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Fig 1.

The movement of Cauchy distribution and Lévy flight.

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Fig 1 Expand

Table 1.

The experimental of HGJO with different γ.

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Table 1 Expand

Fig 2.

The variation curves of the two escape energies.

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Fig 2 Expand

Table 2.

The benchmark functions of CEC2022.

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Table 2 Expand

Table 3.

Runtime environment.

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Table 3 Expand

Table 4.

The parameters setting of all algorithms.

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Table 4 Expand

Fig 3.

The average time slots for all algorithms.

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Table 5.

The results of CEC2022 for all algorithm.

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Table 6.

The Wilcoxon signed-rank test for CEC2022.

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Table 6 Expand

Fig 4.

The convergence curves for all algorithms on CEC2022 benchmark functions.

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Fig 4 Expand

Fig 5.

The box plots for all algorithms on CEC2022 benchmark functions.

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Fig 5 Expand

Fig 6.

The selected images for segmentation.

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Fig 6 Expand

Fig 7.

The RGB histogram of C0080 and C0088.

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Fig 8.

The RGB histogram of C0132 and C0135.

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Fig 9.

The RGB histogram of C0180 and C0536.

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Fig 10.

The RGB histogram of C1088 and L0032.

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Fig 11.

The RGB histogram of L0064 and L0135.

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Fig 12.

The RGB histogram of L0158 and L0226.

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Fig 13.

The RGB histogram of L0699 and L0879.

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Fig 14.

The RGB histogram of L1074 and X0017.

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Table 7.

The PSNR results for all algorithms.

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Table 7 Expand

Table 8.

The SSIM results for all algorithms.

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Table 9.

The FSIM results for all algorithms.

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Table 9 Expand

Table 10.

Comparison of the Wilcoxon signed-rank test for Otsu method.

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Table 10 Expand

Fig 15.

The segmentation results for C0180.

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