I. Fister et al.

    A comprehensive review of firefly algorithms

    Swarm Evol. Comput.

    (2013)
  • H. Shareef et al.

    Power quality and reliability enhancement in distribution systems via optimum network reconfiguration by using quantum firefly algorithm

    Int. J. Electr. Power Energy Syst.

    (2014)
  • S. Debbarma et al.

    Solution to automatic generation control problem using firefly algorithm optimized I λ D µ controller

    ISA Trans.

    (2014)
  • M.H. Horng et al.

    Multilevel minimum cross entropy threshold selection based on the firefly algorithm

    Expert Syst. Appl.

    (2011)
  • V. Rajinikanth et al.

    RGB histogram based color image segmentation using firefly algorithm

    Proc. Comput. Sci.

    (2015)
  • P.D. Sathya et al.

    Modified bacterial foraging algorithm based multilevel thresholding for image segmentation

    Eng. Appl. Artif. Intell.

    (2011)
  • B. Akay

    A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding

    Appl. Soft Comput.

    (2013)
  • A.K. Bhandari et al.

    Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur's entropy

    Expert Syst. Appl.

    (2014)
  • A.K. Bhandari et al.

    Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur's, Otsu and Tsallis functions

    Expert Syst. Appl.

    (2015)
  • P.Y. Yin

    Multilevel minimum cross entropy threshold selection based on particle swarm optimization

    Appl. Math. Comput.

    (2007)
  • M.H. Horng

    Multilevel minimum cross entropy threshold selection based on the honey bee mating optimization

    Expert Syst. Appl.

    (2010)
  • S. Sarkar et al.

    A multilevel color image thresholding scheme based on minimum cross entropy and differential evolution

    Pattern Recognit. Lett.

    (2015)
  • P.D. Sathya et al.

    Optimal multilevel thresholding using bacterial foraging algorithm

    Expert Syst. Appl.

    (2011)
  • P.D. Sathya et al.

    Modified bacterial foraging algorithm based multilevel thresholding for image segmentation

    Expert Syst. Appl.

    (2011)
  • B. Sowmya et al.

    Colour image segmentation using fuzzy clustering techniques and competitive neural network

    Appl. Soft Comput.

    (2011)
  • Cited by (0)

    Lifang He received the B.S. degree in Electronics and Communications Engineering from the Kunming University of Science and Technology, China in 2002, the Ph.D. degrees in Mineral processing equipment automation from the Kunming University of Science and Technology, China in 2014. Since 2005 she has been with the Kunming University of Science and Technology, where she is currently an associate professor in the Department of Information Engineering. Her current research interest includes image segmentation, artificial intelligence and swarm intelligence algorithm.

    Songwei Huang received the B.S. degree in Automatic control from the Kunming University of Science and Technology, China in 1989. Since 2009 he has been with the Kunming University of Science and Technology, where he is currently a professor in the Department of Automatic control. His current research interest includes image processing, pattern recognition and artificial vision.

    View full text