Multilevel Thresholding According to Histogram

Multilevel Thresholding According to HistogramMake Multilevel Thresholding According to Histogram by Cooperative Algorithm establish on AFSA and Fuzzy Logic determine segmentation is a proficiency which is usu everyy applied in the start footprint of figure of speech analysis and pattern recognition and is an important component of them. This technique is taken into account as one of the or so difficult and the most clear problems in image analyzing. In this paper, a cooperative algorithmic program is proposed establish on AFSA and k-means. The proposed algorithm is utilize to make multilevel thresholding for image segmentation jibe to histogram. In the proposed algorithm, first, artificial weight (AF) complete optimisation process in AFSA. afterwards swarm convergence, obtained crew centers by AFs ar utilise as sign chunk centers of k-means algorithm. After forwarding AFSAs output to k-means, AFs argon reinitialized and performs globing again. The proposed algorithm is used for segmenting 2 well-known images and obtained results are compared with distributively early(a). Experimental results show that part images quality by the proposed algorithm is much intermit than four other tested 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 component of them. This technique is taken into account as one of the most difficult and the most sensitive problems in image analyzing. In fact, quality of final result of image analysis depends highly on the quality of image segmentation result. In image segmentation process, an image is divided into different regions. Segmentation approaches of mono-color images are with keep to discontinuity and/or similarity of aged level amounts in one region. If the approach performs segmentation based on discontinuities, the image is segmented w ith respect to abrupt changes on white-haired level by means of recognizing dots, lines and edges 1.The purpose 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-color images segmentation 2. Generally, images are composed of regions with various gray levels. Therefore, an images histogram can consist of some peaks that separately of them is related to one region. To separate boundaries of two peaks from each other, a threshold value is considered between valleys of two neighboring peaks. Indeed, histogram thresholding is a no unseasonedorthy technique which is looking for peaks and valleys in a histogram 3. Various cloding algorithms much(prenominal) as k-means 4 and FCM 5 have been used for histogram thresholding so far. As a matter of fact, crowd approaches, because of simplicity and effectiveness, function to the most famous techniques that could be u sed for natural image segmentation. Applying glob algorithms in histogram thresholding are such that first colors histogram is built and afterward that, chunk is done concord to color distribution among pixels. One of the clustering methods is to use such swarm intelligence algorithms as particle swarm optimization (PSO) 6, and artificial fish swarm algorithm (AFSA) 7. PSO was pre moveed by Kenedy and Eberhart in 1995 8. Different versions of this algorithm have been used many time in data clustering 9. Artificial fish swarm algorithm (AFSA) was presented by Li Xiao Lei in 2002 10. This algorithm is a technique based on swarm behaviors that was inspired from social behaviors of fish swarm in nature. AFSA works based on population, random face and behaviorism. This algorithm has been applied on different problems including machine learning 11, 12, 13, PID controlling 14, image segmentation 16, data 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 convergence rate, but has some weaknesses such as sensitivity to initial values of cluster centers and convergence to topical anesthetic optima. Re dependers have tried to remove these weaknesses by hybridizing this algorithm with other algorithms such as swarm intelligence ones 6, 19 and to utilize 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 particle 20. Hence, at the beginning of the algorithm, k-means cranial orbites to a local optimum with its high convergence rate and after that PSO takes the responsibility of increase 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) p erform 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 planetary attempt and k-means is used for a local search. 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 appropriate and acceptable efficiency.The remainder of the paper is organized as follows in sections 2 and 3, standard AFSA and k-means algorithm will be described respectively 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 can find areas that have more(prenominal) foods, which is done with individual or swarm search by fishes. According to this characteristic, artificial fish (AF) model is represented by prey, free-move, and swarm and follow behaviors. AFs search the problem space by those behaviors. The environment, which AF lives in, substantially is solution space and other AFs domain. Food consistence degree in water area is AFSA objective function. Finally, AFs reach to a point which its food consistence degree is maxima (global optimum).In artificial fish swarm algorithm, AF perceives external concepts with sense of sight. Current assign of AF is shown by vector X=(x 1, x 2,, x n). The visual is allude to sight field of AF and Xv is a position in visual where the AF wants to go. Then if Xv has better 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 better than X v, it continues searching in its visual area. Food consistence in position X is seaworthiness 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 parts of variables and functions. Variables include X (current AF position), step (maximum length step), visual (sight field), try-number (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 find randomly. The following steps are repeated a) for each data vector data vector is allocated to a cluster that its Euclidean distance from its center is littler than the other clusters centers. Distance from cluster center is calculated by equivalence (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 cente rs is updated by Equation (2)(2)Where, nj is the number of data vectors that proceed 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 criterion 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 minimize 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 colo r 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 moldiness do on its structure. The best institute position by swarm members so far in AFSA is saved in bulletin and AF which has found it mightiness go even toward worse positions with performing a free-move behavior. Therefore, AFs cannot utilize their best swarm experience for improving the convergen ce rate because they just save it in bulletin. On the other hand, performing free-move behavior is inevitable 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 capital punishment 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 scheming 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 extent but cannot gua rantee 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 input 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 searchin g locally. Consequently, in the proposed algorithm, global search might of AFSA has been used and after converging, a great part of optimization process will be given to k-means to utilize high cap superpower 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 being 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 liberty chit local optima, the obtained result cannot 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 t he 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, huge amount of computations for local search is prevented. In the proposed algorithm, it has been tried to utilize this conserved 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 also performed once. In the proposed algorithm, to determine the convergence of artificial fish swarm, the leaving of obtained results in consecutive iterations of performing the algorithm is used. When particles converge, the obtained results difference in consecuti ve iterations decreases, 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 displaced. Pseudo code of the proposed algorithm is represented in token (1).Experiments are done on two known gray scale images, Lenna and Barbara, of sizes 512*512 in check (2). In this paper, the well-known criterion of amity is used to compare images segmen tation 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 Swarm behavior on Xi(t) and Compute Xi,swarm8Perform Follow Behavior on Xi(i) and Compute Xi,follow9if F(Xi,swarm) F(Xi,follow)10then Xi(t+1)= Xi,follow11Else12Xi(t+1)= Xi,swarm13Endif14Endfor15if swarm is converged16then Execute k-means on XBest-AF until stopping criterion of k-means is met17Endif18if F(Xk-means) F(Blackboard)19then Blackboard = Xk-means20reinitialize AFSA21Endif22until stoppin g 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 Barbara, 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 congruity obtained from 5 algorithms on tw o images with thresholds 2, 3, 4 and 5 are shown in Table (1). As it is observed 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-meansPSOKPS OProposed 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 performed 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 responsible for taking ou t the result from local optimum however, it sometimes may not be successful. Indeed, improper 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 almost 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 utilized 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 teaching method India, Fifth Indian reprint, 2000.2 S. Arora, J. Acharya, A. Verma., and K. 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