Table 5.

Literature reports on HIOA based multi-level thresholding

SL	Proposed Method	Objective Function	Paper Details	Image Type	Comparison	Quality parameters considered	Observations
1	Imperialist Competitive Algorithm (ICA) for multi-threshold image segmentation	Otsu’s and Kapur	Wang et al. in the year 2021 [20]	Standard Gray scale images	ICA with PSO, GWO and TLBO	Maximum and average values of Objective functions, threshold values	The proposed algorithm has quicker convergence speed, superior quality as well as stability in solving multi-threshold segmentation problems as compared to other methods
2	Identification of apple diseases using the Gaining-Sharing Knowledge-Based Algorithm (GSK) for multilevel thresholding	Minimum Cross-Entropy	Ortega et al. in the year 2021 [224]	Standard Color Images	GSK with FFO, PSO, SCA, ABC, HS and DE	PSNR, SSIM and FSIM	The proposed algorithm generates superior quality segmentation compared with other approaches
3	Application of Teaching Learning Based Optimization in Multilevel Image Thresholding	Kapur	Anbazhagan in the year 2021 [108]	Standard Gray scale images	TLBO with SCA, WOA, HHA, SSA, BA, PSO, CSA, and EO	Maximum and average values of Objective functions, threshold values and J-Index	The proposed algorithm is increasingly powerful in finding the global optimal solution for image thresholding issues
4	An efficient method to minimize cross-entropy for selecting multi-level threshold values using an Improved Human Mental Search algorithm (IHMSMLIT)	Minimum Cross-Entropy	Esmaeili in the year 2021 [189]	Standard Gray scale images	IHMSMLIT with PSOMLIT, FAMLIT, BBOMLIT, CSMLIT, GWOMLIT and WOAMLIT	PSNR, SSIM, FSIM and stability analysis	The proposed algorithm obtains best result among the compared algorithms in terms of the quality parameters considered proving the efficacy of the algorithm proposed
5	Medical image segmentation using Exchange Market Algorithm (EMA)	Kapur, Otsu and Minimum Cross Entropy	Sathya et al. in the year 2021 [273]	Medical Images	EMA with KHA, TLBO and CSA	PSNR, and SSIM	The proposed algorithm especially Otsu based EMA method is found to be more accurate and robust for improved clinical decision making and diagnosis
6	Color image segmentation using kapur, otsu and minimum cross entropy functions based on Exchange Market Algorithm	Kapur, Otsu and Minimum Cross Entropy	Sathya et al. in the year 2021 [148]	Standard Color images	EMA with KHA, TLBO and CSA	PSNR, Computational Time and SSIM	The proposed algorithm obtains best result among the compared algorithms and converges quickly than the other algorithms
7	Multilevel thresholding image segmentation based on improved Volleyball Premier League algorithm using Whale Optimization Algorithm (VPLWOA)	Otsu’s	Elaziz et al. in the year 2021 [208]	Standard Gray scale images	VPLWOA with FA, SCA, SSO,VPL and WOA	PSNR, SSIM, RMSE, CPU Time and FSIM	The proposed algorithm outperforms the other algorithms in terms of PSNR, SSIM, and fitness function
8	Image segmentation based on Determinative Brain Storm Optimization (DBSO)	Renyi’s and Otsu’s	Sovatzidi et al. in the year 2020 [274]	Standard Gray scale images	DBSO with BSO, EMO	Mean PSNR values	The proposed algorithm obtains segmentation results of comparable or higher quality, in less iterations, than the ones obtained by state-of-the-art optimization-based multilevel thresholding methods
9	Human Mental Search (HMS)-based multilevel thresholding for image segmentation	Otsu’s and Kapur	Mousavirad et al. in the year 2020 [190]	Standard Gray scale images	HMS with TLBO, BA, FA, PSO, DE and GA	Objective function value, PSNR, SSIM, FSIM, and Curse of dimensionality	The proposed algorithm has better performance than other compared algorithms based on different parameters however, computational time is slightly higher
10	Social-Group-Optimization based tumor evaluation tool for clinical brain MRI of Flair/diffusion-weighted modality (SGO)	Shannon	Dey et al. in the year 2019 [275]	CT and MR Images: Medical Images	No comparison performed	JI, DC, ACC, PRE, SEN, SPE, BCR and BER	The proposed algorithm has acceptable performance generating a Hybrid Image Processing procedure
11	Social Group Optimization and Shannon’s Function-Based RGB Image Multi-level Thresholding	Shannon	Monisha et al. in the year 2018 [276]	Standard Color Images	SGO with PSO, BFO, FA, and BA	MSE, PSNR, SSIM, NCC, AD, and SC	The proposed algorithm generates better result compared with the other algorithms considered in this paper
12	Backtracking Search Algorithm for color image multilevel thresholding (MFE-BSA)	Modified Fuzzy Entropy (MFE), Tsalli’s	Pare et al. in the year 2018 [223]	Standard Color natural images and Satellite images	MFE-BSA with Energy-Tsalli’s-CS, Tsalli’s-CS MFE-BFO	PSNR, MSE and CPU Time	The proposed algorithm shows very good segmentation results in terms of preciseness, robustness, and stability
13	Robust Multi-thresholding in Noisy Grayscale Images Using Otsu’s Function and Harmony Search Optimization Algorithm (HSOA)	Otsu’s	Suresh et al. in the year 2018 [277]	Standard Gray scale images	No comparison performed	Optimal threshold, PSNR, RMSE	The proposed algorithm with Otsu’s function offers promising results. However, it near future, it can be further compared with other heuristic algorithms
14	Hybrid Multilevel Thresholding and Improved Harmony Search Algorithm for Segmentation (MT-IHSA)	Otsu’s	Erwin and Saputri in the year 2018 [57]	Standard Gray scale images	MT-IHSA with MT-FA, MT-SSA and Mt-HSA	PSNR	The proposed algorithm with Otsu’s function offers high degree of accuracy
15	Jaya Algorithm Guided Procedure to Segment Tumor from Brain MRI	Otsu’s	Satapathy et al. in the year 2018 [72]	MR Images: Medical Image	JAYA with FA, TLBO, PSO, BFO, and BA	RMSE, PSNR, SSIM, NCC, AD, SC and CPU Time	The proposed algorithm with Otsu’s function offers improved picture excellence measures, image likeness measures, and image statistical measures
16	Robust RGB Image Thresholding with Shannon’s Entropy and Jaya Algorithm	Shannon	Maheswari et al. in the year 2018 [9]	General color images	No comparison performed	PQM, RMSE, NCC, SC, NAE, IQM and PSNR	The proposed algorithm with Shannon entropy when applied over normal and noise stained images indicate that the PQM obtained for both the image cases are relatively identical and helps to achieve PSNR values
17	Entropy based segmentation of tumor from brain MR images–Teaching Learning Based Optimization	Kapur, Tsallis and Shannon	Rajinikanth et al. in the year 2017 [278]	MR Images: Medical Image	TLBO-Kapur with TLBO-Shannon and TLBO-Tsallis	PSNR, NCC, NAE, SSIM, PRE, FM, SEN, SPE, BCR, BER, ACC, FPR, FNR, J-Index	The proposed algorithm with Shannon’s entropy based thresholding and level set segmentation offers better result for the considered dataset
18	Parameter-Less Harmony Search (PLHS) for image multi-thresholding	Shannon	Dhal et al. in the year 2017 [54]	General Gray scale images	Eight different variants of PLHS with HS	CT, PSNR, Fitm and Fitstd	The proposed algorithm with lower population size are better for maximizing the Shannon’s entropy based objective function with less standard deviation is comparatively better than HS but consumes more computational time when Iteration based stopping criterion is used
19	Otsu and Kapur Segmentation Based on Harmony Search Optimization (HSMA)	Otsu’s and Kapur	Cuevas et al. in the year 2016 [56]	Standard Gray scale images	Otsu-HSMA with Kapur-HSMA. GA, PSO and BF	STD, RMSE and PSNR	The proposed algorithm demonstrates outstanding performance, accuracy and convergence in comparison to other methods
20	Multilevel Thresholding Segmentation Based on Harmony Search Optimization (HSMA)	Otsu’s and Kapur	Oliva et al. in the year 2013 [55]	Standard Gray scale images	Otsu-HSMA with Kapur-HSMA. GA, PSO and BF	PSNR, STD, mean of the objective function values	The proposed algorithm demonstrates the high performance for the segmentation of digital images as compared to other algorithms considered in the paper
21	Image thresholding optimization based on Imperialist Competitive Algorithm	Otsu’s	Razmjooy et al. in the year 2011 [279]	Standard Gray scale images	ICA with GA	MSE and PSNR	The proposed algorithm demonstrates the good performance and generated acceptable result