Neutrosophic Set Based Image Segmentation Approach Using Cricket ...

Neutrosophic Set Based Image Segmentation Approach Using Cricket Algorithm Murat CANAYAZ

Kazım HANBAY

Department of Computer Engineering Yuzuncu Yil University, Turkey, Email: [email protected]

Informatics Department Bingol University,Turkey Email: [email protected]

Abstract—Image segmentation is important part of image processing applications. A given image is separated the different regions with homogeneous characteristics at image segmentation process. This paper will introduce an image segmentation approach that can be used in image processing applications. Recently Neutrosophic Set (NS) that use to evulate indeterminacy information, and metaheuristic algorithms are frequently used in image segmentation process. Our study contain both these methods. At first, an image is transformed to NS domain that has T, I, F subset, and then, features of image are extracted. Then, according to Shannon entopy model, threshold values that correspond to the values maximizing the function in the entropy, is found on the image. Finally, image is thresholded with this value. This search of maximum entropy values is made using the Cricket Algorithm, a new metaheuristic algorithm inspired behaviour of cricket, minimizing the complexity of operation and search time. To summarize, this study aims not only to represent image segmentation technique but also introduce the Cricket Algorithm. At the end of study, the performance of this approach on test images will be shown.

I. I NTRODUCTION Thanks to the advantages offered by developing technology today, the number of images is increasing fast in the social media or other various platforms. This fast expansion brings along many problems. Therefore, image processing applications have gained importance and been used frequently. Image segmentation has an important place among these applications. Many studies have been conducted on this subject and these studies recommended different methods [1], [2], [3], [4], [5]. From among the methods used, meta-heuristic algorithms offer more effective results by operating efficiently in areas of applications requiring optimization and minimizing the complexity of operation and calculation time [6], [7], [8], [9]. These methods are still used in many image processing applications, not only in segmentation. The method that we used in our study, the Cricket Algorithm [10], [11], [12], is a new metaheuristic algorithm approach and can be used in areas requiring optimization in image processing applications, just like in other metaheuristic algorithms. The purpose of this study is to introduce image segmentation approach based on neutrosophic set that can be used in image processing applications. Entropy calculation is made on the images subject to segmentation based on the Shannon entropy model. Before the calculation of entropy, the image will be transferred to Neutrosophic Set c 978-1-4673-9910-4/16/$31.00 2016 IEEE

(NS) domain [13] that derived from a branch of psychology. It is encountered to eliminate the indeterminacy as an approach. Several methods that developed using NS are available in the image processing field [14], [15], [16]. The information is evaluated at three subset in this domain: T, I, F, true set, indeterminacy set and false set, respectively. Thanks to transformation to this domain, it is eliminated indeterminacy of pixels on the image and used to obtain significant image features. After that, coefficient matrix is found using T, I subset and then the threshold values that correspond to the values maximizing the function in the entropy are determined on this coefficient matrix. The Cricket Algorithm will be used for that maximization. These threshold values will then be used in the representation of image and thus the image will be segmented. This study is organized as follows; the Cricket Algorithm that is used to find the entropy values will be introduced in the first section and the NS that is applied to extract the properties of image will be described in the second section. Then, the Shannon entropy model will be explained. In the final section, proposed image segmentation method will be introduced, and its performance on test images will be shown. II. C RICKET A LGORITHM As the name suggests, the algorithm was developed with inspiration from behaviours of an insect known as cricket. The crickets are known with the sound they make during the summer as we can hear often in our daily lives. Male crickets copulate with females by attracting them making those sounds [17]. Our approach include some common features like other metaheuristic algorithms. For example, there is tropism to the highest light in the firefly algorithm [18]. In our approach, the tropism is to the highest sound. Another common characteristic is that bats in the bat algorithm [19] can identify a space using the echolocation, while the crickets change their places (coordinates) based on the intensity of sound. These coordinate updates can be likened to the search for candidate solution in the Particle Swarm Optimization (PSO) [20]. In short, our algorithm seeks candidate solutions for a mathematically given fitness function just like in other meta-heuristic algorithms. It uses common aspects in some algorithms while searching for these candidate solutions. Besides, some unique characteristics of cricket are added to the algorithm and thus more effective results can be obtained. Examining the crickets, Dolbear

found that there is a relationship between the air temperature and the rate at which crickets flap and expressed this using the following equations [21]. The studies conducted after Dolbear confirm this as well [22]. Our algorithm starts with randomly generated fitness population values. Then random flapping number is generated within the value range of [0, 120] and air temperature is calculated using these generated flapping number in the equation 1 and 2. The algorithm is developed using the equations obtained under some physical laws pertaining to the propagation of sound in the nature [23]. The equations used in the algorithm are provided below. N − 40 ) TF = 50 + ( 4 TF : The air temperature in degrees Fahrenheit N: is the chirping number in 1 minute N − 40 TC = 10 + ( ) 7 TC : The air temperature in degrees Celsius V = 20.1 ∗

√

273 + C

(1)

(2)

(3)

Lw : The source’s sound power level (dB ) Q: Orientation coefficient direction factor (Q is taken as 1 on rough land and 2 in plain land) r: Distance from the source (m.) Aatm = 7.4(f 2 r/Ø)10−8 (7)

(8)



(9)

fi :frequency values,fmin : minimum frequency, fmax :maximum frequency, β:Scale coefficient vit = vit−1 + (xi − x∗ )fi + Vit

xi = xbest + 0.01 ∗ rand(0, 1)

(12)

where xbest is current best solution.   d  rij = xi − xj  =  (xi,k − xj,k )2

(10)

vi :current velocity value, vit−1 =previous velocity values, xi =current coordinate, x∗ = best coordinate, Vi : velocity of sound

(13)

k=1

K = K0 ∗ e−γr 2

I is the intensity of sound (W/m2), W is the volume of sound (W), r is distance (m) (interval)   Q Lp = Lw + 10 ∗ log (6) 4πr2

Lp is Real sound pressure level fi = fmin + (fmax − fmin )β

(11)

2

xi = xi + K0 ∗ e−γrij ∗ (xj − xi ) + αi

where C is the celsius degree, and V is the velocity of sound. V (4) f= λ f: frequency(Hz), V: velocity(m/sn), λ: wavelength(m). W = I ∗ 4πr2 (5)

f: is the frequency of the transmitted sound (Hz) r: Distance from source (m) Ø: Relative humidity in the air  Lp = Lp − Aatm

xti = xt−1 + vit i

(14) (15)

where γ is the sound absorption coefficient of air, αi are the coefficients used for scaling at lower and upper limits according to the given problem and xi is the coordination of the cricket (the candidate solution). To summarize the steps of algorithm; In the cricket algorithm, the first step is to generate solutions in upper and lower limit ranges for the individuals of population. These solutions are sent to the objective function and initial values of sound intensity of the cricket. After the flapping number is generated randomly, the relationship between the rate at which cricket flaps and air temperature is calculated correlatively according to the Dolbears law. Speed and frequency values of the sound are found in the calculated temperature. These speed and frequency values are used in the equations 9 and 11. So, locations of crickets are calculated. Existing locations are sent again to the fitness function and new fitness values are found. These new values are then compared with the previous results. The best value that gives the minimum or maximum value depending on the type of problem is assigned as the global best. While these steps are ongoing, equations related to the propagation of sound in the nature (Equations 3-8) are used in the course of algorithm. The coefficient of sound absorption by air is found according to the definition set out in the ISO standard [24]. This coefficient is used in the identification of new locations. This coefficient is compared with a number generated within the random range [0.1] and the values that will be used in the coordinate updates of crickets are decided. Two different ways are adopted to identify the coordination of crickets in this decision-making process. In the first method, the update is made as in the equation 11. In the second method, crickets go towards the one with higher sound based on the equations 13-15 or have a random walking as in the equation 12. When sufficient iteration is found as a result of these tropisms, the algorithm is ended and the best value is shown in the end. Since maximization is used to find the entropy values, pseudo code of the algorithm will be as follows. The following parameter values are used in the algorithm; α :0.5 (reduced by multiplication with 0.95 at every turn), Ø:50%, β: Random[0,1], : Random[0,1], n: 10.

Algorithm 1 Cricket Algorithm Pseudo Code Input: {Algorithms parameters} fmin ,α,d,β,lb,ub,n Output: xbest ,Fmax Begin: Objective function f(x), x = (x1 ,...,xd ) Initialize a population of cricket xi (i = 1,2,...,n) Find Fmax for objective function while Max do for i = 1:n do all n crickets Random Define Ni , cricket chirp count Find Ti (Dolbear Law) Calculate Vi for this Ti Calculate λi and Fi Generate new solutions using frequency, update velocity and new coordinat Calculate γ for this Fi and Ti value for j = 1:n do if Si < Sj then Move cricket i which has low sound towards j which has loud sound else Generate a new solution by walking randomly end if end for j if rand > γ then Use cricket’s coordinate in Eq. 11 else Use cricket’s coordinate in Eq. 15 or Eq.12 end if if Fnew > Fmax then Accept the new solutions end if end for i Find best solution end while End

domain besides the element to be true or false. After image transferred to NS, the main aim is to decide the values of membership of pixels. A P(i,j) pixel can be demonstrated as: PN S (i, j) = T(i, j), I(i, j), F(i, j) and are the membership values identified as: T (i, j) =





g(m, n)

(17)

m=i−w/2 n=j−w/2

I(i, j) =

δ(i, j) − δmin δmax − δmin

(18)

δ(i, j) = abs(g(i, j) − g(i, j))

(19)

F (i, j) = 1 − T (i, j)

(20)

where g(i,j) (i,j), g(i, j) is the local mean value of g(i,j), δ(i,j) is the absolute value of the difference between intensity g(i,j) and its local mean value g(i, j) [13]. α and β-enhancement process is applied to eliminate the indeterminacy in the NS image. Equations of these process are given below [13]. For α process: P N S (α) = P (T (α), I(α), F (α))  T, I