Fig 1.
The three-layer pyramid structure of particle swarm.
Fig 2.
The curve of inertia weight (wmin = 0.5, wmax = 0.9).
Fig 3.
Grayscale images with 12-bit depth and their corresponding histogram.
Image (1) Histogram (1) Image (2) Histogram (2) Image (3) Histogram (3) Image (4) Histogram (4) Image (5) Histogram (5) Image (6) Histogram (6) Image (7) Histogram (7) Image (8) Histogram (8) Image (9) Histogram (9) Image (10) Histogram (10) Image (11) Histogram (11) Image (12) Histogram (12) Image (13) Histogram (13) Image (14) Histogram (14) Image (15) Histogram (15) Image (16) Histogram (16).
Table 1.
Hyperparameters of the above comparison algorithm.
Table 2.
The Kapur entropy obtained by algorithms over the 16 benchmark images with 12-bit depth.
Fig 4.
The convergence curve of the algorithms for image (2) and image (9).
Image (2) nTh = 4 nTh = 6 nTh = 8 Image (9) nTh = 4 nTh = 6 nTh = 8.
Fig 5.
Images of brain tumors used in the experiments and their corresponding histograms.
Image (a) Histogram (a) Image (b) Histogram (b) Image (c) Histogram (c) Image (d) Histogram (d) Image (e) Histogram (e) Image (f) Histogram (f) Image (g) Histogram (g) Image (h) Histogram (h) Image (i) Histogram (i).
Table 3.
The fitness values (Kapur entropy) obtained by the above algorithms.
Table 4.
The Friedman statistic and p-value of PSO and its variants.
Table 5.
The average ranks.
Table 6.
Results of the PSNR measure for all algorithms.
Table 7.
Results of the SSIM measure for all algorithms.
Table 8.
Results of the FSIM measure for all algorithms.