Table 12 2D kapur’s entropy values at different threshold levels on breast cancer images.

From: Gaussian bare‑bone JAYA algorithm for multi-threshold medical image segmentation

Image	Thresholds	GBJAYA	JAYA	DE	ABC	MVO	HHO	CGPSO	IWOA	ASMA	GBSFSSSA	SRDSGO
K	4	4.02 × 10¹	4.02 × 10¹	4.02 × 10¹	4.02 × 10¹	4.00 × 10¹	3.99 × 10¹	4.01 × 10¹	3.99 × 10¹	4.02 × 10¹	4.01 × 10¹	4.02 × 10¹
	5	4.59 × 10¹	4.59 × 10¹	4.59 × 10¹	4.59 × 10¹	4.57 × 10¹	4.54 × 10¹	4.58 × 10¹	4.56 × 10¹	4.59 × 10¹	4.58 × 10¹	4.59 × 10¹
	6	5.14 × 10¹	5.11 × 10¹	5.14 × 10¹	5.13 × 10¹	5.09 × 10¹	5.04 × 10¹	5.13 × 10¹	5.01 × 10¹	5.13 × 10¹	5.13 × 10¹	5.14 × 10¹
	12	7.81 × 10¹	7.62 × 10¹	7.71 × 10¹	7.66 × 10¹	7.53 × 10¹	7.42 × 10¹	7.70 × 10¹	7.39 × 10¹	7.67 × 10¹	7.65 × 10¹	7.70 × 10¹
	16	9.08 × 10¹	8.99 × 10¹	8.93 × 10¹	8.95 × 10¹	8.92 × 10¹	8.75 × 10¹	8.92 × 10¹	8.79 × 10¹	8.98 × 10¹	9.07 × 10¹	9.01 × 10¹
	20	1.03 × 10²	1.00 × 10²	1.00 × 10²	1.00 × 10²	9.89 × 10¹	9.89 × 10¹	1.00 × 10²	9.75 × 10¹	1.01 × 10²	1.02 × 10²	1.02 × 10²
L	4	4.38 × 10¹	4.38 × 10¹	4.38 × 10¹	4.38 × 10¹	4.35 × 10¹	4.27 × 10¹	4.38 × 10¹	4.24 × 10¹	4.38 × 10¹	4.38 × 10¹	4.38 × 10¹
	5	4.96 × 10¹	4.96 × 10¹	4.96 × 10¹	4.95 × 10¹	4.94 × 10¹	4.85 × 10¹	4.94 × 10¹	4.77 × 10¹	4.95 × 10¹	4.95 × 10¹	4.96 × 10¹
	6	5.49 × 10¹	5.47 × 10¹	5.49 × 10¹	5.48 × 10¹	5.40 × 10¹	5.35 × 10¹	5.46 × 10¹	5.33 × 10¹	5.48 × 10¹	5.48 × 10¹	5.49 × 10¹
	12	8.06 × 10¹	7.93 × 10¹	7.94 × 10¹	7.96 × 10¹	7.82 × 10¹	7.69 × 10¹	7.93 × 10¹	7.58 × 10¹	7.95 × 10¹	8.01 × 10¹	7.99 × 10¹
	16	9.45 × 10¹	9.20 × 10¹	9.16 × 10¹	9.16 × 10¹	9.06 × 10¹	9.02 × 10¹	9.18 × 10¹	8.99 × 10¹	9.33 × 10¹	9.34 × 10¹	9.31 × 10¹
	20	1.06 × 10²	1.02 × 10²	1.03 × 10²	1.03 × 10²	1.02 × 10²	9.73 × 10¹	1.02 × 10²	9.82 × 10¹	1.03 × 10²	1.05 × 10²	1.04 × 10²
M	4	3.75 × 10¹	3.71 × 10¹	3.75 × 10¹	3.73 × 10¹	3.72 × 10¹	3.61 × 10¹	3.70 × 10¹	3.62 × 10¹	3.75 × 10¹	3.75 × 10¹	3.75 × 10¹
	5	4.31 × 10¹	4.25 × 10¹	4.31 × 10¹	4.30 × 10¹	4.26 × 10¹	4.24 × 10¹	4.15 × 10¹	4.22 × 10¹	4.30 × 10¹	4.31 × 10¹	4.31 × 10¹
	6	4.83 × 10¹	4.78 × 10¹	4.80 × 10¹	4.82 × 10¹	4.79 × 10¹	4.73 × 10¹	4.79 × 10¹	4.71 × 10¹	4.82 × 10¹	4.81 × 10¹	4.83 × 10¹
	12	7.52 × 10¹	7.05 × 10¹	7.25 × 10¹	7.19 × 10¹	7.16 × 10¹	7.06 × 10¹	7.21 × 10¹	6.89 × 10¹	7.49 × 10¹	7.40 × 10¹	7.29 × 10¹
	16	8.92 × 10¹	8.14 × 10¹	8.43 × 10¹	8.64 × 10¹	8.22 × 10¹	8.35 × 10¹	8.44 × 10¹	8.09 × 10¹	8.63 × 10¹	8.75 × 10¹	8.74 × 10¹
	20	1.02 × 10²	9.29 × 10¹	9.42 × 10¹	9.69 × 10¹	9.42 × 10¹	9.19 × 10¹	9.49 × 10¹	9.35 × 10¹	9.81 × 10¹	9.87 × 10¹	9.81 × 10¹
N	4	3.98 × 10¹	3.95 × 10¹	3.97 × 10¹	3.97 × 10¹	3.94 × 10¹	3.90 × 10¹	3.97 × 10¹	3.94 × 10¹	3.97 × 10¹	3.97 × 10¹	3.97 × 10¹
	5	4.57 × 10¹	4.55 × 10¹	4.57 × 10¹	4.57 × 10¹	4.52 × 10¹	4.46 × 10¹	4.51 × 10¹	4.49 × 10¹	4.57 × 10¹	4.57 × 10¹	4.57 × 10¹
	6	5.10 × 10¹	5.09 × 10¹	5.09 × 10¹	5.07 × 10¹	5.03 × 10¹	4.80 × 10¹	5.05 × 10¹	4.87 × 10¹	5.10 × 10¹	5.09 × 10¹	5.10 × 10¹
	12	7.81 × 10¹	7.52 × 10¹	7.60 × 10¹	7.52 × 10¹	7.51 × 10¹	7.21 × 10¹	7.68 × 10¹	7.46 × 10¹	7.58 × 10¹	7.63 × 10¹	7.61 × 10¹
	16	9.22 × 10¹	8.66 × 10¹	8.80 × 10¹	8.77 × 10¹	8.75 × 10¹	8.54 × 10¹	8.82 × 10¹	8.53 × 10¹	8.87 × 10¹	8.95 × 10¹	8.93 × 10¹
	20	1.03 × 10²	9.71 × 10¹	9.90 × 10¹	9.96 × 10¹	9.81 × 10¹	9.34 × 10¹	9.97 × 10¹	9.60 × 10¹	9.95 × 10¹	1.01 × 10²	1.01 × 10²
O	4	3.87 × 10¹	3.86 × 10¹	3.87 × 10¹	3.86 × 10¹	3.86 × 10¹	3.82 × 10¹	3.86 × 10¹	3.81 × 10¹	3.87 × 10¹	3.86 × 10¹	3.87 × 10¹
	5	4.46 × 10¹	4.44 × 10¹	4.46 × 10¹	4.46 × 10¹	4.43 × 10¹	4.41 × 10¹	4.43 × 10¹	4.39 × 10¹	4.44 × 10¹	4.46 × 10¹	4.46 × 10¹
	6	5.00 × 10¹	4.98 × 10¹	5.00 × 10¹	5.00 × 10¹	4.97 × 10¹	4.95 × 10¹	4.99 × 10¹	4.92 × 10¹	5.01 × 10¹	5.00 × 10¹	5.00 × 10¹
	12	7.80 × 10¹	7.74 × 10¹	7.74 × 10¹	7.72 × 10¹	7.65 × 10¹	7.54 × 10¹	7.71 × 10¹	7.44 × 10¹	7.75 × 10¹	7.78 × 10¹	7.75 × 10¹
	16	9.26 × 10¹	9.07 × 10¹	9.08 × 10¹	9.12 × 10¹	9.02 × 10¹	8.93 × 10¹	9.13 × 10¹	8.81 × 10¹	9.15 × 10¹	9.20 × 10¹	9.17 × 10¹
	20	1.05 × 10²	1.02 × 10²	1.03 × 10²	1.03 × 10²	1.01 × 10²	1.01 × 10²	1.03 × 10²	9.91 × 10¹	1.03 × 10²	1.04 × 10²	1.04 × 10²
P	4	3.95 × 10¹	3.93 × 10¹	3.95 × 10¹	3.95 × 10¹	3.94 × 10¹	3.91 × 10¹	3.94 × 10¹	3.89 × 10¹	3.95 × 10¹	3.95 × 10¹	3.95 × 10¹
	5	4.56 × 10¹	4.52 × 10¹	4.55 × 10¹	4.55 × 10¹	4.50 × 10¹	4.47 × 10¹	4.53 × 10¹	4.50 × 10¹	4.55 × 10¹	4.55 × 10¹	4.55 × 10¹
	6	5.12 × 10¹	5.11 × 10¹	5.12 × 10¹	5.10 × 10¹	5.10 × 10¹	5.01 × 10¹	5.09 × 10¹	5.07 × 10¹	5.12 × 10¹	5.12 × 10¹	5.12 × 10¹
	12	7.80 × 10¹	7.68 × 10¹	7.59 × 10¹	7.61 × 10¹	7.59 × 10¹	7.54 × 10¹	7.64 × 10¹	7.40 × 10¹	7.67 × 10¹	7.76 × 10¹	7.70 × 10¹
	16	9.15 × 10¹	8.85 × 10¹	8.95 × 10¹	8.93 × 10¹	8.88 × 10¹	8.63 × 10¹	8.94 × 10¹	8.59 × 10¹	9.00 × 10¹	9.04 × 10¹	9.02 × 10¹
	20	1.04 × 10²	1.00 × 10²	1.00 × 10²	1.00 × 10²	9.89 × 10¹	9.91 × 10¹	9.93 × 10¹	9.57 × 10¹	1.01 × 10²	1.02 × 10²	1.01 × 10²
Q	4	3.96 × 10¹	3.96 × 10¹	3.96 × 10¹	3.96 × 10¹	3.95 × 10¹	3.89 × 10¹	3.96 × 10¹	3.93 × 10¹	3.96 × 10¹	3.96 × 10¹	3.96 × 10¹
	5	4.55 × 10¹	4.55 × 10¹	4.55 × 10¹	4.55 × 10¹	4.54 × 10¹	4.50 × 10¹	4.55 × 10¹	4.49 × 10¹	4.55 × 10¹	4.55 × 10¹	4.55 × 10¹
	6	5.10 × 10¹	5.09 × 10¹	5.09 × 10¹	5.09 × 10¹	5.09 × 10¹	4.93 × 10¹	5.08 × 10¹	5.04 × 10¹	5.09 × 10¹	5.09 × 10¹	5.10 × 10¹
	12	7.81 × 10¹	7.72 × 10¹	7.72 × 10¹	7.72 × 10¹	7.68 × 10¹	7.48 × 10¹	7.73 × 10¹	7.28 × 10¹	7.73 × 10¹	7.77 × 10¹	7.75 × 10¹
	16	9.25 × 10¹	9.08 × 10¹	8.98 × 10¹	9.01 × 10¹	8.80 × 10¹	8.69 × 10¹	9.05 × 10¹	8.70 × 10¹	9.03 × 10¹	9.21 × 10¹	9.13 × 10¹
	20	1.04 × 10²	1.02 × 10²	1.02 × 10²	1.02 × 10²	9.94 × 10¹	9.85 × 10¹	1.02 × 10²	9.80 × 10¹	1.02 × 10²	1.04 × 10²	1.02 × 10²
R	4	3.79 × 10¹	3.74 × 10¹	3.79 × 10¹	3.79 × 10¹	3.79 × 10¹	3.78 × 10¹	3.76 × 10¹	3.75 × 10¹	3.79 × 10¹	3.79 × 10¹	3.79 × 10¹
	5	4.37 × 10¹	4.35 × 10¹	4.37 × 10¹	4.37 × 10¹	4.36 × 10¹	4.22 × 10¹	4.37 × 10¹	4.32 × 10¹	4.37 × 10¹	4.37 × 10¹	4.37 × 10¹
	6	4.89 × 10¹	4.89 × 10¹	4.89 × 10¹	4.89 × 10¹	4.89 × 10¹	4.88 × 10¹	4.89 × 10¹	4.83 × 10¹	4.89 × 10¹	4.89 × 10¹	4.89 × 10¹
	12	7.56 × 10¹	7.42 × 10¹	7.48 × 10¹	7.48 × 10¹	7.44 × 10¹	7.33 × 10¹	7.49 × 10¹	7.19 × 10¹	7.48 × 10¹	7.54 × 10¹	7.50 × 10¹
	16	9.02 × 10¹	8.70 × 10¹	8.87 × 10¹	8.79 × 10¹	8.69 × 10¹	8.60 × 10¹	8.82 × 10¹	8.56 × 10¹	8.86 × 10¹	8.94 × 10¹	8.92 × 10¹
	20	1.02 × 10²	9.83 × 10¹	9.98 × 10¹	9.88 × 10¹	9.81 × 10¹	9.65 × 10¹	9.93 × 10¹	9.60 × 10¹	9.96 × 10¹	1.01 × 10²	1.01 × 10²
S	4	4.02 × 10¹	4.02 × 10¹	4.02 × 10¹	4.02 × 10¹	4.01 × 10¹	3.97 × 10¹	4.01 × 10¹	3.96 × 10¹	4.02 × 10¹	4.02 × 10¹	4.02 × 10¹
	5	4.59 × 10¹	4.59 × 10¹	4.59 × 10¹	4.59 × 10¹	4.58 × 10¹	4.51 × 10¹	4.58 × 10¹	4.54 × 10¹	4.59 × 10¹	4.59 × 10¹	4.59 × 10¹
	6	5.12 × 10¹	5.10 × 10¹	5.11 × 10¹	5.12 × 10¹	5.09 × 10¹	5.08 × 10¹	5.11 × 10¹	5.07 × 10¹	5.11 × 10¹	5.12 × 10¹	5.11 × 10¹
	12	7.82 × 10¹	7.60 × 10¹	7.69 × 10¹	7.64 × 10¹	7.59 × 10¹	7.54 × 10¹	7.64 × 10¹	7.32 × 10¹	7.75 × 10¹	7.74 × 10¹	7.69 × 10¹
	16	9.20 × 10¹	8.89 × 10¹	8.93 × 10¹	8.99 × 10¹	8.88 × 10¹	8.72 × 10¹	8.93 × 10¹	8.61 × 10¹	9.06 × 10¹	9.07 × 10¹	9.01 × 10¹
	20	1.04 × 10²	9.94 × 10¹	1.01 × 10²	1.00 × 10²	9.77 × 10¹	9.52 × 10¹	9.93 × 10¹	9.71 × 10¹	1.02 × 10²	1.02 × 10²	1.01 × 10²
T	4	3.82 × 10¹	3.80 × 10¹	3.81 × 10¹	3.82 × 10¹	3.82 × 10¹	3.77 × 10¹	3.80 × 10¹	3.76 × 10¹	3.82 × 10¹	3.83 × 10¹	3.82 × 10¹
	5	4.43 × 10¹	4.35 × 10¹	4.41 × 10¹	4.41 × 10¹	4.41 × 10¹	4.33 × 10¹	4.39 × 10¹	4.34 × 10¹	4.42 × 10¹	4.43 × 10¹	4.42 × 10¹
	6	4.98 × 10¹	4.90 × 10¹	4.96 × 10¹	4.97 × 10¹	4.97 × 10¹	4.86 × 10¹	4.93 × 10¹	4.90 × 10¹	4.98 × 10¹	4.98 × 10¹	4.98 × 10¹
	12	7.68 × 10¹	7.46 × 10¹	7.58 × 10¹	7.54 × 10¹	7.52 × 10¹	7.37 × 10¹	7.63 × 10¹	7.32 × 10¹	7.57 × 10¹	7.65 × 10¹	7.61 × 10¹
	16	9.10 × 10¹	8.72 × 10¹	8.90 × 10¹	8.92 × 10¹	8.91 × 10¹	8.80 × 10¹	8.93 × 10¹	8.53 × 10¹	9.01 × 10¹	9.03 × 10¹	8.97 × 10¹
	20	1.03 × 10²	9.78 × 10¹	1.00 × 10²	1.01 × 10²	9.93 × 10¹	9.93 × 10¹	9.98 × 10¹	9.67 × 10¹	1.01 × 10²	1.03 × 10²	1.02 × 10²

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Table 12 2D kapur’s entropy values at different threshold levels on breast cancer images.

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