RANDOM ADJUSTMENT - BASED CHAOTIC METAHEURISTIC ALGORITHMS FOR IMAGE CONTRAST ENHANCEMENT

Metaheuristic algorithm is a powerful optimization method, in which it can solve problems by exploring the ordinarily large solution search space of these instances, that are believed to be hard in general. However, the performances of these algorithms significantly depend on the setting of their parameter, while is not easy to set them accurately as well as co mpletely relying on the problem’s characteristic. To fine-tune the parameters automatically, many methods have been proposed to address this challenge, including fuzzy logic, chaos, random adjustment and others. All of these methods for many years have been developed independently for automatic setting of metaheuristic parameters, and integration of two or more of these methods has not yet much conducted. Thus, a method that provides advantage from combining chaos and random adjustment is proposed. Some popular metaheuristic algorithms are used to test the performance of the proposed method, i.e. simulated annealing, particle swarm optimization, differential evolution, and harmony search. As a case study of this research is contrast enhancement for images of Cameraman, Lena, Boat and Rice. In general, the simulation results show that the proposed methods are better than the original metaheuristic, chaotic metaheuristic, and metaheuristic by random adjustment.


Introduction
Image enhancement is one of the main concerns in image processing that aims to improve the appearance of an image, to enhance their visual quality on human eyes, including to sharpen the features and to increase the contrast. Image enhancement it is useful to further image application, such as facilitating image segmentation, recognizing and interpreting useful information from the image, but does not increase nor decrea-se the essential information of the original image. In general, the image enhancement methods can be divided into four classes, i.e. contrast enhancement, edge enhancement, noise enhancement and edge restoration [1]. Among those techniques, contrast enhancement is the focus of this paper.
There are many variations of image enhancement algorithms have been proposed. Some of the famous methods are contrast manipulations and histogram equalization for enhancing the contrast image. Contrast manipulations or linear June 2017 contrast stretching employs a linear transformation that remaps the gray-levels in a given image to fill the full range of values, and histogram equalization applies a transformation that produces a close to uniform histogram for the relative frequency of the gray-levels in the image [2].
In recent times, many metaheuristic methods have been developed for image processing applications, including image enhancement problems. Some paper [2][3][4] report that these methods outperform for image contrast enhancement than classical point operation. Based on some principles of biology, physics or ethology; almost all of metaheuristic are nature-inspired. Other classifications form of this method is single-solution and population-based based metaheuristic [5].
Three main purposes of metaheuristic algorithm: solving large problems, solving prob-lems faster, and obtaining robust algorithms [6]. Besides, they are simple to design, flexible, and also not difficult to implement. However, setting parameters of these methods are not easy, and entirely depend on the problems. Some of the methods have been recommended to adjust the parameters of metaheuristic automatically . Liu and Lampinen [7] proposed FADE (fuzzy adaptive differential evolution), where the fuzzy logic is used to ad the param-eter controls of mutation and crossover. Di and Wang [8] use harmony search with chaos for training RBFNN (radial basis function neural network). Coelho et al. [1] use chaos to optimize DE for image contrast enhancement. Ferens et al [9] proposed CSA (chaotic simulated annealing) for task allocation in a multiprocessing system. Noman et al. [10] proposed adaptive DE (aDE) based on random adjustment, where the strategy is by com-paring the objective of spring with the average value of the current generation. Li et al. [11] introduced market-oriented task-level scheduling in cloud workflow systems using chaos to particle swarm optimization (PSO).
All of that methods have each of advantage on automatically adjusting of metaheuristic parameters, however, integration two or more of them are rarely conducted. In this paper, we integrate 2 methods, chaos and random adjustment for attaining benefit from both of them. Chaos can be used to avoid being trapped into a local minimum and to enrich the searching behavior. On the contrary, random adjustment can be applied to achieve greater accuracy. Four types of metaheuristic algorithms are selected to represent all categories for test the proposed method performance: physics phenomena and a single solution based represent by SA, biology phenomena and population-based represent by DE, ethologic phenomena and also population-based represent by PSO, and musical phenomena as well as population-based, represents by HS. This paper is organized as follows: Section 1 is introduction; Section 2 gives description of image contras enhancement; Section 3 describe the proposed methods; Section 4 we present simulation result; and conclusion of this paper in Section 5 (one blank single space line, 10 pt)

Image Contrast Enhancement
Contrast enhancement is applied to transform an image based on the psychophysical characteristics of the human visual system. Two techniques that are usually used for contrast enhancement are indirect and direct methods of contrast enhancement [12]. The indirect image contrast enhancement algorithms enhance the image without measuring the contrast. The direct local contrast enhancement algorithms create a criterion of contrast measure and improving the contrast measurement directly to enhance the images [1]. The proposed method in this paper are applied using a direct image enhancement approach to adjust the gray-level intensity transformation in the image. The setting up of a suitable image contrast measure is a critical step in direct image enhancement approach.
In spatial domain to the gray-level image, the enhancement uses transformation function. To generate the enhanced image, the transformation function generates a new intensity value for each pixel of original image as shown in equation (1).
where f(i, j) is the gray value of the (i, j)th pixel of the input images, h(i, j) is the gray value of the (i, j)th pixel of the enhanced images and S is the transformation function [4]. The contrast of the image can be measured locally and globally. A local contrast functions regarding the relative difference between a central region and a larger surrounding area of a given pixel. By some of the contrast enhancement functions, the contrast values are then enhanced. The enhancement function such as the square root function, the exponential, the logarithm and the trigonometric functions [12].
The transformation functions T that is based on the gray-level distribution in the neighborhood of every pixel in a given image, applied by local enhancement methods [7]. The following method applies to each pixel at the location (x, y) shown in equation (2), is used in this paper for a transformation function as shown in equation (2).
where (x,y) and m(x, y) are the standard deviation and the gray-level mean respectively, computed in a neighborhood centered at (x, y). Where M is the global mean of the image, f(x, y) and g (x, y) is the gray-level intensity and the pixels output graylevel intensity value of input image pixel at location (x, y) [1]. A nonzero value for q in (2) allows for zero standard deviation in the neighborhood while c allows for only a fraction of the mean m(x, y) to subtracted from the original pixels gray-level f(x, y). The last term m(x, y)p may have a brightening and smoothing effect on the image. The parameters of p, q, r and s defined over the positive real number and they are the same for the whole image [3]. According to an objective function that describes the contrast of the image, the task of metaheuristic in this formula is to find the combination of parameters p, q, r and s.
A criterion for enhancement method should be chosen to apply an automatic image enhancement technique, which does not require human intervention and no objective parameters are given by the user. This criterion will be directly related to the objective function of the metaheuristic methods. The objective function adopted in this paper for an enhancement criterion shown in equation (3).

Proposed Method
Most of the metaheuristic algorithms have relevant parameters, such as amplification factor (F) and crossover rate (CR) in DE, initialize temperature (T) and reduction factor (c) in SA, har-mony memory considering rate (HMCR) and pitch adjusting rate (PAR) in HS, as well as acceleration coefficients (c1, c2) in PSO. All of these parameters are usually sensitive, in while an improper setting of them can result in the poor performance of the system. Some studies have been conducted to adjust automatically these parameters based on the characteristic of the problems, including fuzzy logic, chaos, random adjustment, and others.
In this paper, we proposed a combination of chaos and random adjustment to improve the performance of some metaheuristic algorithms. Characteristic of chaos is nonlinear systems. Although it looks like to be stochastic, then it occurs in a deterministic nonlinear system under deterministic condition [13]. This method can avoid being trapped into local optimum and improve the performance of searching [1]. One of the systems is chaotic sequence, defined in equation (4).
where n and µ is sample parameter and control parameter. Substantially both of the param-eters decides whether x stabilizes at a constant size, behaves chaotically in an unpredictable pattern, or oscillates between a limited sequence of sizes. A very small difference in the initial value of x causes substantial differences in its long-time behavior. In this work, the variety of µ is 1 < µ < 4; x is distributed in the range [0, 1] provided the initial x(1) ∉ 0, 0.25, 0.50, 0.75, 1.
In case of random adjustment, for instances DE algorithms, the strategy by comparing objective value of the offspring f( ℎ ) with the average of objective value in current generation favg . If f( ℎ ) is better than favg , then mutation factor and crossover rate of the primary parent are retained in offspring, or else the parameters are changed randomly.

Random Adjustment-based Chaotic SA
Simulated annealing (SA) is a robust and compact technique was first proposed by Kirk-patrick et al. [14]. With a substantial reduction in computation time, SA provides excellent solutions to single and multiple objective optimization problems. The origin of this method is Metropolis algorithm [15]. Inspired by annealing technique, this method aims to obtain the solid state of minimal energy or ground states of matter. This technique consists in heating a material to the high temperature, then in lowering the temperature slowly.
The Boltzmann distribution is the quantitative key of SA method which species that the 70 Jurnal Ilmu Komputer dan Informasi (Journal of a Science and Information), volume 10, issue 2, June 2017 probability of being in any particular state x is given by equation (5).
where f(x) is the energy of the configuration, k is Boltzmanns constant, and T is temperature. In this paper, we proposed 3 variant of methods for chaotic SA based on random adjustment. First is CSARA-1, where parameter of k is replaced by generating the value from chaotic sequence. Otherwise, the reduction factor parameter c is adjusted randomly. This value of c is used in a process when the result of the new objective function is better than the old objective function, or when the random value r is bigger than the Boltzmann distribution p(x). This process will continue until the desired criteria have been achieved.
The second variant is CSARA-2, by replacing parameter of c with chaotic sequence and parameter of k is selected randomly. As long as the new objective function is better than the old objective function, or the random value of r is bigger than the value of p(x), the value of k is still used in the process.
The third variant is CSARA-3, in which the parameter of k is constant, and c is produced from a chaotic sequence. The value of c is not substituted, as long as the new objective function is better than the old objective function, or the random value of r is bigger than the value of p(x).

Random Adjustment-based Chaotic DE
Differential Evolution (DE) is one of the latest evolutionary algorithms proposed by Price and Storn in 1995 that applied to a continuous optimization problem. This method proposed to solve the chebyshev polynomial fitting problem and have proven for many different tasks to be a very reliable optimization strategy [5]. Starts by sampling the search space at multiple, DE algorithm randomly selected search points and creates new search points through perturbation of the existing points. DE creates new search points which are evaluated against their parents using the operation of differential mutation and recombination. Furthermore to promote the winners to the next generation, a selection mechanism is applied. Until the termination criterion is satisfied, this cycle is iterated [10]. Price et al. have suggested different variant of DE, which are conventionally named DE/x/y/z. DE/rand/1/bin is the classical version as shown in equation (6), the target vector is randomly selected in mutation process, and only one different vector is used. The acronym of bin indicates a binomial decision rule that controlled the crossover.
In this paper, we proposed 3 variant methods for DE. First is CDERA-1, where CR parameter is generated by chaotic sequence and mutation factor F is created randomly. On condition that new objective function is better than the average of old objective function, parameter of F is kept in used in the process. However, if not the new parameter of F is created randomly. All of the procedure will continue until the termination criterion is satisfied. The second variant is CDERA-2, where F parameter is created by chaotic sequence and CR parameter is selected randomly. In case of the new objective function is better than the average of old objective function, CR is kept in used in the process. Otherwise, CR is created randomly. The third variant is CDERA-3, in which the parameter of F is constant, and CR is created from chaotic sequence. The value of CR is not replaced, as long as the new objective function is better than the average of old objective function. Otherwise, it uses the next value of chaotic sequence.

Random Adjustment-based Chaotic PSO
Particle swarm optimization (PSO) is an adaptive algorithm based on social-psychological metaphor; a population of particles adapts by returning stochastically toward previously successful regions. The metaphor of the flocking behavior of birds uses by PSO to solve an optimization problem. Introduced in 1995 by J. Kennedy and R. Eberhart [16], this method was initial as a global optimization technique. In this algorithm, many particles are stochastically generated in the search space. As a candidate solution to the problem, each particle is represented by a velocity, a location in the search space and has a memory which helps it in remembering its previous best position. In the initialization phase of PSO, the position and velocities of all individuals are randomly initialized. The velocity defines direction and distance of particle should go. It is updated according to the equation (7).
where i = 1, 2, , N. N is the size of the swarm; pibest is the particle best-reached solution and gbest is the swarm global best solution. Two random numbers r1 and r2 are uniformly distributed in the Vina Ayumi and Aniati M. Arymurthy, Random Adjustment 71 range [0,1], constant multiplier terms c1 and c2 are known as acceleration coefficients. They represent the attraction that a particle has either towards its own success or towards the success of its neighbors, respectively. To overcome the premature convergence problem of PSO, the inertia weight ω is used. A large inertia weight encourages global exploration while a smaller inertia weight encourages local exploitation [5]. The position of each particle is also updated in every each iteration by adding the velocity vector +1 to the position vector, using equation (8).
In this paper, we proposed three alternative methods for PSO. First is CPSORA-1, where parameters of r1 and r2 are replaced by generating their values from the chaotic sequence. These values of r1 and r2 are kept in used as long as the new objective function is better than average objective function. Otherwise, the next value of the chaotic sequence is used. This process will continue until the desired criteria have been achieved. The second variant is CPSORA-2, where r1 is a constant value, and r2 is created from the chaotic sequence. On condition that the new objective function is better than the average of old objective function, r2 is kept in used in the process. Otherwise, it uses the next value of chaotic sequence The third variant is CPSORA-3, where essentially is the same with the second variant, but in this case, r1 is created from the chaotic sequence, and r2 is a constant value.

Random Adjustment-based Chaotic HS
Harmony search (HS) proposed by Zong Woo Geem et al in 2001 is a search algorithm considered to be a population-based. By the musical process of searching for a perfect state harmony, this method is inspired. The optimization solution vector analogous to the harmony in music, and the local and global search schemes in optimization techniques analogous to the musicians improvisations. The HS algorithm uses a stochastic random search that is based on the harmony memory considering rate (HMCR) and the pitch adjusting rate (PAR) so that derivative information is unnecessary [17].
Three possible options exist when a musici-an improvises one pitch: (1) playing any one pitch from his/her memory, (2) playing an adjacent pitch of one pitch from his/her memory, (3) playing a totally random pitch from the possible sound range. Similarly, when each decision variable chooses one value in the HS algorithm, it follows any one of three rules: (1) choosing any one value from HS memory (defined as memory considerations), (2) selecting an adjacent value of one value from the range (defined as pitch adjustments), (3) choosing the random value from the possible value range (defined as randomization) [17]. In this paper, 3 alternative methods for HS are proposed. First is CHSRA-1, where parameters of HMCR and PAR are replaced by generating their values from the chaotic sequence. These values are kept in used, as long as the new objective function is better than the averages the old objective function. Otherwise, the next value of the chaotic sequence is used. This process will continue until the desired criteria have been achieved. The second variant is CHSRA-2, where HMCR parameter is created by chaotic sequence and PAR parameter is selected randomly. In case of new objective function is better than average objective function; PAR is kept in used in process, else PAR is created randomly. The third variant is CHSRA-3, wherein essential is the same with the second variant. In this case, PAR is created from chaotic sequence, and HMCR is selected randomly.

Results and Analysis
The optimization problem in this paper is to enhance the image contrast using chaotic metaheuristic algorithms based on random adjustment approaches. The simulation objective is to increase the overall intensity at the edges, increasing the measurement of entropy, and maximize the number of pixel in the edges. Moreover, the simulation with original metaheuristic, metaheuristic use chaotic sequence, and metaheuristic by random adjustment are also conducted.
Since to ensure the control parameters in metaheuristic is difficult, we decided to run 30 times for all images in all simulation, as well as for all the methods stopping criterion is 40. We also set all the parameters that are looked for as M = (p q r s), with boundaries: p = [0 1.5], q = [0 2], r = [0. 5 2], and s = [0.5 30].

Jurnal Ilmu Komputer dan Informasi (Journal of a Science and Information), volume 10, issue 2, June 2017
All of the algorithms were programmed and implemented in MatlabR211a, on personal computer with processor Intel Core i7-4500U, 8 GB RAM running memory, in Windows 8.1. To evaluate the image enhancements based on these proposed methods, four images were evaluated, i.e. Cameraman, Rice, Boat, and Lena; all of them have been resized at 256x256 pixels, and are converted into double precision for numerical computation. In case of contrast color image enhancement, at the first time, the RGB color spaces (red, green, blue) is converted into YIQ color space (luminance, hue, saturation), and then apply them to the methods only for the Q component. After that process, they convert back to the RGB color space Simulation results for all SA algorithms are given in Table 1 Moreover, the best objective function of proposed methods also gives better value for all images: CSARA1 with SARA3 for the image of

Simulation of DE, DERA, CDE and CDERA
Simulation of differential evolution algorithm is carried out in 14 conditions. First, group is 5 simulations on the original differential evolution: DE1 (F = CR = 0. Simulation results for all DE algorithms are given in Table 2. These results show that, mean objective function of the proposed methods achieve the higher value only for 2 images: CDERA3 for image of Boat (M2=0.1420) and CDERA2 with DE1 for image of Cameraman (M3=0.1587). Other images are achieved for the higher value of mean objective function on DE1 for images of Lena (M1=0.1577) and Rice (0M4=0.2536). In case of computation times show that, the best computation time for Lena image is CDERA1 (T1=104.42s), Boat image is CDE3 (T2=91.04s), Cameraman image is CDE1 (T3=86.41s), and Rice image is CDERA1 (T4=88.26s).
Furthermore, the best objectives function of proposed methods, only for image of Rice (CDE-RA2, CDERA3 = 0.2538), together with DE1, DERA1, DERA3, CDE2 and CDE3. Other images are achieved for the higher value of the best objective function on DE1 for image of Lena (0.1592), CDE2 for image Boat (0.1436), and DERA2 for image of Cameraman (0.1655). In a

Simulation of PSO, PSORA, CPSO and CPSORA
Simulation on particle swarm optimization algorithm is performed in 13 conditions. First group is 4 simulations on the original particle swarm optimization: PSO1 (r1 = r2 = 1. Simulation results for all PSO algorithms are given in Table 3. These results show that, mean objective function of the proposed methods achieve the higher value for all images: Simulation results for all HS algorithms are given in Table  Comparison of images for the original (Ori), the best objective function and the worst objective function on all algorithms are shown in figure 1. Moreover, some examples for combination of parameters p, q, r and s are presented in relation to objective function F as well as intensity of edge E(I(M)) that is detected by Sobel edge detector, number of edge pixels ne(I(M)) and entropy of the images H(I(M)). Simulation results parameters for the best objective function (BOF) are given in Table 5 and for the worst objective function are shown in Table 6.

Conclusion
The objective of these proposed methods has been achieved to enhance the detail and the contrast of images. The indicator from the proposed methods is the objective function are better than the original of images. As an example, the mean objective function of Lena image on CSARA1 is 0.1551, while on the original is 0.0812. Based on the mean objective functions from simulation results, the performance of the proposed methods for all images is better than the original of metaheuristic, metaheuristic with chaos, and metaheuristic by Random adjustment, except Lena and Rice images in DE algorithms. In this case, mean objective function of DE1 for images of Lena (0.1577) and Rice (0.2536) are better than the proposed methods, i.e. CDERA1 (Lena: 0.1558, Rice: 0.2529), CDERA2 (Lena: 0.1557, Rice: 0.2533) and CDERA3 (Lena: 0.1573, Rice: 0.2531).
The probabilities of this case, since setting parameters of DE1 are fit with the characteristic of Lena and Rice images. The performance of metaheuristic algorithms depends on their parameter settings. As an example, the best objective function of Lena image (0.1592) is DE1 (F = CR = 0.8). However, the worst objective func-tion of this image (0.1281) is variant of DE1, which is DE5 (F=0.2, CR=0.8). In case of compu-tation time, the best computation time of Lena image is SA1 (43.17 s). However, the worst computation time is the variant of this method, that is SA3 (286.30 s).
Moreover, the performance of metaheuristic algorithms also depends on characteristic of the problem, in this case is images of Lena, Cameraman, Boat and Rice. For example, the best objective function of Lena (0.1590) and Boat (0.1436)