Multilevel Thresholding According to Histogram

multilevel Thresholding According to HistogramMake Multilevel Thresholding According to Histogram by Cooperative Algorithm ground on AFSA and blurry LogicImage segmentation is a technique which is usually use in the first metre of theatrical role analysis and pattern course credit and is an important comp unitynt of them. This technique is interpreted into account as 1 of the most difficult and the most hand whatever problems in outside(a)ize analyzing. In this paper, a conjunctive algorithmic programic ruleic programic ruleic programic programic programic programic programic rule is proposed ground on AFSA and k- implys. The proposed algorithm is employ to make multilevel thresholding for plan segmentation according to histogram. In the proposed algorithm, first, sentimental fish (AF) suffice optimisation process in AFSA. later set lap, obtained thump internalitys by AFs be leave as sign clunk pertains of k-means algorithm. After forwarding AFSAs outpu t to k-means, AFs be reinitialized and performs glob again. The proposed algorithm is use for segmenting 2 well-know enters and obtained responses argon comp ard with each an some other(prenominal). Experimental results supply that divide anatomys quality by the proposed algorithm is much violate than four-spot other strained algorithms.Keywords Multilevel Thresholding Histogram Cooperative Algorithm k-means.Image segmentation is a technique which is usually applied in the first step of image analysis and pattern recognition and is an important comp iodinent of them. This technique is briben into account as 1 of the most difficult and the most sore problems in image analyzing. In fact, quality of final examination result of image analysis depends exaltedly on the quality of image segmentation result. In image segmentation process, an image is divided into antithetic expanses. Segmentation nuzzlees of mono- emblazon images argon with lever to discontinuity and/or similarity of grey level amounts in one region. If the approach performs segmentation based on discontinuities, the image is part with respect to abrupt changes on time-worn level by means of recognizing dots, lines and edges 1.The plan of image segmentation approaches is to classify and convert pixels into regions.Histogram thresholding is one of the techniques, which has been applied extensively in mono- pretension images segmentation 2. Generally, images ar composed of regions with various gray levels. Therefore, an images histogram smoke consist of some peaks that each of them is related to one region. To sepa score boundaries of cardinal peaks from each other, a threshold value is considered between valleys of twain neighboring(a) peaks. Indeed, histogram thresholding is a noteworthy technique which is looking for peaks and valleys in a histogram 3. non-homogeneous bundle uping algorithms such(prenominal) as k-means 4 and FCM 5 have been used for histogram threshold ing so farthermost. As a matter of fact, plunking approaches, because of simplicity and military unitiveness, belong to the most noted techniques that could be used for natural image segmentation. Applying bundle uping algorithms in histogram thresholding are such that first alters histogram is built and by and by that, bundleing is through with(p) according to color distribution among pixels. unitary of the roll uping modes is to use such hatch intelligence algorithms as fragment buzz optimization (PSO) 6, and stilted fish lot algorithm (AFSA) 7. PSO was presented by Kenedy and Eberhart in 1995 8. Different versions of this algorithm have been used many generation in info chunk 9. faux fish hum algorithm (AFSA) was presented by Li Xiao florilegium in 2002 10. This algorithm is a technique based on group behaviors that was inspired from social behaviors of fish swarm in nature. AFSA works based on population, random attend and behaviorism. This algorithm ha s been applied on different problems including machine learning 11, 12, 13, PID controlling 14, image segmentation 16, info clustering 7, 16 and scheduling 17. K-means or famous Lloyd algorithm is one of the famous data clustering algorithms 18. This algorithm is of high playnce rate, but has some impuissancees such as sensitivity to initial set of cluster centers and convergence to topical anesthetic optima. Re inquisitioners have tried to remove these weaknesses by hybridizationizing this algorithm with other algorithms such as swarm intelligence ones 6, 19 and to use their advantages. One of these algorithms is KPSO in which first, k-means is performed and after that outcome of k-means is delivered to PSO as a touch 20. Hence, at the beginning of the algorithm, k-means reaches to a topical anesthetic anesthetic anaesthetic optimum with its high convergence rate and after that PSO takes the responsibility of increasing the result accuracy and exiting form local optimum .In this paper, a cooperative algorithm is proposed based on AFSA and k-means. The proposed algorithm is used to make multilevel thresholding for image segmentation according to histogram. In the proposed algorithm, first, artificial fish (AF) perform optimization process in AFSA. After swarm convergence, obtained cluster centers by AFs are used as initial cluster centers of k-means algorithm. After forwarding AFSAs output to k- means, AFs are reinitialized and performs clustering again. In fact, in the proposed algorithm, AFSA is used for a international seem and k-means is used for a local seek. The proposed algorithm along with four other algorithms is used for image segmentation on two known images Lenna and Barbara. Efficiency comparison shows that the proposed algorithm has an conquer and accept equal to(p) efficiency.The remainder of the paper is organized as fol pitifuls in sections 2 and 3, standard AFSA and k-means algorithm will be described separately and in section 4, the proposed algorithm will be presented. Section 5 studies the experiments and analyzes their results and final section concludes the paper.In water world, fish so-and-so find areas that have more forages, which is do with individual or swarm chase by fishes. According to this characteristic, artificial fish (AF) model is delineate by prey, free-move, and swarm and follow behaviors. AFs inquisition the problem outer space by those behaviors. The environment, which AF lives in, good is solution space and other AFs domain. Food eubstance degree in water area is AFSA objective function. Finally, AFs reach to a point which its forage consistence degree is maxima (global optimum).In artificial fish swarm algorithm, AF perceives external concepts with sense of sight. Current daub of AF is shown by vector X=(x 1, x 2,, x n). The visual is equal to sight field of AF and Xv is a station in visual where the AF wants to go. Then if Xv has collapse food consistence than current position of AF, it goes one step toward X v which causes change in AF position from X to Xnext , but if the current position of AF is give away than X v, it continues probing in its visual area. Food consistence in position X is fittingness value of this position and is shown with f(X). The step is equal to maximum length of the movement. The distance between two AFs which are in Xi and Xj positions is shown by Dis ij =X i-Xj (Euclidean distance).AF model consists of two part of variables and functions. Variables include X (current AF position), step (maximum length step), visual (sight field), try- subject (the maximum test interactions and tries) and crowd factor (0The standard k-means algorithm is summarized as follows Initial position of K cluster centers is determined randomly. The following steps are perennial a) for each data vector data vector is allocated to a cluster that its Euclidean distance from its center is smaller than the other clusters centers. Distance from cluster center is calculated by comparability (1)(1)In equation (1), Xp is data vector p, Zj is the center of cluster j and d is the number of dimensions of data vectors and cluster center vectors. b) After allocating all data to clusters, each of cluster centers is updated by comparison (2)(2)Where, nj is the number of data vectors that belong to cluster j and Cj is a subset of all data vectors which belong to cluster j. The resulted cluster center of Equation (2) is the average vector of data vectors comprising cluster. (a) and (b) steps are iterated until the stopping meter is satisfied.In this section, the proposed algorithm is described. In the proposed algorithm, there exists a population of AFSAs AFs. This population of AFs is initialized randomly in problem space. Each AF consists of K cluster center positions in one dimensional image histogram space. Therefore, search space for AFSA for K cluster centers has K components. Fitness function which AFSA has to calumniate is shown in Equation (3).(3)Clustering on histogram is done by Equation (3) based on color distribution between given images pixels. The image is divided into K clusters (Ci) according to color attribute by K-1 thresholds. In Equation (3), the distance between color Xj on image histogram and the center of a cluster which it belongs to ( Zi), is multiplied by the frequency of pixels (fj) which have color value Xj on given image. This value is computed for all color values with respect to the center of a cluster which they belong to. Each color becomes the member of a cluster in which their distance from that cluster center is less than other cluster centers. Finally, the obtained results of all clusters are summed with each other. Indeed, Equation (3) calculates sum of intra cluster distances for one dimensional gray scale images, which is one of the most well-known clustering criteria.For improving obtained results by AFSA, some modifications mustiness do on its structure. The bes t bring position by swarm members so far in AFSA is salvage in bulletin and AF which has found it might go even toward worse positions with playacting a free-move behavior. Therefore, AFs stinkernot utilize their best swarm experience for improving the convergence rate because they serious save it in bulletin. On the other hand, performing free-move behavior is essential for maintaining diversity of the swarm. In this paper, to remove this problem, every AF except best AF can perform free-move behavior. In fact, during execution of the proposed algorithm, this behavior is not performed for the best AF of the swarm at all. Hence, the best found position by the swarm would be the position of the best AF of the swarm. As a result, other members of the swarm can move in the direction of the best found position by executing follow and swarm behaviors.The purpose of designing the proposed algorithm is to take advantages of both AFSA and k-means algorithms and remove their weaknesses . K-means is of high convergence rate, but its very sensitive to initializing the cluster centers and in the case of selecting inappropriate initial cluster centers, it could converge to a local optimum. AFSA can pass local optima to some result but cannot guarantee reaching to global optima. However, AFSAs computational complexity for optimization process is much more than k-means. How the proposed algorithm functions remove weaknesses of these two algorithms and apply their advantages is as followingIn the proposed algorithm, first, the AFs are initialized in AFSA. Each of AFSA contains K cluster centers (K-1 threshold) which are displaced in the problem space by performing AFSAs behaviors. AFSA continues to perform until the AFs converge. After convergence of AFSA, best AFs position including the best cluster centers which have found by AFs so far is considered as the remark of k-means. Then, k-means algorithm starts working and while it is not converged, it continues working. Therefore, AFSA searches globally and as far as it can, it passes local optima. After convergence of AFSAs AFs, its output would have an appropriate initial cluster centers for k-means. Hence, after sending AFSAs outcome to k-means, this algorithm starts searching locally. Consequently, in the proposed algorithm, global search ability of AFSA has been used and after converging, a great part of optimization process will be given to k-means to utilize high capability of local search of this algorithm and its high convergence rate. Since initial cluster centers for k-means are obtained by AFSA and k-means is used for local search, k-means weakness of sensitivity to initial cluster centers is removed. But, AFSA capability may not be enough for preventing from be trapped in local optima. If this algorithm is trapped in local optima, it cannot present proper initial cluster values to k-means. Thereafter, according to low ability of k-means in passing local optima, the obtained result can not be acceptable. To raise this problem, after convergence of AFSA, the output of this algorithm is sent to k-means. Simultaneously with starting of k-means, AFSAs AFs are initialized and start global search again. In fact, in one time of executing the proposed algorithm, AFSA has several times of chance to perform an acceptable global search. It should be noted that in the proposed algorithm, in each time of executing AFSA, AFs just search globally and converge after a short time and k-means undertakes the remaining of optimization process which is local search. Therefore, with respect to low computational complexity of k-means, considerable amount of computations for local search is prevented. In the proposed algorithm, it has been tried to utilize this conserve computation load for giving new opportunities to AFSA in order to perform an acceptable global search in at least one of given opportunities to it. Hence, for each execution of global search by AFSA, k-means is too perf ormed once. In the proposed algorithm, to determine the convergence of artificial fish swarm, the difference of obtained results in consecutive iterations of performing the algorithm is used. When particles converge, the obtained results difference in consecutive iterations diminishs, so by considering a threshold for the difference between best AFs fitness values in iterations i and j, it can determine their convergence. In the proposed algorithm, because AFSA and k-means algorithms are performed multiple times, always, it has to save the best found cluster centers by algorithm so far. For this purpose, a blackboard is applied that each time k-means finishes after convergence of AFSA, the obtained result of that will be compared with saved result in blackboard. If obtained cluster centers are better than saved result in blackboard, saved value in blackboard is updated. K- means execution finishes when after two consecutive iterations of its execution, cluster centers wouldnt be di splaced. Pseudo code of the proposed algorithm is represented in understand (1).Experiments are done on two known gray scale images, Lenna and Barbara, of sizes 512*512 in Figure (2). In this paper, the well-known criterion of uniformity is used to compare images segmentation qualitatively 3 which is shown in Equation (4) (4)Where, c is the number of thresholds. Rj is the segmented region j. N is the total number of pixels in the given image, fi shows the gray level of pixel I, i is the mean gray level of pixels in jth region, finally, fmin and fmax are the minimum and maximum gray level of pixels in the given image, respectively. Usually, u0, 1 and larger amount for u declares that the thresholds are specified with better quality on the histogram.Proposed Algorithm1for each AFi2initialize xi3Endfor4blackboard = arg min F(Xi)5Repeat6for each AFi7Perform set bearing on Xi(t) and Compute Xi,swarm8Perform Follow Behavior on Xi(i) and Compute Xi,follow9if F(Xi,swarm) F(Xi,follow)10 thusly Xi(t+1)= Xi,follow11Else12Xi(t+1)= Xi,swarm13Endif14Endfor15if swarm is converged16then work out k-means on X crush-AF until stopping criterion of k-means is met17Endif18if F(Xk-means) F(Blackboard)19then Blackboard = Xk-means20reinitialize AFSA21Endif22until stopping criterion is metFigure (1) Pseudo code of proposed algorithm.The proposed algorithm along with standard AFSA, PSO algorithm, hybrid algorithm called KPSO 20, and k-means is used to segment two images, Lenna and Barbara. PSO and KPSO parameters are adjusted according to 6, and for k-means, initializing Forgy method is applied 21. AFSA parameters and are adjusted according to 7. AFSA settings in the proposed algorithm are the same as 7. With respect to various experiments, if fitness value relating to Best AF is less than 0.1 in 3 iterations, it means that artificial fish swarm is converged. The following results are obtained from 50 times repeated experiments. Figure (3) shows segmented images, Lenna and Barb ara, by the proposed algorithm with 5 and 3 thresholds.Figure 2 Orginal gray level Lenna (left) and Barbara (right) imagesFigure 3 The thresholded images of Lenna and Barbara using 5, and 2-level thresholds, from top to bottom.Average uniformity obtained from 5 algorithms on two images with thresholds 2, 3, 4 and 5 are shown in Table (1). As it is discovered in Table (1), obtained results from the proposed algorithm is better than the other algorithms for all cases. AFSA algorithm has the worst result for all cases because of low ability in local search. K-means algorithm has found better results than AFSA because of high capability of k-means in local search. The reason for superiority of k-means to AFSA is the problem space property in histogram clustering. In fact, because of low dimensions of problem space in this environment, local search ability is of greater importance than global search ability. Also, it can reduce k-means weakness of sensitivity to initial values by means of one of the initializing methods of k-means like Forgy. Thereafter, with respect to considerable superiority of k-means local search ability in contrast to AFSA, k-means results are better than AFSAs. table I Comparison of uniformity for the five AlgorithmsImageTAFSAK-meansPSOKPSOProposed methodLenna20.91380.96340.97300.97280.977530.93610.97490.97810.97830.979540.94950.97620.98160.98110.982650.95170.98040.98350.98340.9838Barbara20.97580.97610.97650.97680.978130.97830.98020.98080.98050.982040.97970.98340.98430.98510.986250.98220.98490.98550.98500.9884Obtained results from PSO are better than k-means in all cases and its because of global search ability superiority of PSO to k-means. Moreover, in PSO, theres a trade-off between global search and local search abilities 16 and PSO also can perform a proper local search beside an acceptable global search. KPSO results are better than k-means results for all cases because after executing k-means in this algorithm, PSO algorithm is perfo rmed and improves obtained results from k-means. But obtained results from KPSO are not better than PSO for all cases. The reason is that sometimes k-means converges toward a local optimum and obtained result from that is not appropriate. Therefore, PSO is obligated for taking out the result from local optimum however, it sometimes may not be successful. Indeed, indecent result of k-means causes fast convergence of particles to local optimum. Obtained results from the proposed algorithm are better than other algorithms in all cases. The reason is usage of strategies which have been used for global search in this algorithm. In fact, the proposed algorithm is successful in finding the global optima in most runs and can prevent final result from being trapped in local optima, whereas, this ability is observed less in other algorithms and they cannot guarantee passing local optima. This weakness causes that other algorithms to be of less robustness and not to be able to reach to almo st the same results in their various implementations. Also, in the proposed algorithm, k-means algorithm performs local search after finding global optimum region by AFSA. Consequently, with respect to high ability of k-means in local search and taking proper initial cluster centers from AFSA, local search is done well in the proposed algorithm, too. As a result, both k-means and AFSA algorithms abilities are utilised in the proposed algorithm and the weakness of k- means algorithm cant decrease the algorithms efficiency. As it is observed in all algorithms except KPSO, with rising up the number of thresholds, uniformity amount is improved. In KPSO, since the weakness of k-means has an undesirable effect on PSO efficiency, obtained results are not stable.In this paper, a new cooperative algorithm based on artificial fish swarm algorithm and k-means was proposed for image segmentation with respect to multi-level thresholding. In the proposed algorithm, AFSA performs global search and k-means is responsible for local search. The process of the proposed algorithm is such that the robustness and ability of preventing from being trapped in local optimums is improved. The proposed algorithm along with four other algorithms is used for segmenting 2 well-known images and obtained results are compared with each other. Experimental results show that segmented images quality by the proposed algorithm is much better than four other tested algorithms.1 R. C. Gonzalez, and R. E. Woods, Digital image processing, In Pearson Education India, fifth Indian reprint, 2000.2 S. Arora, J. Acharya, A. Verma., and K. Panigrahi, Multilevel thresholding for image segmentation through a fast statistical recursive algorithm, In journal on Pattern intelligence Letters 29, pp. 119125, 2008.3 Maitra. M, A. Chatterjee, A hybrid cooperative-comprehensive learning based PSO algorithm for image segmentation using multilevel thresholding, In diary on sound System with applications 34, pp. 134 1-1350, 2008.4 M. 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