Multilevel Multiobjective Particle Swarm Optimization Guided Superpixel Algorithm for Histopathology Image Detection and Segmentation
Abstract
:1. Introduction
 The MMPSO algorithm with three different objective functions is used to identify the optimal threshold values for multilevel image thresholding. The MOPSO algorithm is applied for the first time in the field of histopathology image segmentation for multilevel image thresholding. This framework opens a new avenue for researchers to propose segmentation models which include more than one segmentation criterion. It should be noted that in the past, only the PSO algorithm with a single objective function has been used for the segmentation of nuclei regions from histopathology images;
 The proposed MMPSOS algorithm combines the segmentation output of the MMPSO algorithm and the superpixel clustering algorithm; specifically, the threshold values obtained from the MMPSO algorithm are used to refine the output of the superpixel algorithm. This combined algorithm helps to improve the segmentation results;
 The proposed algorithm is applied to four different H&Estained histopathology datasets for the detection and segmentation of various ROIs;
 The performance of the proposed method is compared with other single and multiobjective algorithms and also with the existing work performed on the datasets.
2. Related Works
2.1. Image Segmentation Using PSO and Its Variants
2.2. Image Segmentation Using Multiobjective Algorithms
2.3. Image Segmentation Using Superpixel Algorithm
3. Dataset Description
3.1. TripleNegative Breast Cancer Dataset
3.2. MultiOrgan Nuclei Segmentation Dataset
3.3. MultiOrgan Nuclei Segmentation and Classification Dataset
3.4. Lymphocyte Detection Dataset
4. The Proposed Method
4.1. PreProcessing
4.2. MMPSOS Algorithm for Detection and Extraction of ROIs
4.2.1. MMPSO for Multilevel Image Thresholding
 KeyTerms of MOPSO Algorithm
 Decision space: Decision space/search space is the vector space of all decision variables. The search space varies depending on the problem domain.
 Objective space: Objective space is the vector space of all solutions obtained from the evaluation of the decision variables.
 Particles and swarm: Swarm is a collection of particles. Particles are individuals, such as birds or fishes, in the swarm. Let i represent a particle in the swarm and i = 1, 2, …, ${N}_{par}$, where ${N}_{par}$ is the population size.
 Position: Each particle i in the search space has two properties, i.e., position and velocity. The position of a particle i is denoted as ${X}_{i}$ and is considered as the feasible solution to the optimization problem. It has upper and lower limits, which are the boundary of the search space denoted as $[{X}_{min},{X}_{max}]$.
 Velocity: Velocity of a particle ${V}_{i}$ defines its ability to move in the search space, which allows the particle to update its position. The upper and the lower limits of the velocity are denoted as $[{V}_{min},{V}_{max}]$.
 Objective function: It is also known as the fitness function/cost function. The objective function maps an element from the decision space to the objective space. The objective function is evaluated using the position ${X}_{i}$ and the outcome is a real number known as the cost value or the fitness value. In the case of MOPSO, the outcome of all objective functions form a vector.
 Local best: The local best value for a particle is the position value which gives the best fitness value in the whole history of its movement. It is denoted by $pBes{t}_{i}$.
 Feasible solution set: A solution that satisfies all the constraints of an MOP is called a feasible solution. A set of all feasible solutions is called the feasible solution set.
 Nondominated solution: A feasible solution is nondominated if there does not exist another feasible solution better than the current one in some objective function without worsening another objective function.
 External repository: It is a storage space to store all the best particles (nondominated solutions) [10]. This repository is often known as an external archive and is denoted by A. External repository has a maximum size (${A}_{max}$). To avoid the high computational cost of searching and updating the external repository, its size is limited.
 Leader: From the external repository, one solution (L) is selected as the leader for the entire swarm and its position is taken as the $pBes{t}_{L}$ value.
 Initialization Phase of MOPSO Algorithm
 Objective Functions
 (a)
 Otsu’s multilevel thresholding: Otsu’s method is an unsupervised and nonparametric threshold selection method [40]. In Otsu’s method, the threshold is selected by the discriminant criterion, that is to maximize the betweenclass variance among segmented regions/classes [43]. Otsu’s objective function (${f}_{1}$) for the multilevel grayscale image segmentation is given by Equation (4).$${f}_{1}\left({t}_{1},{t}_{2},\dots ,{t}_{k}\right)=\sum _{i=1}^{k+1}{\omega}_{i}{\left({\mu}_{i}{\mu}_{T}\right)}^{2}$$
 (b)
 Kapur’s multilevel thresholding: Kapur’s entropy is a generalization of Shannon’s entropy. In Kapur’s method, the threshold is selected by the discriminant criterion, that is to maximize the betweenclass entropy [41,44]. Kapur’s objective function (${f}_{2}$) for the multilevel segmentation of grayscale images is given by Equation (5).$${f}_{2}\left({t}_{1},{t}_{2},\dots ,{t}_{k}\right)=K{H}_{1}+K{H}_{2}+\dots +K{H}_{k+1},$$$$K{H}_{1}=\sum _{i=0}^{{t}_{1}1}\frac{{P}_{i}}{{\omega}_{0}}ln\frac{{P}_{i}}{{\omega}_{0}},\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}K{H}_{2}=\sum _{i={t}_{1}}^{{t}_{2}1}\frac{{P}_{i}}{{\omega}_{1}}ln\frac{{P}_{i}}{{\omega}_{1}},\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}\dots ,\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}K{H}_{k+1}=\sum _{i={t}_{k}}^{255}\frac{{P}_{i}}{{\omega}_{k}}ln\frac{{P}_{i}}{{\omega}_{k}}$$
 (c)
 Renyi’s multilevel thresholding: Renyi’s entropy is a generalized form of Shannon’s entropy with a parameter $\alpha $ used to evaluate the randomness of a system. When $\alpha $ = 1, Renyi’s entropy is equal to Shannon’s entropy [42]. Renyi’s objective function (${f}_{3}$) for the multilevel segmentation of grayscale images is given by Equation (7).$${f}_{3}\left({t}_{1},{t}_{2},\dots ,{t}_{k}\right)=R{H}_{1}+R{H}_{2}+\dots +R{H}_{k+1},$$$$R{H}_{1}=\frac{1}{1\alpha}ln\sum _{i=0}^{{t}_{1}1}{\left(\frac{{P}_{i}}{{\omega}_{0}}\right)}^{\alpha},\dots ,\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}R{H}_{k+1}=\frac{1}{1\alpha}ln\sum _{i={t}_{k}}^{255}{\left(\frac{{P}_{i}}{{\omega}_{k}}\right)}^{\alpha}$$
 Iterative Phase of MOPSO Algorithm
 Leader selection from the external archive:The repository with the nondominated solutions is mapped to an adaptive grid with a grid size ${G}_{size}$ comprising hypercubes [10]. Each nondominated solution from the archive is placed in the hypercube by considering its fitness values as the coordinates. A hypercube can hold $ns$ number of nondominated solutions where $ns>1$. The following steps are used to select a leader from the nondominated solutions:
 (a)
 The fitness value of a hypercube is calculated by dividing any number x ($x>$ 1) by the number of particles in that hypercube.
 (b)
 A roulette wheel algorithm is used to select a hypercube using the fitness values.
 (c)
 If the selected hypercube has one particle, then the particle is set as the leader of the swarm. Otherwise, if the number of particles in the selected hypercube is greater than 1 (i.e., $ns>1$), then one particle is chosen randomly and is set as the leader of the swarm.
 Update position and velocity of each particle:Once the leader is selected, the velocity and position of all the particles in the swarm are updated using Equations (9) and (10).$${V}_{i}(t+1)=\omega {V}_{i}\left(t\right)+{c}_{1}{r}_{1}({X}_{i}\left(t\right)pBes{t}_{i}\left(t\right))+{c}_{2}{r}_{2}({X}_{i}\left(t\right)pBes{t}_{L}\left(t\right))$$$${X}_{i}(t+1)={X}_{i}\left(t\right)+{V}_{i}(t+1),$$
 Compute fitness values for each particle:Once the position value of each particle i in the swarm is updated, the fitness values of each particle are calculated for all the fitness functions.
 Update the local best value of each particle:If the current $pBes{t}_{i}$ value of a particle i is dominated by the new position value ${X}_{i}(t+1)$ of the particle, then the current $pBes{t}_{i}$ value of the particle is replaced with the ${X}_{i}(t+1)$ value. Otherwise, the current $pBes{t}_{i}$ value of the particle i is kept as it is. If neither the current $pBes{t}_{i}$ value nor the new position value of a particle are dominating each other, then one of the values is randomly selected as the $pBes{t}_{i}$.
 Update the external repository:The nondominated particles are identified based on the pareto dominance condition [10]. The nondominated particles are compared with the particles already existing in the external archive in order to decide their inclusion to the external archive. The MOPSO algorithm follows four rules to add a nondominated particle to the archive:
 (a)
 If the archive is empty, then the new particle is added to the archive.
 (b)
 If the particle is dominated by any of the particles in the archive, then the new particle is discarded.
 (c)
 If none of the particles in the archive dominate the new particle, and if the archive has enough space, then the new particle is added to the archive. During the entry, any particle in the archive dominated by the new particle is deleted from the archive.
 (d)
 If none of the particles in the archive dominate the new particle and the archive does not have enough space, then the particle from the most crowded hypercube is removed and the new particle is inserted in the archive. During the time of entry, any particle in the archive that is dominated by the new particle is removed from the archive.
 Apply mutation operator to the particles:The relevance of the mutation operator in the MOPSO algorithm is to allow the algorithm to explore the search space with a high exploratory capability. During the initial iterations of the algorithm, the mutation operator affects all the particles in the search space; however, the number of particles affected by the operator decreases as the number of iterations increases. In this work, the mutation rate ($\mu $) is set to 0.1.
 Obtaining the Optimal Threshold Values
 Generating segmentation maps:
4.2.2. Segmentation by Superpixel Algorithm
 Refining the clusters:
4.3. Combining Segmentation Maps and PostProcessing
Algorithm 1: MMPSO algorithm. 
Input: Preprocessed image ${I}_{pre}$ Output: Segmentation map ${I}_{1}$ Parameters: MMPSO parameters, i.e., ${N}_{par}$, ${N}_{ite}$, k, ${X}_{min}$, ${X}_{max}$, ${V}_{min}$, ${V}_{max}$ and ${A}_{max}$

Algorithm 2: Superpixel algorithm, cluster refinement, output merging, and postprocessing. 
Input: Histopathology colour image, ${I}_{color}$ and output image from MOPSO algorithm $I1$ Output: Image after postprocessing ${I}_{output}$ Parameters: Expected number of superpixels to be generated $nc$, Cluster centres ${C}_{1},{C}_{2},\dots ,{C}_{nc}$

5. Results and Discussion
5.1. Parameter Tuning
5.2. Segmentation Performance
 Segmentation Performance on the MoNuSeg Dataset:
 Segmentation Performance on the TNBC Dataset:
 Segmentation performance on the MoNuSAC dataset:
 Detection performance on the LD dataset:
 Discussion:
5.3. Normalised Execution Time
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Evaluation Metrics
References
 Sikandar, A. Histopathology: An Old Yet Important Technique in Modern Science. In Histopathology; Srivastava, S., Ed.; IntechOpen: Rijeka, Croatia, 2018; Chapter 1. [Google Scholar] [CrossRef] [Green Version]
 Hayakawa, T.; Prasath, S.; Kawanaka, H.; Aronow, B.; Tsuruoka, S. Computational Nuclei Segmentation Methods in Digital Pathology: A Survey. Arch. Comput. Methods Eng. 2021, 28, 1–13. [Google Scholar] [CrossRef]
 Sapna, S.; Renuka, A. Computeraided system for Leukocyte nucleus segmentation and Leukocyte classification based on nucleus characteristics. Int. J. Comput. Appl. 2020, 42, 622–633. [Google Scholar] [CrossRef]
 Angel Arul Jothi, J.; Mary Anita Rajam, V. A survey on automated cancer diagnosis from histopathology images. Artif. Intell. Rev. 2017, 48, 31–81. [Google Scholar] [CrossRef]
 Pei, G. Digital Orthopedics; Springer: Ansterdam, The Netherlands, 2018. [Google Scholar]
 Jiao, L.; Shang, R.; Liu, F.; Zhang, W. Chapter 3—Theoretical basis of natural computation. In Brain and NatureInspired Learning Computation and Recognition; Jiao, L., Shang, R., Liu, F., Zhang, W., Eds.; Elsevier: Amsterdam, The Netherlands, 2020; pp. 81–95. [Google Scholar] [CrossRef]
 Coello, C.; Toscano Pulido, G.; Lechuga, M. Handling Multiple Objectives With Particle Swarm Optimization. IEEE Trans. Evol. Comput. 2004, 8, 256–279. [Google Scholar] [CrossRef]
 Emmerich, M.T.; Deutz, A.H. A Tutorial on Multiobjective Optimization: Fundamentals and Evolutionary Methods. Nat. Comput. Int. J. 2018, 17, 585–609. [Google Scholar] [CrossRef] [Green Version]
 Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the ICNN’95—International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December1995; Volume 4, pp. 1942–1948. [Google Scholar] [CrossRef]
 Coello Coello, C.; Lechuga, M. MOPSO: A proposal for multiple objective particle swarm optimization. In Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No.02TH8600), Honolulu, HI, USA, 12–17 May2002; Volume 2, pp. 1051–1056. [Google Scholar] [CrossRef]
 Parsopoulos, K.; Vrahatis, M. MultiObjective Particle Swarm Optimization Approaches; IGI Global: Hershey, PA, USA, 2008; pp. 20–42. [Google Scholar] [CrossRef]
 Ibrahim, A.; Elkenawy, E.S. Image Segmentation Methods Based on Superpixel Techniques: A Survey. J. Comput. Sci. Inf. Syst. 2020, 1, 1–10. [Google Scholar]
 Jothi, J.A.A.; Rajam, V.M.A. Segmentation of Nuclei from Breast Histopathology Images Using PSObased Otsu’s Multilevel Thresholding. In Artificial Intelligence and Evolutionary Algorithms in Engineering Systems; Suresh, L.P., Dash, S.S., Panigrahi, B.K., Eds.; Springer: New Delhi, India, 2015; pp. 835–843. [Google Scholar]
 Liu, Y.; Mu, C.; Kou, W.; Liu, J. Modified Particle Swarm OptimizationBased Multilevel Thresholding for Image Segmentation. Soft Comput. 2015, 19, 1311–1327. [Google Scholar] [CrossRef]
 Chakraborty, R.; Sushil, R.; Garg, M.L. An Improved PSOBased Multilevel Image Segmentation Technique Using Minimum CrossEntropy Thresholding. Arab. J. Sci. Eng. 2019, 44, 3005–3020. [Google Scholar] [CrossRef]
 Li, Y.; Wang, S.; Xiao, J. Image Segmentation Based on Dynamic Particle Swarm Optimization for Crystal Growth. Sensors 2018, 18, 3878. [Google Scholar] [CrossRef] [Green Version]
 Saini, B.; Gupta, S.; Kaur, T. A comparative study on Kapur’s and Tsallis entropy for multilevel thresholding of MR images via particle swarm optimisation technique. Int. J. Comput. Syst. Eng. 2018, 4, 156. [Google Scholar] [CrossRef] [Green Version]
 Xia, P.; Lin, Y.; LiHua, Z. An Improved PSOFCM Algorithm for Image Segmentation. IOP Conf. Ser. Earth Environ. Sci. 2019, 267, 042081. [Google Scholar] [CrossRef]
 Suresh, S.; Lal, S. Multilevel thresholding based on Chaotic Darwinian Particle Swarm Optimization for segmentation of satellite images. Appl. Soft Comput. 2017, 55, 503–522. [Google Scholar] [CrossRef]
 Tang, Q.; Gao, S.; Liu, Y.; Yu, F. Infrared image segmentation algorithm for defect detection based on FODPSO. Infrared Phys. Technol. 2019, 102, 103051. [Google Scholar] [CrossRef]
 Guo, F.; Peng, H.; Zou, B.; Rongchang, Z.; Liu, X. Localization and segmentation of optic disk with the fractionalorder Darwinian particle swarm optimization algorithm. IET Image Process. 2018, 12, 1303–1312. [Google Scholar] [CrossRef]
 Zhe, L.; Bao, X.; Yuqing, S.; Hu, L.; Qingfeng, L. An Improved Unsupervised Image Segmentation Method Based on MultiObjective Particle Swarm Optimization Clustering Algorithm. Comput. Mater. Contin. 2019, 58, 451–461. [Google Scholar] [CrossRef] [Green Version]
 Maryam, H.; Mustapha, A.; Younes, J. A multilevel thresholding method for image segmentation based on multiobjective particle swarm optimization. In Proceedings of the 2017 International Conference on Wireless Technologies, Embedded and Intelligent Systems (WITS), Fez, Morocco, 19–20 April 2017; pp. 1–6. [Google Scholar] [CrossRef]
 Hinojosa, S.; Oliva, D.; Cuevas, E.; Pajares, G.; Zaldivar, D.; Cisneros, M. Reducing overlapped pixels: A multiobjective color thresholding approach. Soft Comput. 2020, 24, 6787–6807. [Google Scholar] [CrossRef]
 Pham, T.X.; Siarry, P.; Oulhadj, H. A multiobjective optimization approach for brain MRI segmentation using fuzzy entropy clustering and regionbased active contour methods. Magn. Reson. Imaging 2019, 61, 41–65. [Google Scholar] [CrossRef]
 Elaziz, M.A.; Oliva, D.; Ewees, A.A.; Xiong, S. Multilevel thresholdingbased grey scale image segmentation using multiobjective multiverse optimizer. Expert Syst. Appl. 2019, 125, 112–129. [Google Scholar] [CrossRef]
 Oliva, D.; Abd Elaziz, M.; Hinojosa, S. Image Segmentation as a Multiobjective Optimization Problem. In Metaheuristic Algorithms for Image Segmentation: Theory and Applications; Springer International Publishing: Cham, Switzerland, 2019; pp. 157–179. [Google Scholar] [CrossRef]
 Sağ, T.; Çunkaş, M. Color image segmentation based on multiobjective artificial bee colony optimization. Appl. Soft Comput. 2015, 34, 389–401. [Google Scholar] [CrossRef]
 Albayrak Abdulkadir, B.G. A Hybrid Method of Superpixel Segmentation Algorithm and Deep Learning Method in Histopathological Image Segmentation. In Proceedings of the Innovations in Intelligent Systems and Applications INISTA, Thessaloniki, Greece, 3–5 July 2018; pp. 1–5. [Google Scholar] [CrossRef]
 Albayrak, A.; Bilgin, G. Automatic cell segmentation in histopathological images via twostaged superpixelbased algorithms. Med. Biol. Eng. Comput. 2018, 57, 653–665. [Google Scholar] [CrossRef]
 Ding, S.; Cong, L.; Wang, L.; Zhang, A.; Jia, W. Image Segmentation Algorithm Based on Superpixel Clustering. IET Image Process. 2018, 12, 2030–2035. [Google Scholar] [CrossRef]
 Zhang, S.; You, Z.; Wu, X. Plant disease leaf image segmentation based on superpixel clustering and EM algorithm. Neural Comput. Appl. 2019, 31, 1225–1232. [Google Scholar] [CrossRef]
 Naylor, P.; Laé, M.; Reyal, F.; Walter, T. Segmentation of Nuclei in Histopathology Images by Deep Regression of the Distance Map. IEEE Trans. Med. Imaging 2018, 38, 448–459. [Google Scholar] [CrossRef] [PubMed]
 Kumar, N.; Verma, R.; Anand, D.; Zhou, Y.; Onder, O.F.; Tsougenis, E.; Chen, H.; Heng, P.A.; Li, J.; Hu, Z.; et al. A MultiOrgan Nucleus Segmentation Challenge. IEEE Trans. Med Imaging 2020, 39, 1380–1391. [Google Scholar] [CrossRef] [PubMed]
 Kumar, N.; Verma, R.; Sharma, S.; Bhargava, S.; Vahadane, A.; Sethi, A. A Dataset and a Technique for Generalized Nuclear Segmentation for Computational Pathology. IEEE Trans. Med. Imaging 2017, 36, 1550–1560. [Google Scholar] [CrossRef]
 Verma, R.; Kumar, N.; Patil, A.; Kurian, N.C.; Rane, S.; Graham, S.; Vu, Q.D.; Zwager, M.; Raza, S.E.A.; Rajpoot, N.; et al. MoNuSAC2020: A Multiorgan Nuclei Segmentation and Classification Challenge. IEEE Trans. Med Imaging 2021, 40, 3413–3423. [Google Scholar] [CrossRef]
 Andrew, J.; Anant, M. Deep learning for digital pathology image analysis: A comprehensive tutorial with selected use cases. J. Pathol. Inform. 2016, 7, 29. [Google Scholar] [CrossRef]
 Ogiela, M.; Tadeusiewicz, R. Preprocessing medical images and their overall enhancement. Stud. Comput. Intell. 2008, 84, 65–97. [Google Scholar] [CrossRef]
 Zuiderveld, K. Contrast Limited Adaptive Histogram Equalization. In Graphics Gems IV; Academic Press Professional, Inc.: New York, NY, USA, 1994; pp. 474–485. [Google Scholar]
 Otsu, N. A Threshold Selection Method from GrayLevel Histograms. IEEE Trans. Syst. Man Cybern. 1979, 9, 62–66. [Google Scholar] [CrossRef] [Green Version]
 Kapur, J.; Sahoo, P.; Wong, A. A new method for graylevel picture thresholding using the entropy of the histogram. Comput. Vis. Graph. Image Process. 1985, 29, 273–285. [Google Scholar] [CrossRef]
 Sahoo, P.; Wilkins, C.; Yeager, J. Threshold selection using Renyi’s entropy. Pattern Recognit. 1997, 30, 71–84. [Google Scholar] [CrossRef]
 Angel Arul Jothi, J.; Mary Anita Rajam, V. Effective segmentation and classification of thyroid histopathology images. Appl. Soft Comput. 2016, 46, 652–664. [Google Scholar] [CrossRef]
 Lang, C.; Jia, H. Kapur’s Entropy for Color Image Segmentation Based on a Hybrid Whale Optimization Algorithm. Entropy 2019, 21, 318. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 O’Neill, B. Chapter 2—Frame Fields. In Elementary Differential Geometry, 2nd ed.; O’Neill, B., Ed.; Academic Press: Boston, MA, USA, 2006; pp. 43–99. [Google Scholar] [CrossRef]
 Achanta, R.; Shaji, A.; Smith, K.; Lucchi, A.; Fua, P.; Süsstrunk, S. SLIC Superpixels Compared to StateoftheArt Superpixel Methods. IEEE Trans. Pattern Anal. Mach. Intell. 2012, 34, 2274–2282. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 Bao, J.; Yin, J.; Yang, J. Superpixelbased segmentation for multitemporal PolSAR images. In Proceedings of the 2017 Progress in Electromagnetics Research Symposium—Fall (PIERSFALL), Singapore, 19–22 November 2017; pp. 654–658. [Google Scholar] [CrossRef]
 Heris, M.K. MOEA/D in MATLAB. 2015. Available online: https://yarpiz.com/95/ypea124moead (accessed on 20 March 2023).
 Heris, M.K. NSGA2 in MATLAB. 2015. Available online: https://yarpiz.com/56/ypea120nsga2 (accessed on 20 March 2023).
 Tillett, J.; Rao, T.; Sahin, F.; Rao, R. Darwinian Particle Swarm Optimization. In Proceedings of the Indian International Conference on Artificial Intelligence IICAI, Pune, India, 20–22 December 2005; pp. 1474–1487. [Google Scholar]
 Couceiro, M.; Ghamisi, P. Fractional Order Darwinian Particle Swarm Optimization: Applications and Evaluation of an Evolutionary Algorithm; Springer Publishing Company, Incorporated: Cham, Switzerland, 2015. [Google Scholar]
 Lagree, A.; Mohebpour, M.; Meti, N.; Saednia, K.; Lu, F.I.; Slodkowska, E.; Gandhi, S.; Rakovitch, E.; Shenfield, A.; SadeghiNaini, A.; et al. A review and comparison of breast tumor cell nuclei segmentation performances using deep convolutional neural networks. Sci. Rep. 2021, 11, 8025. [Google Scholar] [CrossRef] [PubMed]
 Alemi Koohbanani, N.; Jahanifar, M.; Zamani Tajadin, N.; Rajpoot, N. NuClick: A deep learning framework for interactive segmentation of microscopic images. Med. Image Anal. 2020, 65, 101771. [Google Scholar] [CrossRef]
Algorithms  Method  Images 

PSO and its variants  PSObased Otsu’s multilevel thresholding [13]  Histopathology images 
PSObased clustering method [14]  Histopathology images  
PSObased multilevel thresholding [15]  Grayscale images and medical images  
Dynamic PSO [16]  Real crystal growth images  
PSO using Kapur’s and Tsallis entropy [17]  Normal brain MRI  
PSOFCM algorithm [18]  Ultrasonic teeth images  
DPSO [19]  Satellite images  
FODPSO [20]  Infrared images  
FODPSO [21]  Retinal images  
Multiobjective algorithms  UISMOPC [22]  Standard images 
MOPSO [23]  Standard images  
Multiobjective colour thresholding [24]  Standard images  
Multiobjective optimization [25]  Simulated MRI and MRI  
Multiobjective multiverse optimization [26]  Natural grayscale images  
Multiobjective grey wolf optimization [27]  Natural grayscale images  
Multiobjective artificial bee colony [28]  Standard images  
Superpixel algorithm  SLIC and CNN [29]  Histopathology images 
SLIC and clustering algorithm [30]  Histopathology images  
Superpixel algorithm and clustering algorithm [31]  Satellite images  
superpixel and EM [32]  Plant disease leaves images 
Dataset  Task  Total Images  Image Format 

TNBC [33]  Segmentation of nuclei cells  50  .png 
MoNuSeg [34,35]  Nuclei segmentation from multiple organs  44  .tif 
MoNuSAC [36]  Segmentation of lymphocytes  146  .tif 
Segmentation of macrophages  58  .tif  
Segmentation of neutrophils  94  .tif  
Segmentation of epithelial cells  96  .tif  
LD [37]  Detection of lymphocyte cells  100  .tif 
Parameters  Variable  Values 

Population size  ${N}_{par}$  150 
Maximum no. of iterations  ${N}_{ite}$  150 
No. of thresholds  k  2 
Position range  $[{X}_{min},{X}_{max}]$  [0, 255] 
Velocity range  $[{V}_{min},{V}_{max}]$  [−5, 5] 
Repository size  ${A}_{max}$  30 
Algorithm  FMeasure  Dice Value  Jaccard Value 

PSO  0.59  0.59  0.44 
DPSO  0.62  0.62  0.45 
FODPSO  0.62  0.62  0.46 
MOPSO(Kapur + Otsu)  0.69  0.69  0.54 
MOPSO(Renyi + Otsu)  0.61  0.61  0.45 
MOPSO(Kapur + Renyi)  0.69  0.69  0.54 
MOPSO(Kapur + Otsu + Renyi)  0.71  0.71  0.55 
Superpixel algorithm  0.59  0.59  0.43 
MOEA/D  0.38  0.38  0.24 
NSGA2  0.58  0.58  0.43 
Otsu threshold [52]  0.03    0.05 
Watershed transform [52]  0.09    0.08 
The ImageJ2Fiji package [52]  0.18    0.34 
Region growing [53]    0.37  0.16 
Active contour [53]    0.58  0.28 
MMPSOS  0.72  0.72  0.56 
Algorithm  FMeasure  Dice Value  Jaccard Value 

PSO  0.61  0.61  0.46 
DPSO  0.61  0.61  0.46 
FODPSO  0.61  0.61  0.46 
MOPSO(Kapur + Otsu)  0.57  0.57  0.42 
MOPSO(Renyi + Otsu)  0.63  0.63  0.46 
MOPSO(Kapur + Renyi)  0.60  0.60  0.44 
MOPSO(Kapur + Otsu + Renyi)  0.64  0.64  0.47 
Superpixel algorithm  0.54  0.54  0.38 
MOEA/D  0.24  0.24  0.14 
NSGA2  0.58  0.58  0.42 
MMPSOS  0.65  0.65  0.49 
Dataset  Algorithm  FMeasure  Dice Value  Jaccard Value 

MoNuSACL  PSO  0.68  0.68  0.53 
DPSO  0.66  0.66  0.50  
FODPSO  0.67  0.67  0.52  
MOPSO(Kapur + Otsu)  0.68  0.68  0.52  
MOPSO(Renyi + Otsu)  0.67  0.67  0.51  
MOPSO(Renyi + Kapur)  0.67  0.67  0.51  
MOPSO(Kapur + Renyi + Otsu)  0.70  0.70  0.54  
Superpixel algorithm  0.47  0.47  0.32  
MOEA/D  0.42  0.42  0.27  
NSGA2  0.40  0.40  0.31  
MMPSOS  0.70  0.70  0.55  
MoNuSACM  PSO  0.55  0.55  0.38 
DPSO  0.56  0.56  0.40  
FODPSO  0.58  0.58  0.41  
MOPSO(Kapur + Otsu)  0.59  0.59  0.43  
MOPSO(Renyi + Otsu)  0.57  0.57  0.40  
MOPSO(Renyi + Kapur)  0.57  0.57  0.41  
MOPSO(Kapur + Renyi + Otsu)  0.63  0.63  0.47  
Superpixel algorithm  0.34  0.34  0.23  
MOEA/D  0.31  0.31  0.20  
NSGA2  0.62  0.62  0.48  
MMPSOS  0.65  0.65  0.48  
MoNuSACN  PSO  0.44  0.44  0.29 
DPSO  0.45  0.45  0.30  
FODPSO  0.47  0.47  0.31  
MOPSO(Kapur + Otsu)  0.50  0.50  0.35  
MOPSO(Renyi + Otsu)  0.51  0.51  0.36  
MOPSO(Renyi + Kapur)  0.46  0.46  0.31  
MOPSO(Kapur + Renyi + Otsu)  0.50  0.50  0.34  
Superpixel algorithm  0.44  0.44  0.29  
MOEA/D  0.12  0.12  0.07  
NSGA2  0.35  0.35  0.23  
MMPSOS  0.53  0.53  0.38  
MoNuSACE  PSO  0.52  0.52  0.35 
DPSO  0.57  0.57  0.40  
FODPSO  0.59  0.59  0.42  
MOPSO(Kapur + Otsu)  0.61  0.61  0.44  
MOPSO(Renyi + Otsu)  0.58  0.58  0.41  
MOPSO(Renyi + Kapur)  0.59  0.59  0.42  
MOPSO(Kapur + Renyi + Otsu)  0.62  0.62  0.46  
Superpixel algorithm  0.37  0.37  0.25  
MOEA/D  0.18  0.18  0.11  
NSGA2  0.50  0.50  0.34  
MMPSOS  0.63  0.63  0.47 
Algorithm  Precision  Recall  FMeasure 

PSO  0.84  0.96  0.90 
DPSO  0.85  0.99  0.92 
FODPSO  0.86  0.99  0.92 
MOPSO(Kapur + Otsu)  0.87  0.96  0.91 
MOPSO(Kapur + Renyi)  0.88  0.94  0.91 
MOPSO(Renyi + Otsu)  0.87  0.96  0.91 
MOPSO(Kapur + Otsu + Renyi)  0.93  0.99  0.96 
Superpixel algorithm  0.78  0.83  0.80 
NSGA2  0.86  0.94  0.90 
MOEA/D  0.78  0.71  0.74 
MMPSOS  0.96  0.99  0.98 
Algorithm  TNBC  MoNuSeg  MoNuSAC L  MoNuSAC M  MoNuSAC N  MoNuSAC E  LD 

PSO  0.021  0.036  0.022  0.021  0.021  0.038  0.011 
DPSO  0.186  0.203  0.203  0.196  0.192  0.200  0.207 
FODPSO  0.241  0.238  0.276  0.246  0.265  0.255  0.280 
MOPSO(Kapur + Otsu)  0.102  0.098  0.104  0.102  0.092  0.091  0.098 
MOPSO(Renyi + Otsu)  0.100  0.094  0.098  0.096  0.098  0.085  0.092 
MOPSO(Kapur + Renyi)  0.096  0.072  0.093  0.089  0.091  0.087  0.086 
MOPSO(Kapur + Otsu + Renyi)  0.112  0.103  0.084  0.110  0.095  0.097  0.101 
Superpixel algorithm  0.015  0.031  0.020  0.014  0.018  0.031  0.016 
MMPSOS  0.126  0.125  0.100  0.126  0.128  0.116  0.109 
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. 
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Kanadath, A.; Angel Arul Jothi, J.; Urolagin, S. Multilevel Multiobjective Particle Swarm Optimization Guided Superpixel Algorithm for Histopathology Image Detection and Segmentation. J. Imaging 2023, 9, 78. https://doi.org/10.3390/jimaging9040078
Kanadath A, Angel Arul Jothi J, Urolagin S. Multilevel Multiobjective Particle Swarm Optimization Guided Superpixel Algorithm for Histopathology Image Detection and Segmentation. Journal of Imaging. 2023; 9(4):78. https://doi.org/10.3390/jimaging9040078
Chicago/Turabian StyleKanadath, Anusree, J. Angel Arul Jothi, and Siddhaling Urolagin. 2023. "Multilevel Multiobjective Particle Swarm Optimization Guided Superpixel Algorithm for Histopathology Image Detection and Segmentation" Journal of Imaging 9, no. 4: 78. https://doi.org/10.3390/jimaging9040078