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Research article Special Issues

Safeguarding nurses' mental health: The critical role of psychosocial safety climate in mitigating relational stressors and exhaustion

  • Burnout among nurses is a pervasive concern in healthcare, with profound implications for patient care and nurse well-being. While research has highlighted the detrimental effects of burnout on many aspects of nursing, including patient safety and quality of care, the underlying mechanisms driving burnout warrant further investigation. In this cross-sectional study, we surveyed 196 nurses from diverse Italian hospitals using an online questionnaire via Qualtrics. Our findings revealed significant negative correlations between psychological safety climate and both relational stressors and emotional exhaustion. Conversely, relational stressors positively correlated with emotional exhaustion, and a significant negative indirect effect of psychological safety climate was found for emotional exhaustion through relational stressors, emphasizing the pivotal role of psychological safety climate in mitigating nurse burnout. Our study underscores the potential effectiveness of interventions targeting psychological safety climate and relational stressors in alleviating emotional exhaustion and burnout among nurses. Theoretical implications underscore the importance of deepening the role of psychological safety climate in mitigating emotional exhaustion, while practical implications emphasize the need for fostering a positive psychological safety climate and implementing targeted interventions to support nurses' well-being.

    Citation: Teresa Galanti, Michela Cortini, Giuseppe Filippo Giudice, Salvatore Zappalà, Ferdinando Toscano. Safeguarding nurses' mental health: The critical role of psychosocial safety climate in mitigating relational stressors and exhaustion[J]. AIMS Public Health, 2024, 11(3): 905-917. doi: 10.3934/publichealth.2024046

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  • Burnout among nurses is a pervasive concern in healthcare, with profound implications for patient care and nurse well-being. While research has highlighted the detrimental effects of burnout on many aspects of nursing, including patient safety and quality of care, the underlying mechanisms driving burnout warrant further investigation. In this cross-sectional study, we surveyed 196 nurses from diverse Italian hospitals using an online questionnaire via Qualtrics. Our findings revealed significant negative correlations between psychological safety climate and both relational stressors and emotional exhaustion. Conversely, relational stressors positively correlated with emotional exhaustion, and a significant negative indirect effect of psychological safety climate was found for emotional exhaustion through relational stressors, emphasizing the pivotal role of psychological safety climate in mitigating nurse burnout. Our study underscores the potential effectiveness of interventions targeting psychological safety climate and relational stressors in alleviating emotional exhaustion and burnout among nurses. Theoretical implications underscore the importance of deepening the role of psychological safety climate in mitigating emotional exhaustion, while practical implications emphasize the need for fostering a positive psychological safety climate and implementing targeted interventions to support nurses' well-being.



    Image segmentation is the basic work of image processing research. There are primarily four types of segmentation methods: thresholding [1,2,3], boundary-based [4,5], region-based [6,7,8], and hybrid techniques [9,10,11,12]. Several algorithmic techniques such as Artificial Neural Network [13], Convolutional neural Network [14], and K-nearest Neighbors [15] can also be applied in image segmentation.

    Among all the methods of image segmentation, Otsu [16] method is the most popular one. Computational complexity of Otsu methods increases exponentially with the increasing number of thresholds due to exhaustive search. It is a difficult task to study how to improve the segmentation accuracy of Otsu with multi-thresholds method. The expansion of the actual Otsu's thresholding to multilevel thresholding is known as multi-Otsu thresholding [17]. Nevertheless, these methods are unable to obtain effective results for noisy images. To solve this problem, J. Zhuang [18] proposed a 2-D Otsu method that selects the optimal threshold on a 2-D histogram. Jing [19] proposed the maximum between-cluster variance by using a 3-D histogram approach and was named the 3-D Otsu method. In this method, the 3D histogram takes the median value of neighborhood pixels as the third feature of the existing features of the 2D OTSU method, that is, gray information and neighborhood mean value. L. Wang [20] derived a group of recurrence formula for 3-D Otsu's method and eliminated redundancy in the formula by introducing a look-up table. The method reduced the computation of the 3DOtsu. Therefore, in order to optimize the search process, a faster and automatic optimal threshold selection method is needed.

    The traditional exhaustive methods take the large amount of computation. In this case, meta-heuristic methods have attracted much attention in recent years. L. Bian proposed a new multi-threshold MRI image segmentation algorithm based on mixed entropy using Curvelet transformation and Multi-Objective Particle Swarm Optimization [21]. This method could deal with the difficulties caused by noise disturbance, intensity inhomogeneity and edge blurring in Magnetic Resonance Imaging image segmentation. N. Muangkote proposed the nature-inspired meta-heuristic named multilevel thresholding moth-flame optimization algorithm (MTMFO) for multilevel thresholding [22]. This algorithm effectively solved the problem of satellite image segmentation. B. Surina proposed a multi-level thresholding model based on gray-level & local-average histogram (GLLA) and Tsallis–Havrda–Charvát entropy for RGB color image [23]. This method had the effectiveness and reasonability. A. Wunnava proposed an adaptive Harris Hawks optimization (AHHO) technique to solve the multi-level image segmentation [24]. The experimental results were beneficial to the segmentation field of image processing. The optimization algorithm is adopted to solve the threshold selection of the multi-threshold image segmentation method, which effectively improves the segmentation precision of the image segmentation method [25,26].

    The optimization algorithm can solve practical engineering problems in recent years [27]. Different optimization algorithms adapt to different engineering problems and have different optimization capabilities [28,29]. These nature-inspired optimization algorithms were mainly classified into two classes recently which are evolutionary algorithm (EA) and biology-inspired or bio-inspired algorithms. EA imitated the Darwinian theory of evolution [30]. There were many good algorithms in this class. In 1975, GA was invented by John Holland [31], it used the binary representation of individuals. In 1997, Differential evolution was proposed Rainer stone, the essence was a multi - objective optimization algorithm [32]. The most popular class was the biology-inspired or bio-inspired algorithms right now. One of the most famous algorithms was the Particle Swarm Optimizer (PSO) which was developed based on the swarming behavior of fish and birds [33]. In 2015, the ant lion optimizer was proposed by Mirjalili [34]. In 2016, Askarzadeh proposed the crow search algorithm [35]. In 2017, the killer whale algorithm was proposed by Biyanto [36]. These algorithms were inspired from the predation behavior animal, so as to obtain better searching ability. There also some algorithms inspired from the physics and chemistry, these algorithms usually had simple mathematical models, but had good optimization effect. In 2001, the harmony search algorithm was proposed by Geem [37]. In 2015, Zheng Yu-Jun proposed water wave optimization algorithm [38]. In 2019, A. Faramarzi proposed a novel optimization algorithm, called Equilibrium optimizer (EO), which controlled volume mass balance models used to estimate both dynamic and equilibrium states [39]. No-Free-Lunch [40] proved that no algorithm can solve all optimization problems.

    There is no perfect optimization algorithm and the optimization algorithm should be improved to better solve engineering problems. Many scholars study the hybrid optimization algorithm [41]. Pankaj U. proposed a new multistage hybrid optimization algorithm to optimize multilevel threshold [42]. The method had a good performance in test images. Amandeep proposed a fast SAR image segmentation method based on Particle Swarm Optimization-Gravitational Search Algorithm [43]. The method had good segmentation accuracy. D. Kole proposed a new approach to automatic unsupervised efficient image segmentation algorithm using hybrid technique based on Particle Swarm Optimization and Genetic Algorithm [44]. Gao H. presented a learning strategy-based particle swarm optimization algorithm with an exchange method [45]. The experiment shows that the method had a good result using the Berkeley images. So, the hybrid optimization algorithm could use the advantage of the different algorithms to enhance the search ability of the original algorithm.

    This paper focuses on the segmentation of wood fiber images. The wood fiber images have the small target, it takes huge challenge for the segmentation method. We use 3DOtsu as a fitness function to segment wood fiber images. The threshold image method can overcome the difficulty of wood fiber image difference channel. The Equilibrium optimizer algorithm can find the threshold of the wood fiber images, however the segmentation accuracy is low and the CPU time is large. In order to improve the optimal ability of EOA, we use the GOA improve the EOA. The HEOA obtains the strong ability find the optimal threshold from the wood fiber images.

    In this paper, the HEOA is proposed. The main contribution of this study is that the GOA improves the original EOA for multilevel threshold. Experiments are performed on CEC2015 data, classic images and wood fiber images. The proposed algorithm is compared with the original EOA and other six algorithms include CSA, FPA, PSO, HSOA and HWOA. The GOA algorithms can balance the exploration and exploitation of the EOA. The results show the superiority of the proposed algorithm in terms of the objective function value, image quality measures on both normal and high-level thresholding.

    Otsu algorithm is a classical image segmentation method, and its segmentation results are excellent. This method can be extended to multi-threshold Otsu to obtain the maximum variance between two classes, so as to obtain the optimal threshold of the image [46].

    Assuming that there are K thresholds, which divide the image into K+1 classes. The extended between-class variance is calculated by

    f(t)=Ki=0σi (1)

    The sigma terms are determined by Eq. (6) and the mean levels are calculated by Eq. (7):

    σ0=ϖ0(μ0μT)2,σ1=ϖ1(μ1μT)2,,σK1=ϖK1(μK1μT)2 (2)
    μ0=ti=1ipi/ϖ0,μ1=t2i=t1+1ipi/ϖ1,,μK1=Li=tM1+1ipi/ϖK1 (3)

    The optimum thresholds are found by maximizing the between-class variance by Eq. (8):

    t=argmax(K1i=0σi) (4)

    3D-Otsu, the histogram is constructed by taking gray values of pixels along with their spatial information including the neighborhood mean and median [47]. The Otsu only segment the single channel of the image, however the color images have three channels. There are more information in the three channels, so the 3DOtus can use the information of three channels and get the best threshold form the color images. An image I with K gray levels and N number of pixels is considered, where the intensity value of pixel at the location (x,y) denoted by f(x,y). The mean and median value of l×l neighborhood of pixel is denoted by g(x,y) and h(x,y), which is defined by Eq. (9) and Eq. (10).

    g(x,y)=1l2l12i=l12l12j=l12f(x+i,y+j) (5)
    h(x,y)=med{f(x+i,y+j);i,j=l12,...,l12} (6)

    Where, the value of l is taken as 3 in this paper. For every pixel in the image I, mean and median values are calculated in the l×l neighborhood.

    Let (tf,tg,th) as the optimal threshold of the three histograms, and use the Eq. (8) to calculate the optimal threshold from the three histograms. The optimal threshold is expressed as:

    tf=argmax{K1i=0σi(tf)} (7)
    tg=argmax{K1i=0σi(tg)} (8)
    th=argmax{K1i=0σi(th)} (9)

    The final optimum thresholds are average of the result of tf, tg and th, and can be defined by Eq.10:

    t=(tf+tg+th)/3 (10)

    The 3DOtsu image segmentation method uses the information of three channels of color images, the optimal threshold can segment the image exactly.

    The EO method is inspired by the simple well-mixed dynamic mass balance on the control body, in which the mass balance equation is used to describe the coordination of non-active components in the control body as a function of its various source and aggregation mechanisms. Similar to most meta-heuristic algorithms, EO uses the initial population to start the optimization process. The equilibrium candidates' collaboration can be seen from Figure1. The initial concentrations are constructed based on the number of particles and dimensions with uniform random initialization in the search space as follows:

    Figure 1.  Equilibrium candidates' collaboration.
    Cinitiali=Cmin+rand×(CmaxCmin) (11)

    Where, Cinitiali is the initial concentration vector of the ith particle, Cmax and Cmin denote the minimum and maximum values for the dimensions, rand is a random vector in interval of [0, 1].

    The equilibrium state is the final convergence state of the algorithm, which is desired to be the global optimum. At the beginning of the optimization process, there is no knowledge about the equilibrium state and only equilibrium candidates are determined to provide a search pattern for the particles. According to the different experiments under different types of case problems, these candidate particles are the four optimal particles determined in the whole optimization process plus another particle. These particles are nominated as equilibrium candidates and are used to construct a vector called the equilibrium pool:

    Ceq,pool={Ceq(1),Ceq(2),Ceq(3),Ceq(4),Ceq(ave)} (12)

    Where, Ceq(1) is the first particle updates all of its concentrations, Ceq(ave)is the average of the particle.

    The main concentration updating rule is the exponential term (F). In order to guarantee convergence by slowing down the search speed along with improving the exploration and exploitation ability of the algorithm, the version can be seen as:

    F=a1×sign(r0.5)×(eλ×t1) (13)

    Where:

    t=(1IterMax_iter)(a2IterMax_iter) (14)

    Where, Iter and Max_iter present the current and the maximum number of iterations.

    The generation rate is one of the most important terms in the proposed algorithm to provide the exact solution by improving the exploitation phase. The final set of generation rate equation is as follows:

    G=G0eλ×(tt0)=G0F (15)

    Where:

    G0=GCP(CeqλC) (16)
    GCP={0.5r1r2GP0r2<GP (17)

    Where, r1 and r2 are random numbers in [0, 1] and GCP vector is constructed by the repetition of the same value resulted from Eq. (16).

    Finally, the updating rule of EO will be as follows:

    C=Ceq+(CCeq)×F+GλV(1F) (18)

    Where, F is defined in Eq. (13), and V is considered as unit.

    In 2017, Mirjalili Seyedali proposed the grasshopper optimization algorithm [48]. The grasshoppers are a genus of straight fins of insect, they are seen as pests, because they are in crops for food, to cause damage to agriculture. The growth cycle of grasshoppers is shown in Figure 2. The grasshoppers usually exist alone in nature, but they are one of the biggest swarm of all species. The grasshoppers are unique in that they crowd behavior in adults and larvae of between. Millions of larva foraging on the basis of jumping, they feed on almost all plants, and when they reach adulthood, they form a large group in the air, making long migrations, looking for the next food source.

    Figure 2.  Grasshopper growth cycle.

    In larvae stage, the main characteristic of grasshopper is moving slowly, small scale food. When they become adult, collective action has became the main activity characteristics of grasshopper. The natureinspired algorithms logically divide the search process into two tendencies: exploration and exploitation. So mathematical model of the gregarious grasshoppers is represented as follows:

    Xi=Si+Gi+Ai (19)

    where Xi defines the position of the i-th grasshopper, Si is the social interaction, Gi is the gravity force on the i-th grasshopper, and Ai shows the wind advection.

    {Si=Nj=1s(dij)dijs(r)=ferler (20)

    where dij is the distance between the i-th and the j-th grasshopper, calculated as dij=|xjxi|, s is a function to define the strength of social forces, dij is an unit vector from the i-th grasshopper to the j-th grasshopper.

    Gi=geg (21)

    where g is the gravitational constant and eg shows an unity vector towards the center of earth.

    Ai=uew (22)

    Where u is a constant drift and ew is a unity vector in the direction of wind.

    Substituting S, G, and A into Eq. (19), then this equation can be expanded as follows:

    Xi=Nj=1s(|xjxi|)xjxidijgeg+uew (23)

    However, this mathematical model cannot be used directly to solve optimization problems, mainly because the grasshoppers quickly reach the comfort zone and the swarm does not converge to a specified point. A modified version of this equation is proposed as follows to solve optimization problems:

    Xdi=c1(Nj=1c2ubdlbd2s(|xjxi|)xjxidij)+Td (24)

    Among them, ubd and lbd are a type of upper and lower limitation, Td is the optimal value after each iteration, c1=c2=cmaxlcmaxcminL, c1 balances the global search and local search for the target area, c2 balances the relationship among the attraction between two grasshopper, cmax and cmin can set the maximum and minimum search ability, l represents the current iteration number, L is the largest number of iterations.

    In this subsection, we describe the hybrid equilibrium optimizer algorithm in detail. The EOA fall into the local optimal easily. The algorithm cannot balance the exploitation and exploration. In order to solve this problem, we use the advantage of the GOA to improve the optimization ability of the GOA. We use the Eq. (19) to enhance the individual ability of the EOA. The Xi have the strong ability to avoid the EOA drop into the local optimal. The formula can be seen below:

    C=Ceq+(CCeq)×F+GλV(1F)×Xi (25)

    A comprehensive algorithm step of HEOA based multilevel color image segmentation is given in Algorithm 1.

    Algorithm 1 Pseudo-code of HEOA algorithm
    Input: The color image
    Output: Segmentation color image
    Read the input and compute the histogram of three channels of color imageInitialize the parameters r1andr2
    Initialize the random population Ci
    while L < Max_iter do
        Calculate the fitness values of EOA
        for (each hawk Ci) do
          Calculate Ceq, Xi
          Update the C using Eq. (25)
          Calculate the fitness function using Eq.(10)
        end for
        UpdateCbestif there is a better solution
        L=L+1
    end while
    Get the best solution as the multilevel threshold K
    According the K segment the three channels of the images
    Get the segmentation images

     | Show Table
    DownLoad: CSV

    In order to use the information of the three channels of color images, we use the fitness functions Eq. (10) to calculate the histogram of the three channels. And then, we use the HEOA to optimize the fitness function. Finally, we can get the best threshold and segment the color images. The flowchart of the BMPA can be seen from the Figure 3.

    Figure 3.  The flowchart of proposed method.

    The computational complexity of the proposed method depends on the number of each combination (L), the number of generations (g), the number of population (n) and the parameters dimensions (d). So, computational complexity on L combination isO(L). The computational complexity of population location update is O(n*d). The calculation of fitness function values of all seagull populations isO(nL). Therefore, the final computational complexity of the proposed method is:

    O(MBE)O(g(nd+nL)) (26)

    To verify the optimization performance of HEOA, its performance is compared with five other optimization methods including CSA, FPA, PSO, BA and basic EOA. The optimization algorithm compared in this section tests CEC2015 benchmark test functions. The detailed description of CEC 2015 benchmark test functions [49] is presented in Table 2. For fair comparison, the other parameters of all algorithms are set according to their original papers. The results obtained by the algorithms on benchmark functions are presented in Table 3. All parameters of the comparison optimization algorithm are shown in table 1. Figure 4 show the result of the CEC2015. The population size is 30 and the number of iterations is 100. The proposed DLNN are testing in Matlab 2018b.

    Table 1.  Parameters and references of the comparison algorithms.
    Algorithm Parameters Value
    EOA c1 2
    c2 2
    CSA [50] AP 0.5
    FPA [51] P 0.5
    PSO [52] Swam size Cognitive, social acceleration Inertial weight 2002, 20.95–0.4
    BA [53] β (0, 1)
    HEOA Levy 1.5

     | Show Table
    DownLoad: CSV
    Table 2.  CEC 2015 benchmark test functions.
    No. Functions Related basic functions Dim fmin
    CEC-1 Rotated Bent Cigar Function Bent Cigar Function 30 100
    CEC-2 Rotated Discus Function Discus Function 30 200
    CEC-3 Shifted and Rotated Weierstrass Function Weierstrass Function 30 300
    CEC-4 Shifted and Rotated Schwefel's Function Schwefel's Function 30 400
    CEC-5 Shifted and Rotated Katsuura Function Katsuura Function 30 500
    CEC-6 Shifted and Rotated HappyCat Function HappyCat Function 30 600
    CEC-7 Shifted and Rotated HGBat Function HGBat Function 30 700
    CEC-8 Shifted and Rotated Expanded Griewank's plus Rosenbrock's Function Griewank's Function Rosenbrock's Function 30 800
    CEC-9 Shifted and Rotated Expanded Scaer's F6 Function Expanded Scaer's F6 Function 30 900
    CEC-10 Hybrid Function 1 (N = 3) Schwefel's FunctionRastrigin's FunctionHigh Conditioned Elliptic Function 30 1000
    CEC-11 Hybrid Function 2 (N = 4) Griewank's Function Weierstrass Function Rosenbrock's Function Scaer's F6 Function 30 1100
    CEC-12 Hybrid Function 3 (N = 5) Katsuura FunctionHappyCat FunctionExpanded Griewank's plus Rosenbrock's Function Schwefel's FunctionAckley's Function 30 1200
    CEC-13 Composition Function 1 (N = 5) Rosenbrock's FunctionHigh Conditioned Elliptic FunctionBent Cigar FunctionDiscus FunctionHigh Conditioned Elliptic Function 30 1300
    CEC-14 Composition Function 2 (N = 3) Schwefel's FunctionRastrigin's FunctionHigh Conditioned Elliptic Function 30 1400
    CEC-15 Composition Function 3 (N = 5) HGBat FunctionRastrigin's FunctionSchwefel's FunctionWeierstrass FunctionHigh Conditioned Elliptic Function 30 1500

     | Show Table
    DownLoad: CSV
    Table 3.  The result of the compared algorithms.
    Func. HEOA CSA PSO FPA BA EOA
    Mean Std. Mean Std. Mean Std. Mean Std. Mean Std. Mean Std.
    CEC-1 1.05E+05 1.54E+07 4.21E+05 1.47E+08 2.17E+09 3.53E+07 1.76E+08 7.02E+07 4.76E+08 2.86E+08 1.07E+05 3.69E+07
    CEC-2 6.70E+06 1.70E+09 2.06E+04 5.26E+09 7.01E+10 3.53E+09 3.04E+10 4.70E+09 3.36E+10 6.82E+09 6.70E+07 4.05E+09
    CEC-3 3.20E+02 7.12E-02 3.20E+02 1.51E-01 3.22E+02 9.57E-02 3.21E+02 1.43E-01 3.21E+02 2.10E-01 3.55E+02 1.47E-01
    CEC-4 4.10E+02 1.75E+00 4.05E+02 9.03E+00 5.46E+02 1.29E+01 5.30E+02 1.61E+01 5.21E+02 9.70E+00 4.50E+02 2.39E+01
    CEC-5 9.81E+02 1.50E+02 1.22E+03 3.30E+02 4.74E+03 2.40E+02 3.80E+03 3.97E+02 3.65E+03 3.52E+02 9.91E+02 2.97E+02
    CEC-6 2.05E+03 4.75E+06 2.14E+03 2.33E+07 3.79E+09 9.03E+06 4.52E+09 1.14E+07 1.28E+08 2.71E+07 2.10E+03 1.37E+07
    CEC-7 7.02E+02 1.24E+01 7.03E+02 4.37E+01 1.81E+03 1.40E+01 1.78E+03 2.70E+01 1.78E+03 4.99E+01 8.82E+02 2.49E+01
    CEC-8 1.47E+03 1.03E+06 1.41E+04 3.25E+06 2.21E+09 1.05E+06 1.34E+09 1.63E+06 1.34E+09 3.78E+06 1.47E+04 1.08E+06
    CEC-9 1.00E+03 7.30E+00 1.00E+03 4.77E+01 1.33E+03 2.45E+01 1.33E+03 3.46E+01 1.62E+03 5.15E+01 1.00E+04 3.38E+01
    CEC-10 1.23E+03 4.82E+04 2.05E+03 3.09E+06 2.58E+09 4.14E+05 2.97E+07 8.13E+05 4.41E+08 4.49E+06 1.36E+04 7.89E+05
    CEC-11 1.35E+03 4.52E+01 1.40E+03 7.94E+01 2.00E+03 6.39E+01 1.77E+03 1.02E+02 1.77E+03 9.80E+01 1.32E+04 1.24E+02
    CEC-12 1.30E+03 1.03E+01 1.30E+03 1.75E+01 1.76E+03 1.22E+01 1.49E+03 1.28E+01 1.51E+03 3.25E+01 1.34E+05 1.58E+01
    CEC-13 1.30E+03 8.67E+00 1.34E+03 1.49E+00 5.44E+05 1.86E+01 1.54E+03 3.03E+01 1.56E+03 2.48E+00 1.55E+05 3.24E+01
    CEC-14 3.22E+03 2.32E+03 8.88E+03 4.24E+03 2.23E+04 2.92E+03 2.23E+04 4.76E+03 2.23E+04 5.46E+03 3.22E+04 3.59E+03
    CEC-15 1.60E+03 3.36E+02 1.60E+03 6.49E+02 1.28E+04 7.10E+02 9.01E+03 1.34E+03 4.09E+03 1.05E+03 1.80E+03 1.27E+03

     | Show Table
    DownLoad: CSV
    Figure 4.  The result of CEC2015.

    As can be seen from table 3, the results of HEOA algorithm in processing all standard functions are better than those of other comparison algorithms, indicating that the HEOA algorithm can not only solve single-dimensional mathematical functions but also deal with multi-dimensional mathematical functions effectively. It shows that the optimization ability of HEOA algorithm is superior to other comparison algorithms. It can be seen from the Figure 4, the EOA and BA obtains the worst result and the HEOA gets the best result. Above the analysis, HEOA obtains the strong optimal ability, and in the next section we use the HEOA optimize the 3DOtsu.

    In this section, HEOA algorithm is applied to optimize the 3DOtsu. In order to better verify the image segmentation ability of proposed algorithm, it is compared with the optimized 3DOtsu algorithm of CSA, PSO, FPA and BA. The color image has three color channels. In this paper, the images of the three channels are segmented, and then the three resulting images are fused to obtain the final segmentation result graph. Firstly, the segmentation effect and precision of HEOA algorithm are analyzed when the threshold value is increased. Then the segmentation ability, statistical analysis and stability analysis of the proposed HEOA algorithm and other optimization algorithms in 3DOtsu image segmentation are analyzed. All parameters of the comparison optimization algorithm are shown in table 3. The test images and the histogram of three channels of color images are as follows Figure 5. The test images included color natural images and satellite images. It can be seen from the histogram, the histogram of three channels has significant different and it take huge challenge for optimization algorithm to find the optimal threshold. Color image segmentation requires a higher threshold level, so it is more complex to use optimization technology to solve the problem. Therefore, the optimization algorithm has the characteristics of randomness.

    Figure 5.  The color test images and histogram.

    In order to better observe the performance of the algorithm, we select K = 4, 8, 12 and 15. The evaluation index can better observe the performance of the algorithm. In order to comprehensively analyze the performance of the algorithm, we calculate the CPU time, Uniformity (U), Peak Signal-to-Noise Ratio (PSNR) and Feature Similarity Index (FSIM). The evaluation index of many object optimization methods can be seen table 4.

    Table 4.  The evaluation index of many object optimization methods.
    No. Measures Formulation Reference
    1 Uniformity measure U=12×(k1)×dj=1iRj(fiμj)2N×(fmaxfmin)2 [54]
    2 Peak Signal-to-Noise Ratio (PSNR) PSNR=10×log10(2552MSE)
    MSE=1mnm1i=1n1j=1[I(i,j)K(i,j)]2
    [55]
    3 Feature Similarity Index (FSIM) FSIM=x=ηSL(x)PCm(x)x=ηPCm(x) [56]

     | Show Table
    DownLoad: CSV

    In this section, we compare the different segmentation method as fitness function. The EOA and HEOA optimize Otsu and 3DOtsu function. The FSIM of the compared algorithms can be seen from table 5. The Bar chart of the FSIM can be seen in Figure 6.

    Table 5.  The FSIM of the comparison algorithms.
    Image K EOA-Otsu EOA-3DOtsu HEOA-Otsu HEOA-3DOtsu
    Test1 4 0.8628 0.8886 0.8973 0.9106
    8 0.8657 0.8864 0.8957 0.9170
    12 0.9103 0.9332 0.9411 0.9580
    15 0.9293 0.9479 0.9565 0.9695
    Test2 4 0.8644 0.8799 0.8901 0.9015
    8 0.8459 0.8674 0.8736 0.9135
    12 0.9298 0.9511 0.9569 0.9591
    15 0.9287 0.9474 0.9562 0.9671
    Test3 4 0.8586 0.8833 0.8919 0.9056
    8 0.8599 0.8766 0.8859 0.9246
    12 0.9207 0.9370 0.9466 0.9661
    15 0.9049 0.9239 0.9358 0.9688
    Test4 4 0.8518 0.8660 0.8805 0.8963
    8 0.8856 0.9060 0.9125 0.9221
    12 0.8823 0.9034 0.9143 0.9619
    15 0.9012 0.9260 0.9343 0.9742
    Test5 4 0.8379 0.8545 0.8645 0.8988
    8 0.8648 0.8854 0.8992 0.9193
    12 0.9166 0.9305 0.9446 0.9659
    15 0.9055 0.9286 0.9345 0.9750
    Test6 4 0.8725 0.8902 0.9025 0.9157
    8 0.8854 0.9040 0.9160 0.9189
    12 0.9267 0.9484 0.9566 0.9585
    15 0.8904 0.9095 0.9214 0.9663
    Test7 4 0.8708 0.8883 0.9009 0.9147
    8 0.8845 0.9037 0.9155 0.9171
    12 0.9250 0.9478 0.9555 0.9581
    15 0.8898 0.9087 0.9202 0.9648
    Test8 4 0.8704 0.8871 0.9000 0.9143
    8 0.8830 0.9017 0.9142 0.9155
    12 0.9232 0.9469 0.9535 0.9578
    15 0.8886 0.9079 0.9201 0.9629
    Test9 4 0.8716 0.8884 0.9011 0.9151
    8 0.8844 0.9026 0.9157 0.9163
    12 0.9237 0.9470 0.9552 0.9596
    15 0.8897 0.9082 0.9217 0.9633
    Test10 4 0.8720 0.8896 0.9024 0.9171
    8 0.8863 0.9027 0.9162 0.9179
    12 0.9247 0.9482 0.9561 0.9607
    15 0.8915 0.9089 0.9223 0.9645

     | Show Table
    DownLoad: CSV
    Figure 6.  The FSIM result of compared algorithms.

    It can be seen from table 5, the FSIM value of 3DOtsu is better than Otsu. The 3DOtsu can use the information of color image, and get the best segment result. And the result of HEOA is better than EOA, it means that the Hybrid algorithm improves the optimal ability of EOA and makes the algorithm find the best result. Above analyze, we use the 3DOtsu as the fitness function in the next experiment.

    The Figure 6 show the FSIM result of the compared algorithms. The result of 3DOtsu is better than the result of Otsu. The 3DOtsu use the information of three channels and obtains the better threshold than Otsu. At the same time, the result of HEOA is better than EOA, it means that the GOA can improve the optimal ability of the EOA.

    In this experiment, to show the merits of proposed technique, the results are compared with CSA, FPA, PSO, BA, HSOA [57] and HWOA [58] using 3DOtsu objective function. The parameters of the compared algorithms are set in the references.

    The Figure 7 show the curve of Uniformity. It can be seen from figure, the HEOA obtains the best result in compared algorithms, the HSOA and HWOA gets the better result in compared algorithms, the CSA, FPA, PSO and BA obtains the worst result in all cases. It can be kwon that the hybrid optimization algorithms have the better optimal ability than original optimization algorithm. Most of all, the HEOA has the strongest ability in the compared algorithms.

    Figure 7.  The Uniformity result of compared algorithms.

    From Table 6, it can be observed that for all the test images, HEOA is better and more reliable than CSA, FPA, PSO, and BA, because of its precise search capability, at a high threshold level (K). Performance of HSOA and HWOA has closely followed HEOA. The solution update strategy for FPA and PSO may have led to poor results. The comprehensive performance ranking of the comparison algorithm is as follows: HEOA > HSOA > HWOA > PSO > BA > CSA > FPA. So, the HEOA have a better performance than other algorithms.

    Table 6.  The Uniformity measure for the comparison algorithms.
    Image K HEOA HSOA HWOA CSA FPA PSO BA
    Test1 4 0.9571 0.9415 0.9437 0.9245 0.9284 0.9262 0.9243
    8 0.9674 0.9525 0.9594 0.9299 0.9309 0.9392 0.9373
    12 0.9744 0.9641 0.9654 0.9404 0.9456 0.9424 0.9457
    15 0.9795 0.9684 0.9617 0.9428 0.9441 0.9445 0.9458
    Test2 4 0.9544 0.9460 0.9460 0.9224 0.9167 0.9207 0.9216
    8 0.9722 0.9583 0.9624 0.9442 0.9422 0.9425 0.9356
    12 0.9813 0.9717 0.9639 0.9437 0.9458 0.9526 0.9497
    15 0.9824 0.9698 0.9697 0.9499 0.9479 0.9468 0.9515
    Test3 4 0.9528 0.9437 0.9427 0.9244 0.9184 0.9184 0.9165
    8 0.9626 0.9500 0.9482 0.9255 0.9274 0.9323 0.9290
    12 0.9782 0.9657 0.9625 0.9464 0.9453 0.9486 0.9406
    15 0.9812 0.9701 0.9683 0.9467 0.9450 0.9487 0.9513
    Test4 4 0.9518 0.9403 0.9435 0.9201 0.9171 0.9161 0.9187
    8 0.9699 0.9589 0.9520 0.9327 0.9350 0.9331 0.9402
    12 0.9749 0.9623 0.9653 0.9385 0.9398 0.9409 0.9439
    15 0.9806 0.9717 0.9700 0.9486 0.9490 0.9457 0.9485
    Test5 4 0.9541 0.9410 0.9402 0.9257 0.9167 0.9206 0.9207
    8 0.9679 0.9558 0.9560 0.9385 0.9306 0.9399 0.9392
    12 0.9769 0.9670 0.9618 0.9393 0.9441 0.9404 0.9455
    15 0.9808 0.9639 0.9678 0.9468 0.9508 0.9519 0.9467
    Test6 4 0.9507 0.9393 0.9373 0.9169 0.9197 0.9138 0.9154
    8 0.9666 0.9504 0.9512 0.9383 0.9298 0.9355 0.9352
    12 0.9787 0.9644 0.9673 0.9492 0.9505 0.9474 0.9431
    15 0.9824 0.9713 0.9667 0.9470 0.9480 0.9498 0.9472
    Test7 4 0.9514 0.9397 0.9378 0.9183 0.9212 0.9150 0.9167
    8 0.9667 0.9524 0.9529 0.9392 0.9300 0.9360 0.9366
    12 0.9802 0.9648 0.9675 0.9510 0.9521 0.9479 0.9433
    15 0.9841 0.9725 0.9680 0.9473 0.9483 0.9502 0.9487
    Test8 4 0.9508 0.9377 0.9365 0.9165 0.9196 0.9137 0.9161
    8 0.9649 0.9522 0.9520 0.9383 0.9284 0.9349 0.9355
    12 0.9789 0.9642 0.9663 0.9507 0.9507 0.9479 0.9417
    15 0.9837 0.9715 0.9670 0.9468 0.9464 0.9497 0.9479
    Test9 4 0.9503 0.9374 0.9355 0.9158 0.9191 0.9118 0.9151
    8 0.9633 0.9510 0.9500 0.9363 0.9272 0.9346 0.9351
    12 0.9772 0.9634 0.9655 0.9497 0.9488 0.9468 0.9402
    15 0.9820 0.9706 0.9655 0.9462 0.9455 0.9491 0.9460
    Test10 4 0.9505 0.9382 0.9375 0.9171 0.9207 0.9118 0.9167
    8 0.9637 0.9519 0.9510 0.9367 0.9277 0.9360 0.9364
    12 0.9776 0.9653 0.9661 0.9511 0.9493 0.9472 0.9413
    15 0.9838 0.9710 0.9655 0.9481 0.9464 0.9504 0.9479

     | Show Table
    DownLoad: CSV

    Table 7 and table 8 are PSNR and FSIM values of each algorithm respectively. As can be seen from the table, with the increase of the number of threshold values, the PSNR and FSIM values of the image have been significantly improved, indicating that the increase of the number of threshold values significantly improves the segmentation accuracy. The PSNR value of HEOA algorithm is better than other algorithms in all of the 24 groups. So, HEOA have a good competitive than other algorithms. Among all the data of FSIM, HEOA show an improvement of 1.42%, 1.35%, 4.21%, 4.02%, 4.19% and 4.09% over HSOA, HWOA, CSA, FPA, PSO and BA. This means that the segmentation results of HWOA are closer to the original image than other comparison algorithms.

    Table 7.  The PSNR for the comparison algorithms.
    Image K HEOA HSOA HWOA CSA FPA PSO BA
    Test1 4 23.3863 23.2573 23.2526 23.0420 23.0405 23.0397 23.0539
    8 29.2231 29.1025 29.0968 28.9021 28.9007 28.8989 28.9020
    12 32.5692 32.4393 32.4442 32.2300 32.2265 32.2282 32.2414
    15 33.3295 33.1947 33.1953 33.0002 32.9903 32.9903 32.9923
    Test2 4 24.4702 24.3443 24.3386 24.1472 24.1340 24.1342 24.1432
    8 29.4260 29.3020 29.2936 29.0852 29.0987 29.0861 29.1020
    12 32.5786 32.4454 32.4470 32.2471 32.2464 32.2522 32.2424
    15 34.2153 34.0865 34.0884 33.8828 33.8824 33.8823 33.8887
    Test3 4 24.4769 24.3474 24.3453 24.1433 24.1406 24.1517 24.1495
    8 29.9667 29.8287 29.8366 29.6330 29.6383 29.6298 29.6211
    12 32.6661 32.5412 32.5392 32.3369 32.3265 32.3288 32.3254
    15 34.7330 34.6031 34.6015 34.3994 34.3925 34.4084 34.3905
    Test4 4 24.7640 24.6386 24.6369 24.4284 24.4400 24.4423 24.4286
    8 29.5467 29.4208 29.4154 29.2214 29.2193 29.2207 29.2104
    12 33.5823 33.4474 33.4548 33.2561 33.2435 33.2461 33.2509
    15 34.2159 34.0826 34.0820 33.8787 33.8740 33.8707 33.8853
    Test5 4 24.5319 24.3991 24.3994 24.2048 24.1918 24.1918 24.1924
    8 29.5550 29.4198 29.4251 29.2137 29.2181 29.2237 29.2154
    12 34.3322 34.1972 34.1979 34.0010 33.9935 33.9870 33.9959
    15 35.0669 34.9409 34.9366 34.7387 34.7254 34.7407 34.7279
    Test6 4 25.2119 25.0871 25.0842 24.8695 24.8803 24.8734 24.8829
    8 30.9087 30.7880 30.7821 30.5869 30.5821 30.5735 30.5700
    12 34.1912 34.0606 34.0591 33.8576 33.8505 33.8585 33.8626
    15 35.7843 35.6567 35.6607 35.4492 35.4505 35.4438 35.4423
    Test7 4 25.4053 25.1458 25.1450 24.8847 25.0748 24.9284 24.9402
    8 31.0914 30.8883 30.8601 30.7788 30.5828 30.6162 30.6718
    12 34.3507 34.1142 34.1742 34.0164 33.9942 33.8766 33.8983
    15 35.9362 35.6969 35.7545 35.6007 35.4588 35.4937 35.6024
    Test8 4 25.5670 25.2034 25.2799 24.9384 25.1283 24.9787 25.0445
    8 31.2698 31.0054 30.9921 30.8672 30.7368 30.6972 30.8372
    12 34.5283 34.2658 34.2137 34.2017 34.1031 33.9285 34.0632
    15 36.0846 35.7585 35.9118 35.6393 35.6021 35.4988 35.6352
    Test9 4 25.5622 25.0597 25.1265 24.7749 24.9583 24.9368 24.8720
    8 31.1656 30.8841 30.8166 30.7155 30.6732 30.6568 30.8154
    12 34.4249 34.0884 34.1830 34.1183 33.9539 33.7553 33.9067
    15 36.0382 35.7553 35.7737 35.5952 35.5146 35.3593 35.5413
    Test10 4 25.4424 24.9891 25.1108 24.7329 24.7752 24.9286 24.8300
    8 31.1315 30.7681 30.7427 30.5414 30.6599 30.5129 30.6245
    12 34.3961 33.9364 34.1416 33.9835 33.8675 33.7435 33.8129
    15 35.8866 35.7225 35.7457 35.4554 35.4165 35.2905 35.3448

     | Show Table
    DownLoad: CSV
    Table 8.  The FSIM for the comparison algorithms.
    Image K HEOA HSOA HWOA CSA FPA PSO BA
    Test1 4 0.9367 0.9236 0.9225 0.9094 0.9039 0.8944 0.9087
    8 0.9517 0.9414 0.9390 0.9036 0.9077 0.9157 0.9084
    12 0.9587 0.9433 0.9473 0.9135 0.9149 0.9172 0.9135
    15 0.9668 0.9511 0.9540 0.9271 0.9331 0.9287 0.9284
    Test2 4 0.9356 0.9227 0.9262 0.9006 0.8943 0.8936 0.9065
    8 0.9584 0.9422 0.9438 0.9221 0.9123 0.9122 0.9230
    12 0.9632 0.9548 0.9563 0.9283 0.9305 0.9331 0.9233
    15 0.9633 0.9553 0.9506 0.9242 0.9251 0.9255 0.9202
    Test3 4 0.9325 0.9197 0.9181 0.9003 0.9077 0.8898 0.9078
    8 0.9477 0.9333 0.9362 0.9060 0.9062 0.9001 0.9048
    12 0.9599 0.9482 0.9483 0.9289 0.9289 0.9190 0.9162
    15 0.9607 0.9487 0.9468 0.9309 0.9251 0.9325 0.9358
    Test4 4 0.9385 0.9213 0.9207 0.9065 0.9063 0.8982 0.8954
    8 0.9485 0.9362 0.9349 0.9057 0.9058 0.9115 0.9144
    12 0.9580 0.9487 0.9498 0.9240 0.9298 0.9154 0.9200
    15 0.9637 0.9457 0.9532 0.9229 0.9227 0.9321 0.9237
    Test5 4 0.9332 0.9213 0.9264 0.8894 0.9071 0.9082 0.8960
    8 0.9469 0.9377 0.9361 0.9085 0.9141 0.9083 0.9106
    12 0.9642 0.9438 0.9503 0.9210 0.9254 0.9187 0.9270
    15 0.9687 0.9484 0.9489 0.9240 0.9174 0.9240 0.9267
    Test6 4 0.9304 0.9238 0.9186 0.8868 0.9055 0.8972 0.9054
    8 0.9518 0.9317 0.9372 0.9027 0.9099 0.9117 0.9085
    12 0.9579 0.9492 0.9460 0.9280 0.9270 0.9258 0.9158
    15 0.9682 0.9517 0.9490 0.9289 0.9204 0.9315 0.9250
    Test7 4 0.9313 0.9252 0.9198 0.8882 0.9057 0.8984 0.9060
    8 0.9536 0.9322 0.9384 0.9035 0.9109 0.9127 0.9087
    12 0.9590 0.9498 0.9477 0.9287 0.9280 0.9273 0.9177
    15 0.9699 0.9524 0.9510 0.9292 0.9222 0.9335 0.9258
    Test8 4 0.9294 0.9239 0.9181 0.8877 0.9044 0.8970 0.9058
    8 0.9518 0.9309 0.9381 0.9029 0.9096 0.9116 0.9070
    12 0.9573 0.9487 0.9470 0.9276 0.9263 0.9263 0.9175
    15 0.9682 0.9513 0.9494 0.9280 0.9216 0.9324 0.9240
    Test9 4 0.9292 0.9234 0.9161 0.8866 0.9038 0.8956 0.9052
    8 0.9506 0.9296 0.9368 0.9010 0.9089 0.9096 0.9064
    12 0.9569 0.9469 0.9470 0.9273 0.9250 0.9262 0.9160
    15 0.9676 0.9501 0.9474 0.9275 0.9216 0.9308 0.9236
    Test10 4 0.9296 0.9246 0.9170 0.8874 0.9046 0.8962 0.9057
    8 0.9509 0.9306 0.9378 0.9025 0.9093 0.9098 0.9069
    12 0.9589 0.9483 0.9490 0.9275 0.9261 0.9277 0.9165
    15 0.9678 0.9501 0.9479 0.9287 0.9232 0.9316 0.9240

     | Show Table
    DownLoad: CSV

    Table 9 shows the CPU time of each algorithm under different thresholds. When the threshold value K = 4, the results of each optimization algorithm differ little. At this point, the number of thresholds is small, the search space is small, and the optimization capability of each optimization algorithm is basically the same. When K = 15, the computational complexity of image segmentation increases and the CPU time increases absolutely. The average time of each algorithm in the test image is: HEOA < HSOA < HWOA < FPA < CSA < BA < PSO. So, the HEOA algorithm not only has the good performance in image segmentation, but also has the less CPU time than other compared algorithms.Table 6. The Uniformity measure for the comparison algorithms.

    Table 9.  The CPU time for the comparison algorithms.
    Image K HEOA HSOA HWOA CSA FPA PSO BA
    Test1 4 1.2145 1.2251 1.2247 1.2442 1.2405 1.2406 1.2389
    8 1.3154 1.3254 1.3260 1.3452 1.3422 1.3386 1.3385
    12 1.5172 1.5274 1.5279 1.5448 1.5467 1.5451 1.5466
    15 1.8157 1.8260 1.8258 1.8359 1.8435 1.8376 1.8439
    Test2 4 1.2149 1.2259 1.2255 1.2363 1.2392 1.2436 1.2365
    8 1.3154 1.3262 1.3263 1.3388 1.3411 1.3401 1.3371
    12 1.5181 1.5286 1.5288 1.5423 1.5449 1.5466 1.5389
    15 1.8158 1.8266 1.8266 1.8419 1.8398 1.8409 1.8424
    Test3 4 1.2151 1.2257 1.2258 1.2354 1.2367 1.2445 1.2367
    8 1.3158 1.3268 1.3265 1.3402 1.3411 1.3456 1.3436
    12 1.5191 1.5292 1.5292 1.5394 1.5406 1.5474 1.5487
    15 1.8164 1.8270 1.8273 1.8462 1.8369 1.8437 1.8413
    Test4 4 1.2151 1.2254 1.2253 1.2444 1.2358 1.2358 1.2409
    8 1.3166 1.3268 1.3271 1.3432 1.3398 1.3458 1.3461
    12 1.5192 1.5299 1.5301 1.5421 1.5476 1.5483 1.5465
    15 1.8166 1.8275 1.8269 1.8390 1.8466 1.8422 1.8425
    Test5 4 1.2161 1.2269 1.2269 1.2388 1.2447 1.2368 1.2401
    8 1.3167 1.3273 1.3273 1.3456 1.3396 1.3382 1.3431
    12 1.5201 1.5304 1.5302 1.5471 1.5428 1.5454 1.5401
    15 1.8169 1.8274 1.8278 1.8431 1.8379 1.8456 1.8405
    Test6 4 1.2168 1.2271 1.2268 1.2372 1.2413 1.2412 1.2383
    8 1.3172 1.3281 1.3273 1.3412 1.3407 1.3448 1.3379
    12 1.5206 1.5307 1.5313 1.5491 1.5408 1.5445 1.5493
    15 1.8169 1.8278 1.8270 1.8395 1.8463 1.8410 1.8428
    Test7 4 1.2183 1.2275 1.2282 1.2373 1.2421 1.2429 1.2399
    8 1.3179 1.3284 1.3291 1.3429 1.3420 1.3463 1.3391
    12 1.5219 1.5326 1.5316 1.5510 1.5410 1.5462 1.5506
    15 1.8179 1.8293 1.8289 1.8408 1.8466 1.8410 1.8440
    Test8 4 1.2173 1.2270 1.2272 1.2371 1.2403 1.2424 1.2393
    8 1.3167 1.3278 1.3282 1.3409 1.3401 1.3447 1.3386
    12 1.5217 1.5308 1.5303 1.5497 1.5398 1.5460 1.5498
    15 1.8172 1.8273 1.8284 1.8396 1.8446 1.8397 1.8424
    Test9 4 1.2154 1.2265 1.2258 1.2357 1.2391 1.2409 1.2376
    8 1.3166 1.3268 1.3277 1.3398 1.3389 1.3428 1.3375
    12 1.5204 1.5304 1.5291 1.5482 1.5397 1.5453 1.5485
    15 1.8154 1.8272 1.8281 1.8395 1.8431 1.8385 1.8422
    Test10 4 1.2155 1.2282 1.2270 1.2377 1.2404 1.2419 1.2380
    8 1.3172 1.3283 1.3279 1.3401 1.3399 1.3444 1.3391
    12 1.5207 1.5319 1.5305 1.5494 1.5397 1.5460 1.5495
    15 1.8160 1.8272 1.8297 1.8400 1.8440 1.8393 1.8442

     | Show Table
    DownLoad: CSV

    The experimental results of each algorithm are the same, so statistical tests are needed. Parametric statistical tests are based on various assumptions [59]. The well-known non-parametric statistical tests, namely Friedman test [60] and Wilcoxon rank-sum test [61] are used in this section. For the average rank of Friedman's test given in table 10, the method presented in this paper takes the first place in all cases, and as the number of threshold levels increases, the rank value becomes smaller and smaller, which has greater advantages compared with other comparison methods. Through the above analysis, as the dimension of optimization problem increases, the optimization ability of the proposed algorithm HEOA becomes more and more obvious.

    Table 10.  Results of Friedman rank test over all available test images.
    K HEOA HSOA HWOA CSA FPA PSO BA
    4 3.1581 3.4458 3.5147 3.4581 3.6152 3.9951 3.8547
    8 2.9315 3.5514 3.6891 3.5125 3.9156 3.9514 3.6984
    12 1.9984 2.5589 3.6661 3.1285 3.9991 3.9541 3.8854
    15 1.7415 2.6518 3.6581 3.1814 3.8147 3.8574 3.7781
    Overall 2.4574 3.0520 3.6320 3.3201 3.8362 3.9395 3.8042

     | Show Table
    DownLoad: CSV

    The experimental statistical results are shown in Table 11 below. The null hypothesis is constructed as: there is no significant difference between the two algorithms. The alternative hypothesis states that there is a significant difference between the two algorithms. In the experiment, HEOA based method produces better result in 36 out of 40 cases when compared with HSOA based method and produces better result in 35 out of 40 cases when compared with HWOA based method and produces better result in 38 out of 40 cases when compared with CSA based method and produces better result in 38 out of 40 cases when compared with FPA based method and produces better result in 40 out of 40 cases when compared with the PSO based method. As can be seen from the results, there are significant differences among the six algorithms. In most cases, HEOA performs better than other algorithms.

    Table 11.  P-value of Wilcoxon test comparative Kapur based method.
    Images K HSOA HWOA CSA FPA PSO
    Test1 4 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    8 P > 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P > 0.05 P < 0.05 P < 0.05 P < 0.05
    Test2 4 P < 0.05 P < 0.05 P < 0.05 P > 0.05 P < 0.05
    8 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    Test3 4 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    8 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    Test4 4 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    8 P > 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P > 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    Test5 4 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    8 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    Test6 4 P > 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    8 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    Test7 4 P < 0.05 P < 0.05 P > 0.05 P < 0.05 P < 0.05
    8 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    Test8 4 P > 0.05 P < 0.05 P < 0.05 P > 0.05 P < 0.05
    8 P < 0.05 P > 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    Test9 4 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    8 P < 0.05 P > 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    Test10 4 P < 0.05 P > 0.05 P > 0.05 P < 0.05 P < 0.05
    8 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    12 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05
    15 P < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05

     | Show Table
    DownLoad: CSV

    In this section, we compare with the novel image segmentation methods. The compared algorithms are PCNN [62], fuzzy c-means (FCM) [63], grayscale co-occurrence matrix (GLCM) [64]. In order to test the performance of the color image segmentation algorithms, we select the wood fibers which are taken under a high-powered microscope as the test images. The figures 811 show the wood fiber images and the segmentation result.

    Figure 8.  The segmented result of wood fiber image1.
    Figure 9.  The segmented result of wood fiber image2.
    Figure 10.  The segmented result of wood fiber image3.
    Figure 11.  The segmented result of wood fiber image4.

    It can be seen from the figures 47, the result of PCNN has the over-segmentation phenomenon and the segmented images are the worst of the compared algorithms. The FCM and GLCM have the under-segmentation phenomenon and the results of the fiber images are not clear. Among the result of the fiber images, the HEOA-3DOtsu get the best result. The table 12 shows the HEOS obtains a large improvement than the others compared image segmentation methods. The recall and precision are 93.19% and 91.28% respectively. The results show that the performance of this method can provide the segmentation result of the wood fiber image. The Figure12 show the segmentation result of the proposed method. It can be seen from figure, the number of wood fiber can be seen clearly. This method obtains independent wood fiber area. So, the proposed method can segment the wood fiber images successfully and have strong robustness.

    Table 12.  Segmentation accuracy of compared image segmentation methods.
    Method R (%) P (%) AP (%) VAL (%)
    FCM 84.94 90.88 91.23 88.47
    PCNN 80.46 90.69 81.46 79.46
    DLA 70.12 92.95 78.32 77.57
    BMPA 93.19 91.28 91.45 90.38

     | Show Table
    DownLoad: CSV
    Figure 12.  The segmented result of HEOA-3DOtus.

    The analysis of wood fiber graphics can understand the state of the fiber, so as to ensure the production of wood or paper that meets industrial requirements. The scholar Mainly analyze the shape and thickness of individual wood fibers. However, the wood fibers in the collected graphics are more responsible and similar to the background. Traditional segmentation methods cannot solve this problem. So, study the novel image segmentation method is necessary.

    In the field of optimization algorithm, the proposed method has a good optimal ability solve the CEC2015. And the proposed method has a good competitiveness with the CSA, FPA, PSO, BA and basic EOA. Because of the hybrid optimization algorithm use the advantage of the two optimization algorithms to optimize the complex benchmark function. At the same time, the proposed method solves the threshold image segmentation and find the best threshold from the 3DOtsu. The algorithm gets the best result among CSA, FPA, PSO, BA, HSOA and HWOA. The hybrid optimization algorithms enhance the optimal ability of the original optimization algorithm.

    In the field of the fiber wood image segmentation, the proposed method obtains the highest segmentation accuracy with PCNN, FCN and GLCM. The PCNN obtains the worst result in compared algorithms, the performance of PCNN rely on the set of parameters. The FCN and GLCM has strong ability to solve the grey image, however, these two methods take huge challenge to segment color image. The proposed method can overcome the difficult of color image. Finally, the proposed method obtains the wood fiber area exactly.

    The limitations of the proposed method can be divided in two contents. First, similar to other optimization algorithms, this algorithm takes time to iterate to find the best solution, which is time-consuming. Second, this method has strong performance in the field of wood fiber image segmentation. In order to make the proposed method can adopt more real area, we will study the novel optimization algorithm.

    The proposed method can solve the other problem of optimization. At the same time, it can be used in the field of medical image segmentation, forest fire image segmentation and so on. In the future, we will continue to study many object multi-level threshold methods and different optimization algorithms, so as to improve the image segmentation accuracy.

    In this paper, the HEOA algorithm is used to optimize the 3DOtsu algorithm to obtain the optimal multi-threshold image. We use GOA to improve EOA algorithm and enhance the optimization ability of the algorithm. The CEC2015 is selected as benchmark function to test the performance of the hybrid optimization algorithms. The result shows that the hybrid algorithm can enhance the optimal ability of the EOA. And then, the HEOA is compared with other optimization algorithms to jointly optimize 3DOtsu algorithm for classic images and wood fiber images segmentation experiments. From U measure, PSNR and FSIM values, it can be seen that 3DOtsu-HEOA algorithm has the best segmentation accuracy. Finally, we compare the 3DOtsu-HEOA algorithm with the novel image segmentation method. It can be seen from the segmented result that HEOA can get the best segmented result. So, the 3DOtsu-HEOA algorithm proposed in this paper has better image segmentation accuracy and better stability.

    This work was supported by the Fundamental Research Funds for the Central Universities under Grant No. 2572018BH08.

    The authors have no conflict of interest.


    Acknowledgments



    This study has not been funded by any agency and was conducted by the authors independently.

    Author contributions



    Teresa Galanti, Michela Cortini, and Ferdinando Toscano designed and supervised the study; Giuseppe Filippo Giudice and Teresa Galanti collected the data; Ferdinando Toscano and Salvatore Zappalà carried out the statistical analyses; Ferdinando Toscano and Teresa Galanti drafted the manuscript; Ferdinando Toscano, Teresa Galanti, Michela Cortini, Salvatore Zappalà, and Giuseppe Filippo Giudice reviewed and edited the manuscript. All authors read and approved the final version of the manuscript.

    Conflict of interest



    The authors state that there is no conflict of interest in this document.

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