Multilevel Color Image segmentation using Modified ...

Multilevel Color Image segmentation using Modified Genetic Algorithm (MfGA) inspired Fuzzy C-Means Clustering Sunanda Das

Sourav De

Department of Computer Science & Engineering University Institute of Technology, Burdwan, West Bengal, India [email protected]

Department of Computer Science & Engineering Cooch Behar Government Engineering College, Cooch Behar, West Bengal, India [email protected]

segmentation result, the information supplied by different color spaces are applied in the FCM algorithm.

Abstract—Convergence to local minima point is one of the major disadvantages of conventional fuzzy c-means (FCM). Due to this drawback, segmentation result may hamper for not selecting the cluster centroids properly. To overcome this, a modified genetic (MfGA) algorithm is proposed to improve the performance of FCM. The optimized class levels derived from the MfGA are employed as initial input to FCM for finding global optimal solutions in a large search space. An extensive performance comparison of the proposed MfGA inspired conventional FCM and GA based FCM on two multilevel color images establishes the superiority of the proposed approach.

Genetic Algorithm (GA) [7] is an efficient heuristic search method that is inspired on the principles of natural genetics, i.e. population generation, natural selection, crossover and mutation. GA has the capability of finding optimal or near optimal solutions in a large search space. The parallel optimized multilevel sigmoidal (ParaOptiMUSIG) activation function in connection with the multilevel self-organizing neural network (MLSONN) is efficient enough to segment the true color images [8][9]. In this method, the genetic algorithm is applied to generate the ParaOptiMUSIG activation function. This algorithm is also applied for multi objective function without confining within the single objective function. De et al. [10] proposed NSGA II based ParaOptiMUSIG activation function to incorporate the multi-criterion to segment the color images. GA in combination with the weighted undirected graph is employed to segment the color images [11]. FCM is applied to generate the population for the GA to segment the single and multi-featured images [12]. In Jhansi and Subashini [13], a GA based FCM algorithm is proposed and shows that it gives better segmentation result than conventional FCM. In this paper, we have presented an efficient mechanism to segment color images using Modified Genetic Algorithm (MfGA) based FCM. MfGA is an improved version of the conventional GA where improvements are done in population initialization and crossover part. The reason for combining these two techniques is that the solutions of the FCM algorithm generally stuck into local minima whereas GA used to generate the global or near-global optimal solutions. At first, the MfGA is applied to find out the optimized cluster centers which at next stage are used as the initial cluster centers of the FCM algorithm. The output from this method is the optimal desired class levels from which the segmented image is obtained as the final output. The proposed method is compared with the conventional FCM and the GA based FCM algorithm [13]. To show the supremacy of the proposed method we have used two segmentation quality measure metrics, correlation coefficient ( ) [8] [10] [14] and empirical

Keywords—Segmentation, Clustering Algorithm, Fuzzy CMeans algorithm, Genetic Algorithm, Image quality evaluation metrics

I. INTRODUCTION Image segmentation is widely used in the fields of vision, biometric measurements, medical imaging etc. for the purpose of detecting, face recognition or tracking of an object. The utility of image segmentation is to differentiate and group the pixels having similar property based on features like intensity, homogeneity, texture etc. As color images are much more informative and easy to interpret, color images are being introduced in almost all spectrums of application. The FCM algorithm [1], a popular approach for image segmentation that can allow ambiguous boundaries between clusters based on the membership values of different classes. An objective function based on the distance between the data points under consideration has been minimized in this process. A fuzzy partitioning of the data to be processed is carried out through an iterative optimization of the objective function. Many eminent works are done by Chaung et al. [2], Yang et al. [3], Adhikari et al. [4] where different modified FCM are proposed for incorporating spatial information. A modified Fuzzy C-Means where new efficient cluster center initialization and color quantization allows faster and accurate convergence is proposed for color image segmentation [5]. Harrabi and Braiek [6] proposed a modified FCM algorithm to segment the color images. In this method to enhance the information quality and to get a more reliable and accurate

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measure, Q [9] [10] [14] [15], to analyze the performance and quality of the segmented images. Two real time true color images are considered here and it is observed that our proposed MfGA based FCM gives better result than the GA based FCM and conventional FCM on color image.

fiti represents the fitness value of each individual Ci in the population, its probability pi of being selected is, p

i



fit

(2)

i

N

fit

i

i 1

II. PROPOSED MODIFIED GENETIC ALGORITHM Main objective of the conventional Genetic Algorithm is to find out near-optimal solution in a large, complex and multimodal problem space. It is based on the evolutionary ideas of natural selection and genetics. Using three genetically inspired operator: selection, crossover and mutation, from a fixed population size, it upgrades the whole population performance and ultimately discover the optimal desired output. GA also has some drawbacks such that it may sometimes happen that the value of two neighbour class levels are nearly same; so that there is no significance to point out them as different cluster centers; so that it provides an ambiguous result. To overcome this disadvantage, we proposed here a modified genetic algorithm (MfGA). This proposed MfGA algorithm improves the population generation stage as well as the crossover part to produce better solution. Below we discussed the steps of MfGA:

where N is the number of individual in the population. C. Crossover A modification is made in the process of crossover probability to improve the conventional GA’s crossover. We choose more than one parent solutions and produce a child solution from them using single-point crossover. Crossover probability is to indicate a ratio of how many couples will be picked for mating. As a fixed crossover probability is used in the whole process of GA so that it may happen that at all time better chromosomes are not retained for next population; but here to retain good chromosomes in the next population, we decrease the crossover probability as the number of iterations will increase. Here, the crossover probability is inversely proportional to the number of iteration. This can be done with the given equation,

Cr p  Cr max 

A. Population Initialization It may happen that the difference between two neighbour class levels are very negligible so that we concatenate these two in a single class level and also the spatial information of the test image may not be considered. Unlike GA, in MfGA, at very first time we randomly choose N+1 number of temporary class levels T1,T2,T3,....,Tn+1 instead of N no. of class levels. From these temporary class levels, the actual N number of class levels i.e. L1,L2,..,Ln are generated. The weighted mean is employed between the temporary class levels of Ti and Ti+1 to generate the actual cluster centroids Li and it is represented as T

f L

i



j

* I

D. Mutation Mutation is used to maintain the genetic diversity from one generation of a population to the next. After the crossover is done mutation will take place with the help of mutation probability. Mutation probability (or ratio)(which is taken here 0.01) is basically a measure of the likeness that random elements of considered chromosome will be flipped into something else. Thus, new chromosomes are obtained for next generation.

T

j

(1)

i i1

f j  T

(3)

where, Crp is the crossover probability, Crmax is the maximum crossover probability (which is taken here 0.8), Crmin is the minimum crossover probability (which is taken here 0.5). Itermax is the maximum number of iteration to be done on the genetic algorithm and Itercur is the current iteration that is going on.

i 1

j  T

Cr max  Cr min Iter max  Iter cur

j

i

where, fj is the frequency of the jth pixel and Ij shows the intensity value of the jth pixel. This process helps in reducing the percentage of misclassification and increasing the accuracy in the segmentation. By this process, the spatial information is taken into consideration at the time of population initialization.

E. Termination criterion The processes of fitness computation, selection, crossover, and mutation are executed for a predetermined number of iterations. In each generation of population, the fittest chromosome is preserved till the last generation. Thus on termination, it gives us the best solution of chromosome.

B. Selection The selection operator determines which individuals are chosen for mating purpose. This selection is done on the basis of fitness value of each individual. This fitness value is used to associate a probability of selection with each individual chromosome. Here, we apply [8] [10] [14] and Q [9] [10] [14] [15] as fitness function and apply Roulette Wheel selection procedure, a proportional selection algorithm where the no. of copies of a chromosome that goes into the mating pool for subsequent operations is proportional to its fitness. If

III. PROPOSED MFGA INSPIRED FCM ALGORITHM In this paper, the proposed method is introduced to improve the efficiency of the conventional FCM. Drawbacks of FCM are:(a) usually converges to local minima instead of global minima; (b) must have the information that the number of segmented area;(c) only applied to the hyper-spherical structured cluster. Here we wish to improve the convergence problem of FCM. As the initial class levels cannot be assigned

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properly so that it reaches to the converging point (local minima) easily. The selection of initial class levels and fuzzy membership function have crucial role for the quick convergence and drastic reduction of the processing time in FCM algorithm. One more thing is that FCM does not consider the spatial information. The optimized class levels which are derived from MfGA are applied as the initial input of FCM. Another advantage of this proposed method is that the image content heterogeneity is also considered. The pixels, having most occurrences in the image, have the higher probability for being selected as the class levels in the initial stage. The proposed technique is applied to segment the true color images. Any color image can be differentiated into three planes i.e. red, green and blue. The MfGA algorithm is applied on three color planes of a color image.

RGB image. These optimized class levels of the MfGA algorithm is applied as the initial class levels in the FCM algorithm to segment the true color test images. Here at very initial stage we have randomly created chromosomes which consist of nine cluster centers to segment a color image into eight clusters. Now using a weighted mean formula from nine clusters centroids we generate eight cluster centroids. After completion of MfGA we are getting optimal cluster centroids which are input as the initial cluster center of FCM. At the end of FCM ultimate segmented cluster centroids for each plane are created. Now we have merge them into a single plane thus we get the segmented color image. IV. EXPERIMENTAL RESULTS In this section we describe the result of multilevel color image segmentation using MfGA based FCM on two standard color images, viz. Lena and Peppers of dimension 256x256. The test images are segmented in N= {6, 8, 10} segments but we have reported only 8 segmented images results in this article. Experimental results of proposed method are reported here with the comparison of GA based FCM [13] and conventional FCM [1] and the efficiency of all methods are measured based on two quality measure metrics, correlation coefficient ( ) [8] [10] [14] and empirical measure, Q [9] [10] [14] [15]. In the MfGA based FCM method and in GA based FCM method, the size of the population is 100. We experiment all the techniques fifty times separately but only three best results of each technique are presented in table (I – IV). The best results of each method are bold faced. The name of the method, serial number (#), the optimized class levels and the fitness values are presented in these tables. In table I and II, the derived class levels of Lena image by different methods are tabulated. The segmented Lena images by the best results of each method are shown in Fig. 2 (a)-(i). Among them, the first three segmented images are derived by FCM algorithm, next three are segmented by the GA based FCM algorithm and the last three segmented images are obtained by the proposed method. Similarly, the class levels and the corresponding fitness values of the Peppers images are reported on the basis of the fitness function and Q in Table III and IV, respectively. The corresponding segmented Peppers images, using the best results of Table III and IV, are presented in Fig. 2 (j)-(r). From these tables and segmented images, we can conclude that the proposed method outperforms other two methods to segment the true color images. Here we also observed that using our proposed method, FCM part also takes less time than other two methods. In table (V-VI) we also present the mean and standard deviation of evaluation metrics and also the average run time taken by only FCM and from that superiority of our proposed method is proved. We have also done ANOVA as a statistical test for different quality evaluation value for two images. But here we only reported the results of Lena image for different evaluation measures in table (VII-VIII) using ten results. From table VII and VIII we see that our proposed method gives better results than other two methods. In Figure 3 and 4 we plot graphs using 10 results of Q taken as quality evaluation values for Lena and Peppers image accordingly.

Fig. 1. Block diagram of MfGA based FCM

Three chromosome pools, i.e. one pool for red, second for green and third for blue are generated in the population generation step of MfGA. After that, all the stages of MfGA are applied on each pool of chromosomes in simultaneously. After getting the optimized class levels of all three planes that are merged into a single plane and presented as a segmented

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TABLE III. CLASS LEVELS AND CORRELATION COEFFICIENT OF FCM, GA BASED FCM AND MFGA BASED FCM OF PEPPERS IMAGE

TABLE I. CLASS LEVELS AND CORRELATION COEFFICIENT ( ) OF FCM, GA BASED FCM AND MFGA BASED FCM OF LENA IMAGE Method

#

Class levels

FCM

1

R={86,106,138,168,188,205,222,239} G={20,43,67,92,114,135,164,198} B={55,73,90,106,121,139,161,185} R={86,106,138,165,182,201,220,241} G={18,43,65,92,110,135,164,196} B={54,72,89,104,120,138,160,185} R={83,101,128,155,178,202,221,239} G={20,43,69,92,114,135,164,198} B={55,73,90,105,121,139,161,185} R={85,105,138,168,188,205,222,239} G={20, 43, 67,92,114,135,166,198} B={45,63,79,95,112,128,156,183} R={86,106,138,168,188,205,222,239} G={20,43,67,92,114,164,135,198} B={55,73,90,105,121,139,161,185} R={86,106,138,168,188,205,222,239} G={20,67,43,92,114,135,164,198} B={45,63,79,95,112,128,156,183} R={83,101,128,155,178,202,221,239} G={20,43,68,92,114,135,164,198} B={45,63,79,95,112,128,156,183} R={81,101,129,155,175,202,221,239} G={20,43,67,92,114,135,164,198} B={55,73,90,105,121,139,161,185} R={83,101,128,155,178,202,221,239} G={20,43,67,92,114,135,164,198} B={45,63,79,95,112,128,156,183}

2

3

GA based FCM

1

2

3

MfGA based FCM

1

2

3

Method

value

#

FCM

1

0.9126

2

0.9305

3

0.9512

GA based FCM

1

0.9851

2

0.9852

3

0.9855

MfGA based FCM

1

0.9865

2

0.9875

3

0.9862

Class levels R={41,80,110,129,150,172,192,208} G={5,32,54,90,126,159,184,208} B={6,30,44,67,86,109,147,191} R={42,79,111,129,152,172,198,203} G={5,33,54,91,125,159,184,208} B={5,30,43,63,80,108,147,191} R={42,81,109,129,155,172,198,209} G={5,33,54,91,125,160,184,208} B={5,30,44,69,80,108,147,191} R={41,79,109,128,149,171,191,207} G={5,32,53,90,125,159,184,208} B={4,29,43,67,85,108,147,191} R={4,79,110,129,150,172,192,208} G={5,32,53,90,125,159,184, 208} B={5,30,44,68,86,109,148,191} R={41,78,109,128,149,170,191,207} G={5,53,32,90,125,159,184,208} B={5,30,44,68,86,109,147,191} R={40,77,108,127,148,170,190,207} G={5,32,53,90,125,159,184,208} B={6,35,51,74,91,115,193,152} R={41,79,110,129,150,171,192,208} G={5,32,53,90,125,159,184,208} B={5,29,43,67,86,109,147,191} R={41,80,110,129,151,172,192,208} G={5,32,53,90,125,159,184,208} B={5,30,44,68,86,109,148,191}

value 0.9289

0.9436

0.9164

0.9869

0.9868

0.9865

0.9869

0.9871

0.9872

TABLE IV. TABLE II.

CLASS LEVELS AND EMPIRICAL MEASURE (Q) OF FCM, GA BASED FCM AND MFGA BASED FCM OF PEPPERS IMAGE

CLASS LEVELS AND EMPIRICAL MEASURE (Q) OF FCM, GA BASED FCM AND MFGA BASED FCM OF L ENA IMAGE

Method FCM

# 1

2

3

GA based FCM

1

2

3

MfGA based FCM

1

2

3

Class levels R={86,106,138,168,188,205,222,239} G={20,43,67,92,114,135,164,198} B={45,63,79,95,112,128,156,183} R={81,102,139,162,188,206,220,238} G={21,42,65,93,114,135,165,199} B={54,72,86,106,120,138,161,185} R={83,100,128,152,178,202,221,240} G={20,43,69,92,114,135,162,198} B={54,73,90,105,121,139,161,185} R={83,101,128,155,178,202,239,221} G={20, 43,92,68,114,135,164,198} B={55,74,94, 104, 114,129,157,183} R={86,106,138,188,168,205,222,239} G={20,43,68, 93,116,137,199, 167} B={54, 75, 85, 95, 112, 128,156,183} R={83,101,128,155,202,178,221,239} G={20,43,68,92,114,135,164, 198} B={55,73,90,105,121,139,161,185} R={86,106,126,138,168,188,222,239} G={20,43,68,93,114,136,199,165} B={45,63,79,95,112,128,156,183} R={86,106,138,168,188,205,222,239} G={20, 43, 68,93,115,136, 199,165} B={55,73,90,106,121,139,161,185} R={86,106,138,168,188,205,222,239} G={20,43,68,93,115,136,166,199} B={55,73,90,106,121,139,161,185}

Method

Q value

FCM

# 1

70869.63 2 81804.32 3 58701.27 GA based FCM

52879.88

1

2 54166.73 3 58733.25 MfGA based FCM

45447.39

1

2 50974.41 3 51976.51

81

Class levels R={40,80,112,129,155,172,192,208} G={6,35,55,98,132,163,187,209} B={6,35,52,76,91,115,152, 193} R={41,79,110,130,150,172,192,208} G={6,35,56,97,132,187,163,209} B={5,35,52,71,91,112,152, 195} R={41,79,110,129,150,169,192,208} G={4,34,54,97,130,187,163,209} B={6,35,52,74,91,115,152, 193} R={41,79,110,129,150,172,192,208} G={6,35,56,97,132,187,163,209} B={6,35,52,74,91,115,152, 193} R={41, 79,110,129,150,171,192,208} G={5,32,54,90,126,159,184,208} B={6,35,51,74,91,115,152,193} R={41,79,110,129,150,171,192,208} G={5,33,54,92,128,160,185,208} B={6,35,52,75,92,125,152,193} R={41,79,110,129,150,171,208, 192} G={5,34,55,95,130,162,186,209} B={6,35,51,74,90,152,115,193} R={41,79,110,129,150,172,192,208} G={5,32,125,90,53,184,159,208} B={5,31,45,69, 110,123,148,191} R={41,79,110,150,129,152,172,208} G={5,33,54,92,127,160,185,208} B={5,31,44,68,86,110,191,148}

Q value

48149.22

45320.50

49827.90

37085.81

34543.89

35696.43

29257.31

31316.45

30364.66

TABLE V.

MEAN AND STANDARD DEVIATION USING DIFFERENT FITNESS FUNCTION AND MEAN TIME FOR DIFFERENT ALGORITHM FOR LENA IMAGE

Method

Correlation coefficient Mean ± Std. Div

FCM GA based FCM MfGA based FCM

Avg. time

0.9237± 0.0144 0.9855± 0.0001

00:02:39

0.9861± 0.0010

00:02:25

00:02:29

Empirical Measure Mean ± Std. Div

Avg. time

85576.15± 116165.8 57588.67± 8002.06

00:02:35

52706.31± 3555.917

00:02:20

(a)

(b)

(c)

00:02:30

(d)

(e)

(f)

TABLE VI.

MEAN AND STANDARD DEVIATION USING DIFFERENT FITNESS FUNCTION AND MEAN TIME FOR DIFFERENT ALGORITHM FOR PEPPERS IMAGE Method

Correlation coefficient Mean ± Std. Div

Avg. time

Empirical Measure Mean ± Std. Div

Avg. time

FCM

0.9289± 0.0329

00:02:31

41260.53± 21186.26

00:02:37

GA based FCM MfGA based FCM

0.9869± 0.0005

00:02:25

33406.91± 2999.36

00:02:31

0.9871± 0.0003

00:02:22

31374.34± 3857.68

00:02:26

TABLE VII.

(g)

ANOVA RESULT OF CORRELATION COEFFICIENT OF LENA

IMAGE

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

SUMMARY Groups

Count

Sum

Average

Variance

FCM

10

9.2372

0.9237

0.0002

GA based FCM MfGA based FCM ANOVA

10

9.8550

0.9855

10

9.8615

0.9861

1.43E08 1.03E06

Source of Variation Between Groups Within Groups Total

SS

df

MS

F

0.0257

2

0.0128

183.04

0.0018

27

7.02E05

0.0276

29

Pvalue 1.98E16

F crit 3.354

(r)

Fig. 2. (a)-(c) Segmented output Lena image using FCM; (d)-(f) Segmented output Lena image using GA based FCM; (g)-(i) Segmented output Lena image using MfGA based FCM; (j)-(l) Segmented output Peppers image using FCM; (m)-(o) Segmented output Peppers image using GA based FCM; (p)-(r) Segmented output Peppers image using MfGA based FCM.

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TABLE VIII.

V. CONCLUSION Here we consider different types of segmentation techniques to segment true color images. We make a solely attempt to overcome the drawbacks of the conventional FCM which we discussed above. Here we proposed MfGA which enhanced the GA in some extent. Output of MfGA is input to FCM and ultimately we get the global optimized class levels to segment an image. We shows the segmented output for FCM, GA based FCM and MfGA based FCM and also report their quality assessment in a tabular form, and from that it is clear the superiority of our proposed method.

ANOVA RESULT OF EMPIRICAL MEASURE OF LENA IMAGE

SUMMARY Groups

Count

Sum

Average

Variance

FCM

10

8.5E+5

8.5E+4

1.34E+10

GA based FCM MfGA based FCM ANOVA

10

5.7E+5

5.7E+4

6.40E+7

10

5.2E+5

5.2E+4

1.26E+7

Source of Variation Between Groups Within Groups Total

SS

df

MS

F

6.2E+09

2

3.1E+9

0.6954

1.2E+11

27

4.5E+9

1.3E+11

29

References Pvalue 0.5075

F crit

[1]

3.354 [2]

[3]

[4]

[5] [6]

[7] [8]

[9] Fig. 3. Comparison between quality evaluation values (Q) of FCM, GA based FCM and MfGA based FCM for Lena image [10]

[11]

[12]

[13]

[14]

Fig. 4. Comparison between quality evaluation values (Q) of FCM, GA based FCM and MfGA based FCM for Peppers image

[15]

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J. C. Bezdek, “Pattern recognition with fuzzy objective function algorithms”, New York, NY: Plenum. doi:10.1007/978-1-4757-0450-1, 1981. K.S.Chuang, H.L.Tzeng, S.Chen, S., Wu, J., Chen, T.J., “Fuzzy Cmeans clustering with spatial information for image segmentation. Computerized Medical Imaging and Graphics”,vol. 30, no. 1, pp.9– 15,2006. Yang, Z., Chung, F.L., Shitong, W., “Robust fuzzy clustering-based image segmentation”, Applied Soft Computing,vol. 9,no. 1,pp. 80– 84,2009. S. K. Adhikari, J.K. Sing, D. K. Basu, M. Nasipuri, “Conditional spatial fuzzy C-means clustering algorithm for segmentation of MRI images”, Applied Soft Computing,vol. 34, pp. 758–769, 2015. H.L.Capitaine,C. Frelicot,“A fast fuzzy c-means algoritm for color image segmentation”, EUSFLAT-LFA-2011,aix-les-Bains,Frace. R. Harrabi, E. B. Braiek, “Color image segmentation using a modified Fuzzy C-Means technique and different color spaces: Application in the breast cancer cells images”, 2014 1st International Conference on Advanced Technologies for Signal and Image Processing (ATSIP), pp. 231 – 236, 2015. D. E. Goldberg, Genetic Algorithm in Search Optimization and Machine Learning, New York: Addison-Wesley, 1989. S. De, S. Bhattacharyya, and S. Chakraborty, “Color image segmentation using parallel OptiMUSIG activation function”, Appl. Soft Comp. J., vol. 12, pp. 3228-3236, 2012. S. De, S. Bhattacharyya, S. Chakraborty, “True color image segmentation by an optimized multilevel activation function”, IEEE International Conference on Computational Intelligence and Computing Research, pp. 545–548, 2010. S. De, S. Bhattacharyya, S. Chakraborty, “Color Image Segmentation by NSGA-II based ParaOptiMUSIG Activation Function”, IEEE International Conference on Machine Intelligence Research and Advancement, pp. 105 - 109, 2013. A. Amelio, C. Pizzuti, “A Genetic Algorithm for Color Image Segmentation”, A.I. Esparcia-Alc´azar et al. (Eds.): EvoApplications 2013, LNCS 7835, Springer-Verlag Berlin Heidelberg, pp. 314–323, 2013. A. Halder, S. Pramanik, A. Kar, “Dynamic Image Segmentation using Fuzzy C-Means based Genetic Algorithm”, International Journal of Computer Applications, vol. 28, no. 6, 2011. S. Jansi, P. Subashini, “Modified FCM using Genetic Algorithm for Segmentation of MRI Brain Images”, IEEE International Conference on Computational Intelligence and Computing Research,2014. S. De, S. Bhattacharyya, P. Dutta, “Efficient grey-level image segmentation using anoptimised MUSIG (OptiMUSIG) activation function. International Journal of Parallel, Emergent and Distributed Systems”, vol. 26, no. 1, pp. 1–39, 2010. Borsotti, M., Campadelli, P., Schettini, R., “Quantitative evaluation of color image segmentation results”, Pattern Recognition Letters,vol. 19,no.8, pp.741–747, 1998.