Hyper-heuristic method for multilevel thresholding image segmentation

Highlights

• An alternative multi-level image segmentation method is proposed.

• Proposed method depends on hyper-heuristic concepts which consists of two layers.

• In the first layer, the GA is used to control the algorithms in the second layer.

• Meta-heuristic algorithms are used in the second layer to find optimal thresholds.

• Based on experimental results, the proposed method outperforms other algorithms.

Abstract

In digital image processing, one of the most relevant tasks is to classify pixels depending on their intensity level. To perform this process there exist different traditional methods as Otsu or Kapur, such methods are used to compute the thresholds that divide the histogram of the image into different groups. These methods are easy to implement for a single threshold; however, the computational effort is affected when more thresholds are required. Therefore, different meta-heuristic based approaches have been proposed, but each of them has its properties and limitations. So, this paper introduces an alternative concept to the image segmentation which is called hyper-heuristic that at each iteration determines the optimal execution sequence of meta-heuristic algorithms that provides the optimal thresholds. The proposed method consists of two layers, in the first layer, the genetic algorithm (GA) is used to determine the execution sequence of the meta-heuristic algorithms. While the second layer contains the set of four meta-heuristic algorithms that executed in a specific order, assigned by the current solution of GA, to update the threshold population. In order to evaluate the performance of the proposed approach, it has been tested over a set of benchmark images and the results provide a good performance in terms of quality of segmentation. Moreover, experimental comparisons support that the proposed hyper-heuristic is able to find more accurate solutions than other algorithms.

Introduction

One of the most important problems in image processing is to divide the pixels into different groups that permit to separate and identify the objects contained in the scene (El Aziz, Ewees, & Hassanien, 2017). There exist different approaches to solve this task; however, the simplest is the segmentation by using thresholds. This process considers only two factors: 1) the histogram of the image and 2) a set of thresholds. In this context, the thresholds are used to divide the histogram into different classes. When only one threshold is used for image segmentation, the pixels are divided into two classes; this process is called bi-level thresholding. Meanwhile, when the pixels are divided into three or more classes using more than one threshold it is called multilevel thresholding (MTH). Here the main problem is to find the best configuration of thresholds for each image according to the number of classes that the user wants to identify (objects in the image).

For proper identification of the thresholds, different measures as the entropy or the variance are used. Two classical approaches are the intra-class variance proposed by Otsu (1979) and the Kapur’s entropy (Kapur, Sahoo, & Wong, 1985). These methods are very effective in finding a single threshold. However, when it is necessary to divide the image into more than two classes, the complexity increases considerably. To affront this problem, the use of meta-heuristic Algorithms (MA) has been introduced that in most cases provide very accurate results.

The MA are interesting tools for solving complex optimization problems with a high degree of accuracy (Ewees, Elaziz, & Houssein, 2018). In related literature, they have proposed different MA for MTH such as Genetic Algorithms (GA) (Hammouche, Diaf, Siarry, 2008, Tang, Yuan, Sun, Yang, Gao, 2011, Zhang, Li, Tang, Lu, Zheng, Zhou, 2014), Particle Swarm Optimization (PSO) (Gao, Pun, Kwong, 2016, Gao, Xu, Sun, Tang, 2010, Maitra, Chatterjee, 2008, Yin, 2007), Differential Evolution (DE) (Ali, Siarry, Pant, 2012, Cuevas, Zaldivar, Pérez-Cisneros, 2010), Social Spider Optimization (SSO) (Ouadfel & Taleb-Ahmed, 2016), Flower Pollination Algorithm (FPA) (Ouadfel & Taleb-Ahmed, 2016), Whale Optimization Algorithm (El Aziz, Ewees, Hassanien, 2018a, El Aziz, Ewees, Hassanien, Mudhsh, Xiong, 2018b), and Crow Search Algorithm (CSA) (Oliva et al., 2017). However, since each image can be considered as an independent optimization problem, not all the MA provide accurate results using the Otsu’s and Kapur’s objective functions. In other words, one algorithm can find the best configuration of thresholds for a specific image but not for others.

Besides, these meta-heuristic methods have some limitations, such as they need more information about the domain of searching and their parameters must be tuned during the searching process. In PSO (Poli, Kennedy, & Blackwell, 2007), each particle of the PSO population represents the solution of the given problem. This means that the problem information (search space) is a very important factor in the design of particles. Considering this situation, a high dependency on the search knowledge leads to the high difficulty of reusing the particles to solve other problems. Also, according to the No Free Lunch Theorem (Wolpert & Macready, 1997), any optimization method can be considered the best in all problems because each one has limitation and advantages that can be effective for some problems. Considering above, it is necessary to use a strategy to decide when it is better to use one MA or other. So, this paper is motivated in search for the methods that can combine the strength and avoid the limitations of the meta-heuristic methods.

On the other hand, hyper-heuristics (HH) are interesting tools that combine, select or adapt single heuristic mechanism to solve complex optimization problems (Burke, Kendall, Newall, Hart, Ross, Schulenburg, 2003, Gomez, Terashima-Marín, 2018). Basically, a HH combines the features of single algorithms using the configuration for a specific problem. In the related literature, there exist two groups of HH’s, 1) Selection HH’s and 2) Generation HH’s. The Selection HH’s intelligent mechanism of heuristics and meta-heuristics, considering such information the HH are able to decide which algorithm to apply. Meanwhile, Generation HH’s creates new heuristics using the operators of existing methods (Burke, Gendreau, Hyde, Kendall, Ochoa, Özcan, Qu, 2013, Burke, Hyde, Kendall, Ochoa, Özcan, Woodward, 2010). In general, the use of HH’s for hard optimization problems permits to avoid implementing the same algorithm for all the problems. Moreover, HH permits to test different heuristics and define the best for a specific problem. This article is based on Selection HH’s that is a topic highly explored by researchers. HH’s can be used with single heuristics and meta-heuristics. In this sense, different methods have been proposed. In Dowsland, Soubeiga, and Burke (2007), the Simulated Annealing and the Tabu Search algorithms are used to create a HH for determining shipper sizes for storage and transportation. Another HH with an interesting selection method called the Robinhood Hyper-Heuristic is introduced in (Kheiri & Özcan, 2013) for solving different benchmark problems. Meanwhile, the use of Genetic Algorithms in HH’s for a scheduling problem is proposed in (Cowling, Kendall, & Han, 2002).

In general, the HH method consists of two levels 1) high level and 2) low level. Where the low level that is called Low Level Heuristics (LLH) contains a set of local optimization methods and these heuristics depend on the problem and they are simple and their time computational is low. However, the high level contains one method that can be considered as a manger that determines the sequence of the working method in LLH’s (Burke et al., 2003).

In this paper, an alternative image segmentation based on HH’s is proposed. The aim of the proposed method is to enhance the image segmentation performance through determining the optimal threshold values in small CPU time(s). The proposed algorithm is similar to the traditional HH except at the low level the meta-heuristics are used instead of the local search methods. Whereas at the low level, four meta-heuristics namely: Sine cosine Algorithm (SCA) (Mirjalili, 2016), Social-Spider optimization (SSO) (Cuevas, Cienfuegos, ZaldíVar, & Pérez-Cisneros, 2013), Artificial Bee Colony (ABC) (Karaboga, 2005), and Firefly Algorithm (FA) (Yang, 2010) are used. Meanwhile, at the high level the GA is used to control the other four algorithms. The proposed method starts by generating a population for the GA algorithm. The solution in the population represents the sequence of integer numbers that represent the order of each algorithm, at low level, to be executed. Also, the threshold population is assigned as the initial population for low level methods. This population is updated by the first algorithm in the current solution of GA and then the second algorithm and the process continues until the fourth algorithm. This operation is performed for each solution in GA population. Thereafter, the best solution and the best population are selected based on the fitness function value either Kapur or Otsu. This best threshold population is considered as initial population for the low level methods in next iteration. Then the population of GA algorithm is updated using its own operators (crossover, mutation, selection). The steps of updating the GA’s population and the threshold population are repeated until reached to the terminal conditions. Due to the process of updating the threshold population depending on the best solution, the proposed method is called Hyper-heuristic Best (HHB). However, there exists a probability that the solutions in the other threshold populations are better than those solutions in the selected threshold population. Considering such situation, it also provided another version of the HHB called Hyper-heuristic Union Best (HHUB). In HHUB method, after all threshold populations (corresponding to each solution in GA’s) are updated, they are selected as the best top solutions from the union of all threshold populations to form the updated threshold population and select the best solution from the updated threshold solutions. The performance of the proposed method is evaluated using a set of images from Senn (2009), where the results present an evidence about the high quality of the proposed method to find the optimal threshold values in suitable CPU time(s).

Therefore, the main contribution of our paper can be summarized in the following points:

• Propose an alternative method for image segmentation.

• Propose a Hyper-heuristic algorithm method based on meta-heuristic methods.

• Evaluate the performance of the proposed method.

The structure of this paper is organized as follows: Section 2, discusses the definition of the multi-level threshold image segmentation problem and the meta-heuristic algorithms used along the paper. In Section 3, the proposed method is explained. Section 4 presents the experimental results of the proposed method against the other algorithms. Finally, conclusion and future works are introduced in Section 5.