ICQPSO‐based multilevel thresholding scheme applied on colour image segmentation

IET Signal ProcessingVolume 13, Issue 3 p. 387-395 Research ArticleFree Access ICQPSO-based multilevel thresholding scheme applied on colour image segmentation Rupak Chakraborty, Corresponding Author Rupak Chakraborty rupak.jis@gmail.com Department of Information Technology, DIT University, Dehradun, IndiaSearch for more papers by this authorRama Sushil, Rama Sushil Department of Information Technology, DIT University, Dehradun, IndiaSearch for more papers by this authorMadan L. Garg, Madan L. Garg Department of Computer Science and Engineering, DIT University, Dehradun, IndiaSearch for more papers by this author Rupak Chakraborty, Corresponding Author Rupak Chakraborty rupak.jis@gmail.com Department of Information Technology, DIT University, Dehradun, IndiaSearch for more papers by this authorRama Sushil, Rama Sushil Department of Information Technology, DIT University, Dehradun, IndiaSearch for more papers by this authorMadan L. Garg, Madan L. Garg Department of Computer Science and Engineering, DIT University, Dehradun, IndiaSearch for more papers by this author First published: 01 May 2019 https://doi.org/10.1049/iet-spr.2018.5073Citations: 4AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study proposes an improved cooperative quantum-behaved particle swarm optimisation (ICQPSO) algorithm to find multiple threshold levels for colour images with multilevel Renyi entropy (MRE). In the proposed method, the context vector of each particle is updated each time dynamically when a cooperation operation is completed with other particles. The improved search ability and optimisation performance of ICQPSO algorithm with MRE (hence called MRE-ICQPSO) extensively investigated with other well known nature-inspired algorithms such as Levi flight-guided firefly, cuckoo search, artificial bee colony, and beta differential evolution. The proposed method is applied to the Berkley segmentation dataset with 300 distinct colour images to show the effective performance of the algorithm in terms of fidelity parameters and computation time. 1 Introduction Image segmentation is a technique to partition an image into meaningful parts or objects, known as the fundamental step in many images, video, and computer vision-oriented applications. Thresholding is one of the widely accepted segmentation approach amongst various kinds of techniques such as interactive pixel classification, neural network-based approach, edge detection, fuzzy rule-based approach reported in [1-4]. In bi-level thresholding, total image pixels are divided into two regions objects and background. Entropy-based bi-level global thresholding got wide attention from the researchers as it helps to separate two regions effectively. Some of these entropies are Kapur entropy [5], Shannon and Renyi entropy [6], and Tsalli entropy [5] have been widely used for bi-level thresholding. However, the more effective approach of image segmentation is multilevel thresholding, where images are divided into more than one objects and background. The main drawback of multilevel segmentation is that it suffers from its high-level complexities. Arora et al. [7] and Perez and Gonzalez [8] proposed different research algorithms to reduce the time complexity of multilevel thresholding. However, these approaches still lack to reduce complexities in an efficient manner. So problem formulating for multilevel image thresholding by calculating the total entropy and solving it by applying global optimisation algorithms holds recent research interest [9]. In computer science, metaheuristics provide a popular way to generate optimal solutions in search space with limited computation capacity. Some derivative-free popular metaheuristic optimisation algorithms such as differential evolution (DE), firefly (FF), cuckoo search (CS), artificial bee colony (ABC) produced effective multilevel segmentation results in combination with different entropies, namely fuzzy, Shannon, Kapur, and Renyi are reported in the literatures [10-16]. Particle swarm optimisation (PSO) is another useful global optimisation tool because of its simplicity and it does not rely on any assumptions about the problem space. Some useful survey regarding PSO is noted in the literatures [17-20]. The main drawback of conventional PSO is that it cannot guarantee global optimal convergence each time, so it may get stuck in sub-optimal solution regions. To remove the drawbacks of conventional PSO, several researchers tried to include quantum mechanics with standard PSO. Unlike a simple linear system, as the quantum system is based on the complex non-linear system so it encodes more states than the conventional linear system. In the quantum-based system, the particle can appear anywhere in the feasible region based on its probability density function. As a result of that position of particles can differ from its current position which enables the particles to explore better in the search space and helps to avoid local minima convergence. The literature reveals that in 2004, Sun et al. [21] proposed a new quantum-based PSO model to overcome some of the drawbacks of conventional PSO. The survey continued and found some improved quantum-behaved swarm optimisation (QPSO) with chaotic mutation operator [22-25]. The mentioned QPSO methods have been extended in our research in several ways. In the proposed technique, multiple samples instead of selecting one random sample have been chosen and they are finally combined using a cooperation procedure. The generated context vector is updated dynamically after each operation by its corresponding context vector. The proposed improved cooperative QPSO (ICQPSO) has been applied to a set of colour images instead of grey-scale images to find the effectiveness of the algorithm. Colour-image segmentation still holds a challenging task as it involves three-dimensional (3D) histogram unlike 1D histogram of grey-scale images. Here images are subdivided into homogeneous regions based on colour, texture, and edges. Some of the entropy-based techniques for multilevel colour-image segmentation with different optimisation approaches are cited [26-28]. In this work, an automatic colour-image multilevel thresholding approach based on multilevel Renyi entropy (MRE) [29-31] with ICQPSO algorithm has been presented. MRE-ICQPSO has been used to reduce the computational complexity of optimisation problems in search space. The effectiveness and robustness of the algorithm have been compared with known popular optimisation approaches such as beta DE (BDE) [32], CS [33], Levi flight-guided FF (LFF) [26], and modified ABC (MABC) [34] algorithms. The proposed MRE-ICQPSO approach is applied to 300 colour images of Berkley segmentation dataset with 300 (BSDS300) dataset and segmentation quality is measured by the four popular metrics, namely feature similarly index measurement (FSIM) and structural similarity index measurement (SSIM), peak signal-to-noise ratio (PSNR), misclassification error (ME) [14, 26]. This paper is organised as follows. Section 2 illustrates the idea of the ICQPSO algorithm. Section 3 presents MRE-based combined proposed algorithm (MRE-ICQPSO) to solve the multilevel problem of colour-image thresholding. The simulated results of the proposed algorithm compared with other optimisation approaches are shown and discussed in Section 4. Finally, Section 5 draws a conclusion of this paper with a future scope. 2 Overview of the proposed optimisation algorithm 2.1 Particle swarm optimisation In conventional PSO, particles are put into multi-dimensional spaces and fitness of each particle is calculated in each iteration. Pbest value is calculated based on the distance between particle's present position and its best position noted so far, whereas Gbest is measured as the distance between particle's present position and the best position of the particle found among the entire swarm. Let denotes the position, the velocity, the best previous position found so far, and the best position of the particle found in the entire swarm, then standard PSO equation in D-dimensional search space can be defined as (1)where , are accelerated coefficients and usually lie between (0, 4) and , are uniformly generated random numbers from 0 to 1. 2.2 Quantum PSO In conventional PSO, particle's motion may get stuck because of the limited computing resources. This problem may lead to PSO to get prone to local optima convergence. To overcome the drawback of the deterministic particle paths of PSO, researchers introduced the stochasticity element into particle paths with the probabilistic quantum mechanical descriptions of motions of subatomic particles found in the literature [21]. Heisenburg's uncertainty principle claims that the position and the velocity of a particle can never both be determined simultaneously in the quantum world. Here, particle's state must be described probabilistically. Let the wave function , the probability density function , and represents the probability of a particle being discovered within the volume element , at time t within a 3D space, then the wave function can be obtained by solving the Schrodinger equations [21] with the help of delta potential well such as the following equation: (2)where p denotes the centre of the well. Furthermore, Schrodinger equations [21] get solved to finalise the wave function (3)where , , and is the potential well function. is the Hamiltonian operator. Here, is the Laplace operator. So, now probability density function will be (4)Now in quantum theory, the location of a particle can be described probabilistically using the above function. Next, fitness function for numerical optimisation can be obtained by finding the exact and explicit position of a particle. The explicit position of the particle can be achieved by converting the density function based on measurement simulation as follows: let s be a uniformly distributed random manner: (5)Substituting s in , we get (6)and hence (7)calculating (8)It finally generates the desired position () of the i th particle in the D-dimensional search space with as the attractor of the i th particle (9)L can be evaluated by the current particle position () and attractor according to Sun et al. [21] (10)The final position of the particle can be updated based on the delta potential well model (11)where is the ‘expansion factor’ generated from a uniformly distributed random function in the interval [0, 1] and is a unique parameter of the QPSO algorithm. 2.3 ICQ-behaved PSO In cooperative QPSO, context vector is designed to evaluate each dimension of a particle with the help of processing of cooperation. Gao et al. [22] assigned global optimal particle of each generation as the context vector in their proposed work. Li et al. [23] showed in their research work how to set the best of multiple measurement samples as a local context vector for a particular particle. Stochastic search algorithms such as QPSO, genetic algorithm often suffer from the ‘curse of dimensionality’ that may affect overall fitness values of a particle with high-dimensional data. As a result of that, some particles will gain low fitness values though their dimension values lie very close to the global optimal solution. Cooperation operation can remove this problem by acquiring information from ‘best’ dimensions and preventing useful information from being unnecessarily discarded. As high-dimensional space is divided into several 1D spaces, so cooperation between each 1D helps to save the most useful information to accelerate convergence. In our proposed scheme, new individuals are generated at each time for an arbitrary number of measurement samples to perform cooperation between multiple measurements for each particle. It will help to increase the utilisation efficiency of quantum-based uncertainty as well as convergence rate. Now, to go ahead for proving of the approach, assume that the previously mentioned wave function is sampled by the measurement procedure to generate n number of new individuals: then we calculate: (12) (13) (14)where denotes the mean position of total particle swarm, is the best position of a new particle which retrieves information from previous and represents the global best particle through the whole population. M is the population size where and u generate uniformly distributed random numbers from 0 to 1, parameter needs to be specified known as creativity coefficient. After combining sample multiple measurement vectors through the cooperation process, it is time to set them as context vector so that it remains constant throughout the cooperation procedure. However, the constant value of context vector throughout the whole cooperation process may lack information update. So we propose a mechanism to update the value of context vector during the cooperation process dynamically so that new information can be obtained at each successive stage of the cooperation process. This dynamic update procedure of context vector strengthens the rate of convergence by acquiring new information. The update procedure of the context vector of each particle is shown in Fig. 1. In this approach, each particle generates n number of particles through simulated measurements. Then, the best individual value is selected from n individuals according to its fitness value. Then, is assigned as the current local context vector for the i th particle. This generated context vector then cooperates with remaining (n − 1) individuals to test the improvement of fitness value because of substitution of dimensions of others. If it happens, then context vector is replaced by the substituted value. This process continues till the evaluations of all dimensions of (n − 1) measurement vectors have been done. After completion of all these steps, final permutation is selected to form a new particle for the next generation shown in Fig. 1. Fig. 1Open in figure viewerPowerPoint Pseudocode for ICQPSO 3 Problem formulation Multilevel thresholding of colour image determines two or more optimum thresholds for each of the three components [red, green, and blue (RGB)] of the image. To better represent colour, L *a *b * or L *u *v * colour space is used for segmentation problem than non-uniform colour space such as RGB. First, all the RGB images have been converted to commission international de l'eclairage (CIE) L *a *b * colour space using MATLAB. L * indicates lightness, a * red–green, and b * blue–yellow colour, where each component value lies between 0 and 255. 3.1 Multilevel Renyi entropy Here, Renyi entropy is calculated to formulate the objective function of multilevel colour-image thresholding. Let , where is a set of discrete finite n -array probability distributions. Renyi entropy (Renyi, 1960) for independent events can be described as (15)where represents the order of the entropy. The entire distribution can be divided into K number of classes for a colour image such as . Then, a priori Renyi for each distribution can be defined as [6] (16)where Here, denotes the normalised histogram and L is the highest grey-level intensity. Now, additive entropic rule can be applied to generate a threshold vector for optimal thresholding (17)For convenient illustration, two dummy thresholds and are added with . The optimal threshold values can be found by maximising the objective function . The computational complexity of this Renyi entropy for multilevel thresholding may arise to . To reduce the computational complexity, ICQPSO-based optimisation algorithm is applied to maximise the objective function. The working of MRE-ICQPSO algorithm has been shown in Fig. 2. Fig. 2Open in figure viewerPowerPoint Flowchart for the selection of threshold values using MRE-ICQPSO 4 Experimental results 4.1 Experimental setup The colour-image segmentation has been performed by the idea of MRE and the proposed ICQPSO optimisation algorithm. The histogram of colour images has been calculated to form the objective function [shown in (17)] for the proposed ICQPSO optimisation algorithm. The threshold values are achieved by maximising the objective values and final level-wise segmented RGB images are formed as shown in Fig. 3. Fig. 3Open in figure viewerPowerPoint Block diagram of the proposed algorithm All the simulations have been performed in MATLAB R2015a workstation with Intel Core i5 3.2 GHz processor and 4 GB random access memory personal computer. The Initial population and maximum generation of the proposed scheme have been set to 150. We have performed 100 trial runs for each mentioned algorithm and recorded the fitness values , standard deviations , and computation time . Dimensionality (D) of a search space for a L level segmentation is . Segmentation level of the problem has been set as 5, 7, and 10 to avoid the under-segmentation problem. Quantitative measurements are done in the form of , , and , whereas the quality of segmented colour images with the original images has been measured by standard well known metrics such as FSIM, PSNR, SSIM, and ME [14, 26]. 4.2 Performance analysis Table 1. Comparison of different optimisers over BSDS300 set Level Algorithm Runtime, s Fitness value Standard deviation 5 ICQPSO 19.265 LFF 20.109 CS 20.989 MABC 21.578 BDE 22.160 7 ICQPSO 26.109 LFF 27.166 CS 28.199 MABC 29.230 BDE 30.265 10 ICQPSO 36.232 LFF 37.397 CS 38.436 MABC 39.591 BDE 40.697 Bold values indicate the better results of the proposed algorithm as compared to the other state-of-the-art approaches. The proposed approach has been tested on a set of colour images of dimension 484 × 321 from Berkley dataset (BSDS300) freely available at https://www2.eecs.berkley.edu/Research/Projects/CS/vision/bsds/. Images are resized to for comparing with ground-truth images. We have chosen four different currently proposed approaches, namely BDE proposed by Ayala et al. [32]; MABC proposed by Bhandari et al. [34]; an efficient CS algorithm proposed by Suresh and Lal [33]; modified fuzzy entropy-based LFF algorithm proposed by Pare et al. [26] to compare the outcomes of the proposed approach. Table 1 displays the computed average runtime in seconds (), fitness value (), and standard deviation () over 300 colour images of BSDS300 dataset for the tested optimisers, namely ICQPSO, LFF, MABC, CS, and BDE. The generated best values of the proposed algorithm for all the levels of segmentation are marked as bold to differentiate with others. The better mean objective values with quick time for all the levels of 300 images are noted from the table for our algorithm. The robustness and stability of the algorithm depend on the fewer values of standard deviation. The proposed MRE-ICQPSO algorithm claims better stability as per the above result compared with others. Two comparative convergence plots of ‘249061.jpg’ image from BSDS300 dataset have been shown for 7 and 10 level segmentations in Figs. 4 and 5, respectively. The fastest convergence along with high fitness values for both the levels of the proposed algorithm are shown in the above figure. For level 7, it reaches to maximum and level 10 for the proposed algorithm. All the plots are generated for 100 runs of each algorithm. Our proposed algorithm has started to converge at 84 iterations for level 10 segmentation, whereas others struggled to converge at the iteration of 93 has been clearly shown in Fig. 5. Furthermore, two bar graphs of computation time have been drawn of five tested images for both the levels 7 (Fig. 6) and 10 (Fig. 7) to claim the fast working performance of the algorithm. Our algorithm takes near to 26 and 36 s to compute the segmented results for levels 7 and 10, whereas the LFF method immediately follows our approach and overcome challenges of CS, MABC, and BDE algorithms. It is observed from these above quantitative comparisons that all these optimisers may get either trapped in local optima for higher level or failed to generate effective results quickly as compared with the proposed approach. Fig. 4Open in figure viewerPowerPoint Comparison of convergence of Lv = 7 for image ‘249061.jpg’ from BSDS300 set Fig. 5Open in figure viewerPowerPoint Comparison of convergence of Lv = 10 for image ‘249061.jpg’ from BSDS300 set Fig. 6Open in figure viewerPowerPoint Comparison of the computation time of Lv = 7 of 5 images from BSDS300 set Fig. 7Open in figure viewerPowerPoint Comparison of computation time of Lv = 10 of 5 images from BSDS300 set After outperforming the quantitative challenges of the different existing optimisers, the proposed algorithm focuses to measure the quality of segmented images. Some popular images have been chosen from BSDS300 dataset for effective segmentation. Fig. 8 displays the threshold values of the image ‘12074.jpg’ from dataset obtained by the proposed algorithm. The 5, 7, and 10 level segmented images generated by ICQPSO, and 10 level segmented images by the algorithms LFF, CS, MABC, and BDE are reported in Fig. 9. Four popular measurement metrics have been applied now to hold the strong proof of visual clarity of segmented images. SSIM (18) Fig. 8Open in figure viewerPowerPoint Original and thresholded image with level-wise threshold values (a) Original, (b) Lv = 5(74, 120, 139, 187), (c) Lv = 7(39, 81, 119, 138, 175, 222), (d) Lv = 10(35, 73, 105, 118, 127, 141, 170, 207, 233) Fig. 9Open in figure viewerPowerPoint Comparative results of segmented images obtained by the different optimisation algorithms FSIM (19)PSNR (20)ME (21)Table 2 displays the level-wise SSIM and FSIM values for the tested images. The proposed optimisation approach with MRE objective function produces better values for all the levels compared with other approaches. Values of these metrics lies between −1 and +1. Values equal to −1 represent worst segmentation, whereas +1 denotes both original and segmented images are same. It is observed that the values of the metrics are closer to 1 for high level and values are proportionally incrementing with the level of segmentation. The values generated by the proposed MRE-ICQPSO algorithm are marked as bold and carry strong proof for effective segmentation. Similarly, it is observed from Table 3 that PSNR values are higher for the proposed algorithm for all the levels, whereas ME values are inversely proportional to the increase of levels. ME values lie between 0 and +1 and values closer to 0 hold effective outcomes [14]. Table 2. Comparison of SSIM and FSIM computed by ICQPSO, LFF, CS, MABC, BDE using MRE Images Lv ICQPSO LFF CS MABC BDE SSIM FSIM SSIM FSIM SSIM FSIM SSIM FSIM SSIM FSIM 3096 5 0.894 0.792 0.866 0.776 0.851 0.762 0.839 0.747 0.828 0.736 7 0.923 0.845 0.905 0.823 0.885 0.801 0.871 0.787 0.859 0.775 10 0.978 0.901 0.962 0.889 0.949 0.877 0.937 0.864 0.928 0.858 12,074 5 0.896 0.794 0.869 0.780 0.855 0.765 0.842 0.749 0.831 0.740 7 0.927 0.848 0.909 0.826 0.888 0.804 0.875 0.789 0.862 0.778 10 0.980 0.904 0.966 0.892 0.953 0.879 0.939 0.866 0.932 0.861 126,007 5 0.890 0.785 0.861 0.772 0.847 0.758 0.836 0.744 0.825 0.730 7 0.920 0.842 0.902 0.820 0.882 0.798 0.868 0.784 0.854 0.772 10 0.975 0.897 0.959 0.887 0.947 0.875 0.934 0.861 0.923 0.852 145,053 5 0.905 0.799 0.874 0.782 0.860 0.769 0.846 0.753 0.835 0.742 7 0.929 0.854 0.912 0.830 0.894 0.812 0.880 0.795 0.867 0.783 10 0.988 0.909 0.970 0.897 0.958 0.883 0.944 0.873 0.934 0.865 249,061 5 0.895 0.794 0.868 0.778 0.853 0.764 0.840 0.747 0.830 0.733 7 0.925 0.846 0.907 0.821 0.886 0.804 0.872 0.789 0.860 0.776 10 0.979 0.902 0.963 0.890 0.951 0.878 0.939 0.865 0.929 0.859 Table 3. Comparison of PSNR and ME computed by ICQPSO, LFF, CS, MABC, BDE using MRE Images Lv ICQPSO LFF CS MABC BDE PSNR ME PSNR ME PSNR ME PSNR ME PSNR ME 3096 5 35.908 0.752 35.243 0.770 34.876 0.779 34.401 0.786 33.890 0.795 7 37.995 0.542 37.126 0.563 36.670 0.578 36.015 0.597 35.604 0.605 10 39.653 0.354 38.962 0.369 38.202 0.377 37.769 0.394 37.101 0.408 12,074 5 35.912 0.756 35.249 0.775 34.881 0.783 34.407 0.792 33.896 0.799 7 37.999 0.546 37.131 0.569 36.676 0.584 36.029 0.598 35.614 0.608 10 39.658 0.357 38.965 0.373 38.207 0.381 37.774 0.397 37.107 0.414 126,007 5 35.891 0.737 35.232 0.753 34.864 0.762 34.395 0.769 33.881 0.782 7 37.973 0.533 37.105 0.554 36.652 0.572 36.001 0.589 35.594 0.601 10 39.644 0.350 38.957 0.363 38.196 0.371 37.760 0.390 37.089 0.401 145,053 5 35.808 0.672 35.147 0.678 34.770 0.677 34.321 0.689 33.780 0.699 7 37.825 0.512 37.014 0.523 36.562 0.538 35.823 0.547 35.104 0.555 10 39.542 0.307 38.802 0.329 38.303 0.347 37.661 0.364 37.007 0.378 249,061 5 35.937 0.761 35.252 0.775 34.884 0.782 34.432 0.788 33.899 0.797 7 37.997 0.544 37.129 0.566 36.682 0.584 36.214 0.604 35.616 0.611 10 39.657 0.359 38.968 0.376 38.222 0.383 37.776 0.396 37.123 0.411 To evaluate the performance of the proposed approach further, borders are extracted from the segmented images and converted into label matrix so that accuracy of the segmentation can be achieved by comparing with the ground-truth values of the images. The labelled borders of the segmented images along with their ground truth are listed in Fig. 10. Some different class colour images such as medical, hyper-spectral images are also chosen for the experiment. Hyper-spectral multi-band satellite images, namely Indian Pines, Salina images are obtained by the airborne visible/imaging infrared spectrometer (AVIRIS) sensor and the Pavia university images are obtained by the reflective optics system imaging spectrometer (ROSIS) sensor available at [35]. Colour medical images are collected from the Google database. Ground truth, segmented, and extracted border of these images are reported in Fig. 11. Results suggest better visual clarity along with the accuracy of the proposed approach. Colour-image segmentation has been set here as the unsupervised classification problem and then precision–recall framework [31, 36] has been chosen as the solution of the problem. In this framework, F-measure is the weighted average harmonic mean of the precision and recall and can be defined as (22)where , , and . Here, represent true positive, false positive, true negative, and false negative pixels, respectively. Background (one value) is considered as positive, whereas border value 0 represents negative matching in terms of label and ground-truth matrix. It can be observed from Table 4 that the proposed algorithm produces better values of different segmentation accuracy metrics for 10 level segmentation of medical as well as spectral images. Furthermore, F-score values of different algorithms are noted in Table 5 and it is found that the proposed approach outperforming other algorithms in all the aspects. Fig. 10Open in figure viewerPowerPoint Comparative results of edge detections of segmented images obtained by the different optimisation algorithms Fig. 11Open in figure viewerPowerPoint Qualitative results of some medical and hyper-spectral images Table 4. FSIM, average F-measure, accuracy, precision, and recall values of medical and spectral images of 10 level segmentation Images FSIM Accuracy Precision Recall F-measure Med-1 0.7749 0.8596 0.8738 0.7539 0.8034 Med-2 0.7906 0.9114 0.8767 0.8248 0.8500 Med-3 0.7635 0.9099 0.6889 0.6882 0.6886 Med-4 0.7661 0.9109 0.8589 0.8432 0.8510 Pines 0.9361 0.9292 0.9457 0.8074 0.8711 Pavia 0.7540 0.8854 0.7720 0.5900 0.6943 Salinas 0.9429 0.9995 0.9933 0.9828 0.9881 Table 5. Comparison of average F-measure, accuracy, precision, and recall values computed over 300 images of BSDS 300 dataset Algorithm F-measure Accuracy Precision Recall ICQPSO (Lv-5) 0.9682 0.9388 0.9635 0.9730 ICQPSO (Lv-7) 0.9690 0.9404 0.9652 0.9729 ICQPSO (Lv-10) 0.9731 0.9483 0.9699 0.9763 LFF (Lv-10) 0.9453 0.9219 0.9108 0.9402 CS (Lv-10) 0.9409 0.9190 0.9107 0.9312 MABC (Lv-10) 0.8909 0.8650 0.8810 0.8902 BDE (Lv-10) 0.9645 0.9452 0.9657 0.9734 5 Future scopes and conclusion An innovative ICQPSO-based approach is proposed here to overcome the drawback of local minima convergence of standard PSO for the multilevel problem. Furthermore, this algorithm improves the performance of CQPSO by exploiting its contextual information. It is shown that how context variables can be updated dynamically at the time of cooperation procedure to evaluate different individual dimension components so that new information can be used as soon as it becomes available in the system. MRE is applied as an objective function to find the multiple threshold parameters. ICQPSO approach computes best fitness values in quick time with reliable stability as compared with other metaheuristic derivative-free optimisers such as LFF, MABC, CS, and BDE. The qualitative measurements conclude that this approach outperformed other tested approaches for different levels of segmentations. It can be concluded that the proposed approach can be useful for the fast and accurate segmentation of different types of images such as nature scene, medical, and remote-sensing images with promising results. As a future work, we can test this approach to measure some boundary error parameters such as probability rand index, variation of information, global consistency error, boundary displacement error with ground-truth values to check the quality of segmentation. 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