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
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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 
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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