Multi-Level Thresholding Image Segmentation Based on Improved Slime Mould Algorithm and Symmetric Cross-Entropy
Abstract
:1. Introduction
2. Slime Mould Algorithm
3. The Proposed Method
3.1. Elite Opposition-Based Learning
3.2. The Adaptive Probability Threshold
3.3. The Historical Leader
3.4. Pseudo-Code of ISMA
Algorithm 1 Pseudo-code of ISMA |
Initialize the parameters popsize, Max_iteraition |
Initialize the positions of the slime mould |
While (t ≤ Max_iteraition) |
Calculate the fitness of all the slime mould |
Update bestFitness, Xb |
Calculate the W by Equation (4) |
For each search portion, |
Update p by Equation (8) |
Update positions by Equation (9) |
End For |
t = t + 1 |
End While |
Return bestFitness, Xb |
4. ISMA Performance Evaluation Experiments and Analysis
5. Multi-Threshold Segmentation
5.1. Symmetric Cross-Entropy Threshold Segmentation
5.2. Multi-Level Threshold Segmentation Based on ISMA and Symmetric Cross-Entropy
- (a)
- Read the image to be segmented (grayscale image).
- (b)
- Find the grayscale histogram of the image.
- (c)
- Initialize the parameters of ISMA, the size of the population of slime mould (n), the maximum number of iterations (max_t), the initial values of the upper bound (LB) and lower bound (UB), and the number of desired partition thresholds (d).
- (d)
- Find the optimal fitness value using symmetric cross-entropy as the ISMA objective function.
- (e)
- If ISMA reaches the maximum number of iterations max_t, the optimization is completed, and the slime mould location information regarding the best fitness is returned, which is the best segmentation threshold. Otherwise, skip to step (d).
- (f)
- Perform grayscale image segmentation with the best threshold and obtain the segmented image.
6. Threshold Segmentation Experiment Results and Analysis
6.1. Threshold Segmentation Experiment for the Segmentation Criteria
6.2. Threshold Segmentation Experiment of MAs
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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No | Name | Range | D | fmin | Type |
---|---|---|---|---|---|
F1 | Sphere | [−100, 100] | 30 | 0 | UM |
F2 | Schwefel 2.22 | [−10, 10] | 30 | 0 | UM |
F3 | Schwefel 1.2 | [−100, 100] | 30 | 0 | UM |
F4 | Schwefel 2.21 | [−100, 100] | 30 | 0 | UM |
F5 | Rosenbrock | [−30, 30] | 30 | 0 | UM |
F6 | Step | [−100, 100] | 30 | 0 | UM |
F7 | Quartic | [−1.28, 1.28] | 30 | 0 | UM |
F8 | Schwefel | [−500, 500] | 30 | −12,569.487 | MM |
F9 | Rastrigin | [−5.12, 5.12] | 30 | 0 | MM |
F10 | Ackley | [−32, 32] | 30 | 0 | MM |
F11 | Griewank | [−600, 600] | 30 | 0 | MM |
F12 | Penalized | [−50, 50] | 30 | 0 | MM |
F13 | Penalized 2 | [−50, 50] | 30 | 0 | MM |
F14 | Foxholes | [−65.536, 65.536] | 2 | 0.998004 | MM |
Algorithm | Parameters |
---|---|
ISMA | Z = 0.03 |
SMA | Z = 0.03 |
SOA | FC = 2, u = 1, v = 1 |
MFO | b = 1, = 0.001, g ∈ [0, 30], C ∈ [0, 100] |
GWO | a ∈ [2, 0] |
POA | I = 2, R = 0.2 |
ESMA | Z = 0.03 |
DFSMA | Z = 0.03 |
Function | ISMA | SMA | SOA | MFO | POA | GWO | ESMA | DFSMA |
---|---|---|---|---|---|---|---|---|
F1 | 0.000 | 1.500 × 10−323 | 8.496 × 10−12 | 1.341 × 103 | 1.525 × 10−103 | 1.619 × 10−28 | 5.106 × 10−297 | 2.320 × 10−292 |
F2 | 0.000 | 6.348 × 10−147 | 1.590 × 10−8 | 3.685 × 10 | 6.001 × 10−52 | 9.760 × 10−17 | 3.758 × 10−168 | 9.280 × 10−153 |
F3 | 0.000 | 1.446 × 10−313 | 1.258 × 10−4 | 2.109 × 104 | 3.735 × 10−100 | 7.918 × 10−6 | 2.970 × 10−296 | 5.900 × 10−323 |
F4 | 0.000 | 1.007 × 10−148 | 1.758 × 10−2 | 6.794 × 10 | 2.443 × 10−51 | 6.649 × 10−7 | 4.231 × 10−141 | 1.983 × 10−160 |
F5 | 2.550 | 1.207 × 101 | 2.822 × 10 | 2.688 × 106 | 2.810 × 10 | 2.682 × 10 | 5.415 | 3.262 |
F6 | 4.239 × 10−4 | 7.500 × 10−3 | 3.306 | 1.680 × 103 | 2.829 | 7.552 × 10−1 | 5.803 × 10−3 | 5.431 × 10−3 |
F7 | 1.211 × 10−4 | 1.805 × 10−4 | 2.631 × 10−3 | 5.766 | 2.363 × 10−4 | 1.657 × 10−3 | 1.950 × 10−4 | 1.685 × 10−4 |
F8 | −1.257 × 104 | −1.257 × 104 | −4.861 × 103 | 9.933 × 102 | −7.642 × 103 | −5.930 × 103 | −1.256 × 104 | −1.256 × 104 |
F9 | 0.000 | 0.000 | 1.297 | 1.714 × 102 | 0.000 | 4.815 | 0.000 | 0.000 |
F10 | 8.882 × 10−16 | 8.882 × 10−16 | 1.996 × 10 | 1.448 × 10 | 3.257 × 10−15 | 9.456 × 10−14 | 8.882 × 10−16 | 8.882 × 10−16 |
F11 | 0.000 | 0.000 | 2.989 × 10−2 | 1.591 × 10 | 0.000 | 4.596 × 10−3 | 0.000 | 0.000 |
F12 | 3.098 × 10−4 | 5.500 × 10−3 | 3.439 × 10−1 | 8.534 × 106 | 1.926 × 10−1 | 5.065 × 10−2 | 5.237 × 10−3 | 4.620 × 10−3 |
F13 | 1.700 × 10−3 | 1.240 × 10−2 | 2.057 | 2.381 × 102 | 2.589 | 5.603 × 10−1 | 6.689 × 10−3 | 6.933 × 10−3 |
F14 | 9.980 × 10−1 | 1.013 | 2.150 | 1.823 | 1.823 | 4.655 | 9.981 × 10−1 | 9.981 × 10−1 |
Function | ISMA | SMA | SOA | MFO | POA | GWO | ESMA | DFSMA |
---|---|---|---|---|---|---|---|---|
F1 | 0.000 | 0.000 | 1.787 × 10−11 | 4.340 × 103 | 7.328 × 10−103 | 2.412 × 10−27 | 0.000 | 0.000 |
F2 | 0.000 | 3.477 × 10−146 | 1.791 × 10−8 | 2.778 × 10 | 2.117 × 10−51 | 5.044 × 10−17 | 1.776 × 10−156 | 5.082 × 10−152 |
F3 | 0.000 | 0.000 | 5.100 × 10−4 | 9.875 × 103 | 1.932 × 10−99 | 1.388 × 10−5 | 0.000 | 0.000 |
F4 | 0.000 | 5.518 × 10−148 | 7.711 × 10−2 | 6.246 | 1.187 × 10−50 | 5.612 × 10−7 | 2.317 × 10−140 | 1.086 × 10−159 |
F5 | 5.023 | 1.354 × 1001 | 2.883 × 10 | 2.004 × 102 | 8.098 × 10−1 | 2.711 × 10 | 9.366 | 7.662 |
F6 | 7.757 × 10−4 | 3.100 × 10−3 | 4.505 × 10−1 | 3.795 × 103 | 6.616 × 10−1 | 3.078 × 10−1 | 3.336 × 10−3 | 2.451 × 10−3 |
F7 | 1.110 × 10−4 | 1.431 × 10−4 | 2.043 × 10−3 | 1.143 × 101 | 1.797 × 10−04 | 8.672 × 10−4 | 1.527 × 10−4 | 1.715 × 10−4 |
F8 | 3.087 × 10−1 | 1.575 × 101 | 4.834 × 102 | 3.985 × 103 | 7.531 × 1002 | 8.413 × 102 | 4.327 × 10−1 | 3.812 × 10−1 |
F9 | 0.000 | 0.000 | 2.348 | 4.479 × 101 | 0.000 | 7.065 | 0.000 | 0.000 |
F10 | 0.000 | 0.000 | 1.540 × 10−3 | 6.998 | 1.703 × 10−15 | 1.410 × 10−14 | 0.000 | 0.000 |
F11 | 0.000 | 0.000 | 5.084 × 10−2 | 3.407 × 101 | 0.000 | 9.000 × 10−3 | 0.000 | 0.000 |
F12 | 6.516 × 10−4 | 5.000 × 10−3 | 1.016 × 10−1 | 2.492 × 102 | 7.090 × 10−02 | 1.918 × 10−2 | 7.366 × 10−3 | 6.237 × 10−3 |
F13 | 2.100 × 10−3 | 1.230 × 10−2 | 1.449 × 10−1 | 8.193 × 102 | 4.345 × 10−1 | 2.567 × 10−1 | 8.739 × 10−3 | 8.789 × 10−3 |
F14 | 3.593 × 10−13 | 6.655 × 10−2 | 1.891 | 1.399 | 1.399 | 4.146 | 5.955 × 10−13 | 4.627 × 10−13 |
Function | ISMA | SMA | SOA | MFO | POA | GWO | ESMA | DFSMA |
---|---|---|---|---|---|---|---|---|
F1 | 3.292 × 10−1 | 3.207 × 10−1 | 3.090 × 10−1 | 2.812 × 10−1 | 1.963 × 10−1 | 5.205 × 10−1 | 3.533 × 10−1 | 3.450 × 10−1 |
F2 | 3.442 × 10−2 | 3.424 × 10−1 | 3.541 × 10−1 | 3.331 × 10−1 | 2.219 × 10−1 | 5.747 × 10−1 | 3.755 × 10−1 | 3.739 × 10−1 |
F3 | 4.387 × 10−1 | 4.348 × 10−1 | 4.248 × 10−1 | 3.998 × 10−1 | 4.523 × 10−1 | 6.052 × 10−1 | 4.765 × 10−1 | 4.739 × 10−1 |
F4 | 3.334 × 10−1 | 3.262 × 10−1 | 2.783 × 10−1 | 2.425 × 10−1 | 1.583 × 10−1 | 4.419 × 10−1 | 3.593 × 10−1 | 3.354 × 10−1 |
F5 | 3.522 × 10−1 | 3.433 × 10−1 | 2.885 × 10−1 | 2.510 × 10−1 | 1.822 × 10−1 | 4.630 × 10−1 | 3.854 × 10−1 | 3.702 × 10−1 |
F6 | 3.388 × 10−1 | 3.290 × 10−1 | 2.886 × 10−1 | 2.597 × 10−1 | 1.862 × 10−1 | 4.395 × 10−1 | 3.685 × 10−1 | 3.539 × 10−1 |
F7 | 3.892 × 10−1 | 3.812 × 10−1 | 3.171 × 10−1 | 2.853 × 10−1 | 2.595 × 10−1 | 4.876 × 10−1 | 4.282 × 10−1 | 1.071 × 10−1 |
F8 | 3.535 × 10−1 | 3.383 × 10−1 | 3.408 × 10−1 | 2.884 × 10−1 | 2.670 × 10−1 | 4.838 × 10−1 | 3.938 × 10−1 | 3.638 × 10−1 |
F9 | 3.325 × 10−1 | 3.233 × 10−1 | 2.813 × 10−1 | 2.532 × 10−1 | 2.013 × 10−1 | 4.588 × 10−1 | 3.721 × 10−1 | 3.422 × 10−1 |
F10 | 3.396 × 10−1 | 3.255 × 10−1 | 2.830 × 10−1 | 2.560 × 10−1 | 1.781 × 10−1 | 4.495 × 10−1 | 3.654 × 10−1 | 3.598 × 10−1 |
F11 | 3.571 × 10−1 | 3.347 × 10−1 | 3.008 × 10−1 | 2.652 × 10−1 | 2.005 × 10−1 | 4.640 × 10−1 | 3.933 × 10−1 | 3.654 × 105 |
F12 | 5.140 × 10−1 | 4.973 × 10−1 | 4.824 × 10−1 | 4.385 × 10−1 | 5.666 × 10−1 | 6.634 × 10−1 | 5.535 × 10−1 | 5.449 × 10−1 |
F13 | 5.017 × 10−1 | 4.978 × 10−1 | 4.806 × 10−1 | 4.500 × 10−1 | 5.501 × 10−1 | 6.495 × 10−1 | 5.727 × 10−1 | 5.220 × 10−1 |
F14 | 5.090 × 10−1 | 5.042 × 10−1 | 4.681 × 10−1 | 4.547 × 10−1 | 8.880 × 10−1 | 4.741 × 10−1 | 5.748 × 10−1 | 5.382 × 10−1 |
Images | d | Symmetric Cross-Entropy | Minimum Cross-Entropy | Otsu | Kapur’s Entropy | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
PSNR | SSIM | FSIM | PSNR | SSIM | FSIM | PSNR | SSIM | FSIM | PSNR | SSIM | FSIM | ||
Lena | 2 | 13.2058 | 0.4969 | 0.6978 | 12.2497 | 0.4949 | 0.6976 | 12.0066 | 0.4723 | 0.6897 | 7.7212 | 0.1290 | 0.5866 |
3 | 15.7899 | 0.5628 | 0.7660 | 15.6702 | 0.5607 | 0.7654 | 15.6612 | 0.5362 | 0.7542 | 13.3143 | 0.5223 | 0.6812 | |
4 | 16.5512 | 0.5776 | 0.8029 | 16.2183 | 0.5632 | 0.7956 | 16.2183 | 0.5580 | 0.7954 | 15.4882 | 0.5661 | 0.6985 | |
5 | 17.0899 | 0.6802 | 0.8305 | 16.7296 | 0.6115 | 0.8305 | 16.9276 | 0.5814 | 0.8289 | 17.0600 | 0.5998 | 0.7196 | |
Cameraman | 2 | 12.0475 | 0.5555 | 0.7662 | 11.5227 | 0.5562 | 0.7554 | 11.5288 | 0.5551 | 0.7549 | 11.3573 | 0.4941 | 0.6504 |
3 | 12.8391 | 0.5982 | 0.8097 | 11.5551 | 0.5980 | 0.8074 | 11.5670 | 0.5739 | 0.7910 | 12.4609 | 0.5567 | 0.6530 | |
4 | 16.1448 | 0.6089 | 0.8344 | 12.7883 | 0.6089 | 0.8344 | 12.7883 | 0.5984 | 0.8192 | 12.9698 | 0.5646 | 0.6742 | |
5 | 16.6072 | 0.6384 | 0.8584 | 14.8859 | 0.6276 | 0.8447 | 15.7175 | 0.6175 | 0.8576 | 16.4663 | 0.5876 | 0.6746 | |
Butterfly | 2 | 13.2788 | 0.5266 | 0.7363 | 13.1412 | 0.5266 | 0.7330 | 13.1412 | 0.4730 | 0.7363 | 11.7625 | 0.3130 | 0.7101 |
3 | 15.5515 | 0.5759 | 0.7914 | 14.9690 | 0.5759 | 0.7338 | 14.9690 | 0.5603 | 0.7738 | 14.0402 | 0.4095 | 0.7524 | |
4 | 16.4086 | 0.6147 | 0.8153 | 15.9752 | 0.6147 | 0.8079 | 16.0354 | 0.6183 | 0.8153 | 16.0276 | 0.6435 | 0.7821 | |
5 | 16.6381 | 0.6474 | 0.8281 | 16.0354 | 0.6327 | 0.8143 | 16.1095 | 0.7103 | 0.8182 | 16.5343 | 0.6478 | 0.8136 | |
Lake | 2 | 13.1104 | 0.5017 | 0.7314 | 12.9005 | 0.5002 | 0.7313 | 12.9179 | 0.4781 | 0.7313 | 13.3854 | 0.4398 | 0.6234 |
3 | 16.1352 | 0.5589 | 0.7908 | 14.0479 | 0.5589 | 0.7835 | 14.0479 | 0.5180 | 0.7835 | 16.2402 | 0.5150 | 0.6565 | |
4 | 18.0386 | 0.6572 | 0.8391 | 18.0386 | 0.6071 | 0.8257 | 17.3537 | 0.5589 | 0.8257 | 15.8882 | 0.5346 | 0.6918 | |
5 | 18.6824 | 0.6948 | 0.8623 | 18.4376 | 0.6542 | 0.8412 | 18.2994 | 0.6071 | 0.8360 | 15.8486 | 0.6575 | 0.7275 | |
Barbara | 2 | 14.7227 | 0.4756 | 0.7278 | 12.6622 | 0.4756 | 0.7278 | 13.1800 | 0.4631 | 0.7261 | 14.7227 | 0.4663 | 0.6874 |
3 | 16.3754 | 0.5432 | 0.7943 | 16.3754 | 0.5432 | 0.7942 | 15.6470 | 0.5347 | 0.7943 | 15.8715 | 0.4933 | 0.7339 | |
4 | 16.9175 | 0.6023 | 0.8304 | 16.8855 | 0.6023 | 0.8301 | 16.6012 | 0.5770 | 0.8104 | 15.9885 | 0.5687 | 0.8294 | |
5 | 17.9234 | 0.6553 | 0.8512 | 17.0108 | 0.6545 | 0.8500 | 17.1495 | 0.6064 | 0.8289 | 17.9234 | 0.5913 | 0.8441 | |
Columbia | 2 | 13.8785 | 0.3900 | 0.7056 | 11.2266 | 0.3900 | 0.6707 | 12.7799 | 0.3157 | 0.6707 | 13.8758 | 0.2524 | 0.7020 |
3 | 15.3874 | 0.5372 | 0.7812 | 13.0064 | 0.5372 | 0.7338 | 13.0064 | 0.4605 | 0.7618 | 15.3316 | 0.3551 | 0.7812 | |
4 | 16.2809 | 0.6030 | 0.8030 | 14.7853 | 0.5993 | 0.7827 | 15.2117 | 0.6014 | 0.8000 | 15.9069 | 0.3952 | 0.8030 | |
5 | 16.7908 | 0.6269 | 0.8200 | 15.2117 | 0.6250 | 0.8086 | 15.9069 | 0.6250 | 0.8042 | 16.0853 | 0.3905 | 0.8042 | |
Milkdrop | 2 | 15.8750 | 0.6458 | 0.7313 | 12.9792 | 0.5851 | 0.7242 | 15.8750 | 0.5552 | 0.7266 | 13.3613 | 0.5906 | 0.7075 |
3 | 18.4471 | 0.6644 | 0.7845 | 15.4290 | 0.6063 | 0.7511 | 17.4501 | 0.5968 | 0.7544 | 18.4471 | 0.5956 | 0.7371 | |
4 | 19.3641 | 0.6849 | 0.8207 | 17.2172 | 0.6739 | 0.7627 | 18.3448 | 0.6285 | 0.7985 | 19.2545 | 0.6035 | 0.7525 | |
5 | 19.7948 | 0.6880 | 0.8309 | 19.2545 | 0.6849 | 0.8303 | 19.3641 | 0.6621 | 0.8262 | 19.3641 | 0.6727 | 0.7544 | |
Man | 2 | 14.6403 | 0.4300 | 0.6925 | 11.0410 | 0.3867 | 0.6845 | 12.2389 | 0.3681 | 0.6845 | 14.6403 | 0.4033 | 0.6144 |
3 | 16.4136 | 0.4763 | 0.7664 | 13.7597 | 0.4708 | 0.7657 | 14.1385 | 0.4634 | 0.7636 | 16.4136 | 0.4313 | 0.6393 | |
4 | 17.3328 | 0.5114 | 0.8147 | 13.9758 | 0.5114 | 0.7959 | 16.5070 | 0.5053 | 0.7959 | 16.5070 | 0.4696 | 0.6393 | |
5 | 17.7032 | 0.5753 | 0.8453 | 16.1596 | 0.5570 | 0.8362 | 17.3328 | 0.5517 | 0.8362 | 17.7032 | 0.4696 | 0.6545 |
Images | d | Symmetric Cross-Entropy | Minimum Cross-Entropy | Otsu | Kapur’s Entropy |
---|---|---|---|---|---|
Lena | 2 | 82 140 | 82 142 | 92 151 | 163 220 |
3 | 73 120 166 | 74 121 167 | 80 126 170 | 59 164 220 | |
4 | 71 109 140 175 | 70 109 139 175 | 74 113 145 180 | 57 60 164 221 | |
5 | 62 88 118 147 180 | 62 88 117 146 180 | 73 109 136 160 188 | 58 162 180 217 236 | |
Cameraman | 2 | 54 137 | 52 137 | 70 144 | 19 193 |
3 | 31 94 144 | 30 84 145 | 57 116 154 | 18 21 194 | |
4 | 30 77 124 157 | 29 76 125 157 | 40 93 140 170 | 1 17 20 193 | |
5 | 28 71 112 144 172 | 28 71 113 145 172 | 36 83 122 149 173 | 1 16 19 21 194 | |
Butterfly | 2 | 76 138 | 76 138 | 85 148 | 114 206 |
3 | 67 108 158 | 67 107 159 | 75 120 170 | 97 125 207 | |
4 | 62 92 128 172 | 62 93 128 172 | 66 99 135 177 | 57 102 126 208 | |
5 | 59 82 107 137 177 | 57 81 104 135 176 | 36 83 122 149 173 | 57 101 126 205 235 | |
Lake | 2 | 74 143 | 75 142 | 86 155 | 73 228 |
3 | 65 107 163 | 64 162 107 | 80 141 194 | 62 86 228 | |
4 | 60 93 145 196 | 60 94 145 195 | 68 111 158 199 | 9 62 86 228 | |
5 | 53 77 112 155 197 | 55 80 116 160 199 | 60 91 128 166 200 | 10 29 72 89 228 | |
Barbara | 2 | 74 138 | 74 139 | 82 147 | 54 174 |
3 | 67 119 170 | 68 119 171 | 75 127 176 | 55 169 222 | |
4 | 56 93 132 176 | 56 92 133 177 | 66 106 142 182 | 54 128 174 223 | |
5 | 47 76 108 141 181 | 48 76 108 142 180 | 57 88 118 148 184 | 54 129 174 218 241 | |
Columbia | 2 | 59 110 | 60 109 | 75 130 | 93 177 |
3 | 50 83 130 | 50 83 129 | 61 102 152 | 77 147 211 | |
4 | 45 71 105 148 | 45 71 104 148 | 50 79 115 159 | 74 102 162 218 | |
5 | 39 59 81 111 151 | 40 60 82 113 155 | 48 74 103 135 171 | 73 101 152 190 234 | |
Milkdrop | 2 | 65 140 | 68 142 | 76 154 | 120 173 |
3 | 35 83 150 | 33 81 145 | 72 127 188 | 16 120 173 | |
4 | 33 68 99 154 | 33 80 127 185 | 51 90 132 190 | 1 16 121 173 | |
5 | 33 68 96 131 187 | 31 67 95 132 187 | 37 70 97 134 191 | 1 16 118 154 241 | |
Man | 2 | 75 130 | 76 130 | 87 142 | 54 181 |
3 | 67 109 152 | 66 108 152 | 71 114 156 | 55 176 224 | |
4 | 60 90 122 158 | 60 91 122 158 | 68 107 141 173 | 50 59 176 224 | |
5 | 59 85 113 143 173 | 59 85 113 142 173 | 63 94 123 151 182 | 1 50 58 176 225 |
Images | d | ISMA | GWO | SOA | SMA | POA | MFO | ESMA | DFSMA |
---|---|---|---|---|---|---|---|---|---|
Lena | 2 | 13.2058 | 13.2058 | 13.2058 | 13.2058 | 12.0066 | 12.0066 | 12.0066 | 12.0066 |
3 | 15.7899 | 15.7038 | 15.5352 | 15.7810 | 15.5612 | 15.5612 | 15.6512 | 15.6512 | |
4 | 16.5512 | 16.4458 | 16.4631 | 16.5291 | 16.2183 | 16.2183 | 16.2183 | 16.2183 | |
5 | 17.0899 | 16.7296 | 16.7296 | 16.7457 | 16.6878 | 16.7296 | 16.7296 | 16.7296 | |
Cameraman | 2 | 12.0475 | 11.9735 | 11.9735 | 12.0475 | 11.5288 | 11.5288 | 11.5288 | 11.5288 |
3 | 12.8391 | 12.7378 | 12.6314 | 12.7460 | 11.5670 | 11.5670 | 11.5670 | 11.5670 | |
4 | 16.1448 | 16.1086 | 12.8239 | 16.1432 | 12.7883 | 12.7883 | 12.7883 | 12.7883 | |
5 | 16.6072 | 16.3075 | 13.2107 | 16.4663 | 15.7326 | 15.7175 | 14.7133 | 15.4820 | |
Butterfly | 2 | 13.2788 | 13.2280 | 13.1618 | 13.2280 | 13.1412 | 13.1412 | 13.1412 | 13.1412 |
3 | 15.5515 | 15.5453 | 15.5163 | 15.4508 | 14.9690 | 14.9690 | 14.9690 | 14.9690 | |
4 | 16.4086 | 16.2999 | 16.2608 | 16.3081 | 16.0354 | 16.0354 | 15.9752 | 16.0354 | |
5 | 16.6381 | 16.3552 | 16.3139 | 16.4275 | 16.1095 | 16.1095 | 16.0354 | 16.1095 | |
Lake | 2 | 13.1104 | 13.1104 | 13.0815 | 13.1104 | 12.9179 | 12.9179 | 12.9179 | 12.9179 |
3 | 16.1352 | 16.0206 | 15.9760 | 16.0328 | 14.0479 | 14.0249 | 14.0479 | 14.0479 | |
4 | 18.0386 | 18.0386 | 15.1716 | 18.0386 | 18.0386 | 18.0386 | 18.0386 | 18.0386 | |
5 | 18.6824 | 18.3881 | 18.1749 | 18.4822 | 18.3551 | 18.4108 | 18.4822 | 18.4822 | |
Barbara | 2 | 14.7227 | 12.6622 | 12.6622 | 12.6622 | 12.6622 | 12.6622 | 12.6622 | 12.6622 |
3 | 16.3754 | 16.3754 | 16.2787 | 16.3754 | 16.3754 | 16.3754 | 16.3754 | 16.3754 | |
4 | 16.9175 | 16.8855 | 16.8855 | 16.8855 | 16.8855 | 16.8855 | 16.8855 | 16.8855 | |
5 | 17.9234 | 17.0108 | 17.3833 | 17.0108 | 17.1300 | 17.1063 | 17.0108 | 17.0108 | |
Columbia | 2 | 13.8785 | 11.2266 | 11.2266 | 11.2266 | 11.2266 | 11.2266 | 11.2266 | 11.2266 |
3 | 15.3874 | 13.0064 | 13.0064 | 13.0064 | 13.0064 | 13.0644 | 13.0644 | 13.0064 | |
4 | 16.2809 | 14.7119 | 14.7523 | 14.7119 | 14.7119 | 14.7119 | 14.7119 | 14.7119 | |
5 | 16.7908 | 14.2645 | 14.2819 | 14.5631 | 14.2645 | 14.2645 | 14.5631 | 15.2117 | |
Milkdrop | 2 | 15.875 | 13.3168 | 13.4058 | 13.3168 | 13.3168 | 13.3168 | 13.3168 | 13.3168 |
3 | 18.4471 | 15.3029 | 15.3029 | 15.3029 | 15.3029 | 15.3029 | 15.3029 | 15.3029 | |
4 | 19.3641 | 17.2142 | 17.2423 | 17.2142 | 17.2142 | 17.2142 | 17.2142 | 17.2142 | |
5 | 19.7948 | 19.2476 | 19.2335 | 19.2476 | 19.2476 | 19.2476 | 19.2476 | 19.2476 | |
Man | 2 | 14.6403 | 11.0410 | 11.2319 | 11.0410 | 11.0410 | 11.0410 | 11.0410 | 11.0410 |
3 | 16.4136 | 13.6038 | 13.0089 | 13.6038 | 13.6038 | 13.6038 | 13.6038 | 13.6038 | |
4 | 17.3328 | 14.4373 | 14.4710 | 13.9758 | 13.9758 | 13.9758 | 13.9758 | 13.9758 | |
5 | 17.7032 | 16.0751 | 16.6173 | 16.1596 | 16.1596 | 16.1286 | 16.1596 | 16.1596 |
Images | d | ISMA | GWO | SOA | SMA | POA | MFO | ESMA | DFSMA |
---|---|---|---|---|---|---|---|---|---|
Lena | 2 | 0.4969 | 0.4969 | 0.4969 | 0.4969 | 0.4969 | 0.4969 | 0.4969 | 0.4969 |
3 | 0.5628 | 0.5628 | 0.5626 | 0.5628 | 0.5628 | 0.5628 | 0.5628 | 0.5628 | |
4 | 0.5776 | 0.5632 | 0.5632 | 0.5632 | 0.5632 | 0.5632 | 0.5632 | 0.5632 | |
5 | 0.6802 | 0.6115 | 0.6115 | 0.6129 | 0.6090 | 0.6115 | 0.6115 | 0.6115 | |
Cameraman | 2 | 0.5555 | 0.5555 | 0.5555 | 0.5555 | 0.5555 | 0.5555 | 0.5555 | 0.5555 |
3 | 0.5982 | 0.5982 | 0.5982 | 0.5982 | 0.5982 | 0.5982 | 0.5982 | 0.5982 | |
4 | 0.6089 | 0.6089 | 0.6080 | 0.6089 | 0.6089 | 0.6089 | 0.6089 | 0.6089 | |
5 | 0.6384 | 0.6168 | 0.6159 | 0.6357 | 0.6347 | 0.6357 | 0.6222 | 0.6357 | |
Butterfly | 2 | 0.5266 | 0.5266 | 0.5266 | 0.5266 | 0.5266 | 0.5266 | 0.5266 | 0.5266 |
3 | 0.5759 | 0.5759 | 0.5759 | 0.5759 | 0.5759 | 0.5759 | 0.5759 | 0.5759 | |
4 | 0.6147 | 0.6147 | 0.6039 | 0.6147 | 0.6147 | 0.6147 | 0.6147 | 0.6147 | |
5 | 0.6474 | 0.6308 | 0.6165 | 0.6313 | 0.6303 | 0.6303 | 0.6327 | 0.6303 | |
Lake | 2 | 0.5017 | 0.5017 | 0.5017 | 0.5017 | 0.5017 | 0.5017 | 0.5017 | 0.5017 |
3 | 0.5635 | 0.5589 | 0.5585 | 0.5589 | 0.5589 | 0.5635 | 0.5589 | 0.5589 | |
4 | 0.6582 | 0.6071 | 0.5905 | 0.6071 | 0.6071 | 0.6071 | 0.6071 | 0.6071 | |
5 | 0.6948 | 0.6582 | 0.5995 | 0.6582 | 0.6575 | 0.6631 | 0.6607 | 0.6607 | |
Barbara | 2 | 0.4756 | 0.4756 | 0.4756 | 0.4756 | 0.4756 | 0.4756 | 0.4756 | 0.4756 |
3 | 0.5432 | 0.5432 | 0.5413 | 0.5432 | 0.5432 | 0.5432 | 0.5432 | 0.5432 | |
4 | 0.6023 | 0.6023 | 0.5735 | 0.6023 | 0.6023 | 0.6023 | 0.6023 | 0.6023 | |
5 | 0.6553 | 0.6545 | 0.6003 | 0.6545 | 0.6553 | 0.6477 | 0.6545 | 0.6545 | |
Columbia | 2 | 0.3900 | 0.3900 | 0.3900 | 0.3900 | 0.3900 | 0.3900 | 0.3900 | 0.3900 |
3 | 0.5372 | 0.5372 | 0.5372 | 0.5372 | 0.5372 | 0.5372 | 0.5372 | 0.5372 | |
4 | 0.6030 | 0.5993 | 0.5946 | 0.5993 | 0.5993 | 0.5993 | 0.5993 | 0.5993 | |
5 | 0.6269 | 0.6239 | 0.6298 | 0.6195 | 0.6239 | 0.6239 | 0.6195 | 0.6250 | |
Milkdrop | 2 | 0.6458 | 0.5956 | 0.5956 | 0.5956 | 0.5969 | 0.5956 | 0.5956 | 0.5964 |
3 | 0.6644 | 0.6035 | 0.6050 | 0.6035 | 0.6035 | 0.6035 | 0.6035 | 0.6035 | |
4 | 0.6849 | 0.6727 | 0.6712 | 0.6727 | 0.6727 | 0.6727 | 0.6727 | 0.6727 | |
5 | 0.6880 | 0.6813 | 0.6836 | 0.6813 | 0.6813 | 0.6813 | 0.6813 | 0.6813 | |
Man | 2 | 0.4300 | 0.3867 | 0.3878 | 0.3867 | 0.3867 | 0.3867 | 0.3867 | 0.3867 |
3 | 0.4763 | 0.4708 | 0.4708 | 0.4708 | 0.4708 | 0.4708 | 0.4708 | 0.4708 | |
4 | 0.5114 | 0.5064 | 0.5079 | 0.5114 | 0.5114 | 0.5114 | 0.5114 | 0.5114 | |
5 | 0.5753 | 0.5530 | 0.5723 | 0.5570 | 0.5570 | 0.5639 | 0.5570 | 0.5570 |
Images | d | ISMA | GWO | SOA | SMA | POA | MFO | ESMA | DFSMA |
---|---|---|---|---|---|---|---|---|---|
Lena | 2 | 0.6978 | 0.6978 | 0.6978 | 0.6978 | 0.6978 | 0.6978 | 0.6978 | 0.6978 |
3 | 0.7660 | 0.7660 | 0.7658 | 0.7660 | 0.7660 | 0.7660 | 0.7660 | 0.7660 | |
4 | 0.8029 | 0.8006 | 0.7923 | 0.8015 | 0.7954 | 0.7654 | 0.7954 | 0.7954 | |
5 | 0.8305 | 0.8305 | 0.8196 | 0.8305 | 0.8297 | 0.8305 | 0.8305 | 0.8305 | |
Cameraman | 2 | 0.7662 | 0.7628 | 0.7628 | 0.7628 | 0.7549 | 0.7549 | 0.7549 | 0.7549 |
3 | 0.8097 | 0.8097 | 0.8097 | 0.8097 | 0.8097 | 0.8097 | 0.8097 | 0.8097 | |
4 | 0.8344 | 0.8344 | 0.8338 | 0.8344 | 0.8344 | 0.8344 | 0.8344 | 0.8344 | |
5 | 0.8584 | 0.8479 | 0.8405 | 0.8580 | 0.8584 | 0.8580 | 0.8419 | 0.8577 | |
Butterfly | 2 | 0.7363 | 0.7357 | 0.7357 | 0.7363 | 0.7330 | 0.7330 | 0.7330 | 0.7330 |
3 | 0.7914 | 0.7900 | 0.7893 | 0.7909 | 0.7738 | 0.7738 | 0.7738 | 0.7738 | |
4 | 0.8153 | 0.8134 | 0.8130 | 0.8139 | 0.8079 | 0.8079 | 0.8079 | 0.8079 | |
5 | 0.8281 | 0.8260 | 0.8238 | 0.8275 | 0.8182 | 0.8182 | 0.8143 | 0.8182 | |
Lake | 2 | 0.7314 | 0.7314 | 0.7314 | 0.7314 | 0.7314 | 0.7314 | 0.7314 | 0.7314 |
3 | 0.7908 | 0.7889 | 0.7887 | 0.7889 | 0.7835 | 0.7818 | 0.7835 | 0.7835 | |
4 | 0.8391 | 0.8361 | 0.8043 | 0.8361 | 0.8257 | 0.8257 | 0.8257 | 0.8257 | |
5 | 0.8623 | 0.8617 | 0.8271 | 0.8617 | 0.8348 | 0.8329 | 0.8411 | 0.8411 | |
Barbara | 2 | 0.7278 | 0.7278 | 0.7278 | 0.7278 | 0.7278 | 0.7278 | 0.7278 | 0.7278 |
3 | 0.7943 | 0.7942 | 0.7933 | 0.7942 | 0.7942 | 0.7942 | 0.7942 | 0.7942 | |
4 | 0.8304 | 0.8301 | 0.8304 | 0.8301 | 0.8301 | 0.8301 | 0.8301 | 0.8301 | |
5 | 0.8512 | 0.8500 | 0.8455 | 0.8500 | 0.8511 | 0.8512 | 0.8500 | 0.8500 | |
Columbia | 2 | 0.7056 | 0.6707 | 0.6707 | 0.6707 | 0.6707 | 0.6707 | 0.6707 | 0.6707 |
3 | 0.7812 | 0.7338 | 0.7338 | 0.7338 | 0.7338 | 0.7338 | 0.7338 | 0.7338 | |
4 | 0.8030 | 0.7824 | 0.7827 | 0.7824 | 0.7824 | 0.7824 | 0.7824 | 0.7824 | |
5 | 0.8200 | 0.7994 | 0.8064 | 0.8022 | 0.7994 | 0.7994 | 0.8022 | 0.8068 | |
Milkdrop | 2 | 0.7313 | 0.7223 | 0.7223 | 0.7223 | 0.7223 | 0.7223 | 0.7223 | 0.7223 |
3 | 0.7845 | 0.7544 | 0.7576 | 0.7544 | 0.7544 | 0.7544 | 0.7544 | 0.7544 | |
4 | 0.8207 | 0.8202 | 0.8192 | 0.8202 | 0.8202 | 0.8202 | 0.8202 | 0.8202 | |
5 | 0.8309 | 0.8306 | 0.8289 | 0.8306 | 0.8306 | 0.8306 | 0.8306 | 0.8306 | |
Man | 2 | 0.6925 | 0.6845 | 0.6860 | 0.6845 | 0.6845 | 0.6845 | 0.6845 | 0.6845 |
3 | 0.7664 | 0.7636 | 0.7584 | 0.7636 | 0.7636 | 0.7636 | 0.7636 | 0.7636 | |
4 | 0.8147 | 0.7967 | 0.7968 | 0.7959 | 0.7959 | 0.7959 | 0.7959 | 0.7959 | |
5 | 0.8453 | 0.8349 | 0.8386 | 0.8362 | 0.8362 | 0.8369 | 0.8362 | 0.8362 |
Images | d | ISMA | GWO | SOA | SMA | POA | MFO | ESMA | DFSMA |
---|---|---|---|---|---|---|---|---|---|
Lena | 2 | 7.336 × 105 | 7.336 × 105 | 7.336 × 105 | 7.336 × 105 | 7.336 × 105 | 7.336 × 105 | 7.336 × 105 | 7.336 × 105 |
3 | 3.929 × 105 | 3.931 × 105 | 4.012 × 105 | 3.929 × 105 | 3.929 × 105 | 3.929 × 105 | 3.929 × 105 | 3.929 × 105 | |
4 | 2.610 × 105 | 2.616 × 105 | 3.305 × 105 | 2.610 × 105 | 2.610 × 105 | 2.610 × 105 | 2.610 × 105 | 2.610 × 105 | |
5 | 1.845 × 105 | 1.855 × 105 | 2.820 × 105 | 1.845 × 105 | 1.845 × 105 | 1.855 × 105 | 1.855 × 105 | 1.855 × 105 | |
Cameraman | 2 | 7.909 × 105 | 7.909 × 105 | 7.909 × 105 | 7.909 × 105 | 7.909 × 105 | 7.909 × 105 | 7.909 × 105 | 7.909 × 105 |
3 | 4.159 × 105 | 4.163 × 105 | 4.161 × 105 | 4.159 × 105 | 4.159 × 105 | 4.159 × 105 | 4.159 × 105 | 4.159 × 105 | |
4 | 3.027 × 105 | 3.030 × 105 | 3.133 × 105 | 3.027 × 105 | 3.027 × 105 | 3.027 × 105 | 3.027 × 105 | 3.027 × 105 | |
5 | 2.334 × 105 | 2.353 × 105 | 2.795 × 105 | 2.352 × 105 | 2.334 × 105 | 2.351 × 105 | 2.348 × 105 | 2.337 × 105 | |
Butterfly | 2 | 7.835 × 105 | 7.835 × 105 | 7.835 × 105 | 7.835 × 105 | 7.835 × 105 | 7.835 × 105 | 7.835 × 105 | 7.835 × 105 |
3 | 4.570 × 105 | 4.570 × 105 | 4.609 × 105 | 4.570 × 105 | 4.570 × 105 | 4.570 × 105 | 4.570 × 105 | 4.570 × 105 | |
4 | 2.864 × 105 | 2.868 × 105 | 3.655 × 105 | 2.864 × 105 | 2.864 × 105 | 2.864 × 105 | 2.864 × 105 | 2.864 × 105 | |
5 | 2.104 × 105 | 2.111 × 105 | 3.059 × 105 | 2.104 × 105 | 2.104 × 105 | 2.104 × 105 | 2.104 × 105 | 2.104 × 105 | |
Lake | 2 | 7.488 × 105 | 7.488 × 105 | 7.488 × 105 | 7.488 × 105 | 7.488 × 105 | 7.488 × 105 | 7.488 × 105 | 7.488 × 105 |
3 | 4.954 × 105 | 4.956 × 105 | 4.985 × 105 | 4.954 × 105 | 4.954 × 105 | 4.954 × 105 | 4.954 × 105 | 4.954 × 105 | |
4 | 3.311 × 105 | 3.327 × 105 | 3.785 × 105 | 3.311 × 105 | 3.311 × 105 | 3.311 × 105 | 3.311 × 105 | 3.311 × 105 | |
5 | 2.359 × 105 | 2.366 × 105 | 3.184 × 105 | 2.360 × 105 | 2.359 × 105 | 2.360 × 105 | 2.361 × 105 | 2.360 × 105 | |
Barbara | 2 | 8.959 × 105 | 8.959 × 105 | 8.966 × 105 | 8.959 × 105 | 8.959 × 105 | 8.959 × 105 | 8.959 × 105 | 8.959 × 105 |
3 | 5.551 × 105 | 5.552 × 105 | 5.578 × 105 | 5.551 × 105 | 5.551 × 105 | 5.551 × 105 | 5.551 × 105 | 5.551 × 105 | |
4 | 3.583 × 105 | 3.585 × 105 | 3.629 × 105 | 3.583 × 105 | 3.583 × 105 | 3.583 × 105 | 3.583 × 105 | 3.583 × 105 | |
5 | 2.482 × 105 | 2.493 × 105 | 2.597 × 105 | 2.482 × 105 | 2.482 × 105 | 2.482 × 105 | 2.483 × 105 | 2.483 × 105 | |
Columbia | 2 | 7.898 × 105 | 7.898 × 105 | 7.899 × 105 | 7.898 × 105 | 7.898 × 105 | 7.898 × 105 | 7.898 × 105 | 7.898 × 105 |
3 | 4.692 × 105 | 4.692 × 105 | 4.710 × 105 | 4.692 × 105 | 4.692 × 105 | 4.692 × 105 | 4.692 × 105 | 4.692 × 105 | |
4 | 3.038 × 105 | 3.038 × 105 | 3.120 × 105 | 3.038 × 105 | 3.038 × 105 | 3.038 × 105 | 3.038 × 105 | 3.038 × 105 | |
5 | 2.143 × 105 | 2.152 × 105 | 2.329 × 105 | 2.145 × 105 | 2.143 × 105 | 2.148 × 105 | 2.145 × 105 | 2.145 × 105 | |
Milkdrop | 2 | 1.304 × 106 | 1.304 × 106 | 1.305 × 106 | 1.304 × 106 | 1.304 × 106 | 1.304 × 106 | 1.304 × 106 | 1.304 × 106 |
3 | 6.956 × 105 | 6.956 × 105 | 6.968 × 105 | 6.956 × 105 | 6.956 × 105 | 6.956 × 105 | 6.956 × 105 | 6.956 × 105 | |
4 | 4.493 × 105 | 4.505 × 105 | 4.548 × 105 | 4.500 × 105 | 4.497 × 105 | 4.499 × 105 | 4.506 × 105 | 4.497 × 105 | |
5 | 2.561 × 105 | 2.577 × 105 | 2.708 × 105 | 2.566 × 105 | 2.566 × 105 | 2.566 × 105 | 2.566 × 105 | 2.566 × 105 | |
Man | 2 | 6.685 × 105 | 6.685 × 105 | 6.687 × 105 | 6.685 × 105 | 6.685 × 105 | 6.685 × 105 | 6.685 × 105 | 6.685 × 105 |
3 | 3.673 × 105 | 3.675 × 105 | 3.689 × 105 | 3.673 × 105 | 3.673 × 105 | 3.673 × 105 | 3.673 × 105 | 3.673 × 105 | |
4 | 2.496 × 105 | 2.505 × 105 | 2.587 × 105 | 2.496 × 105 | 2.496 × 105 | 2.501 × 105 | 2.496 × 105 | 2.496 × 105 | |
5 | 1.729 × 105 | 1.743 × 105 | 1.924 × 105 | 1.730 × 105 | 1.730 × 105 | 1.735 × 105 | 1.730 × 105 | 1.731 × 105 |
Images | d | ISMA | GWO | SOA | SMA | POA | MFO | × 10SMA | DFSMA |
---|---|---|---|---|---|---|---|---|---|
Lena | 2 | 1.227 × 10−10 | 6.904 × 10 | 2.368 × 10−10 | 2.368 × 10−10 | 2.368 × 10−10 | 2.368 × 10−10 | 2.368 × 10−10 | 1.227 × 10−10 |
3 | 0.000 | 9.720 × 102 | 2.949 × 104 | 2.960 × 10−10 | 2.960 × 10−10 | 2.960 × 10−10 | 0.000 | 0.000 | |
4 | 3.068 × 10−11 | 1.644 × 103 | 4.273 × 104 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | |
5 | 3.068 × 10−11 | 2.522 × 103 | 2.942 × 104 | 8.880 × 10−11 | 8.771 × 10 | 9.163 × 10 | 3.068 × 10−11 | 3.068 × 10−11 | |
Cameraman | 2 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 1.227 × 10−10 | 1.227 × 10−10 |
3 | 6.136 × 10−11 | 2.216 × 103 | 2.472 × 102 | 1.776 × 10−10 | 1.776 × 10−10 | 1.776 × 10−10 | 6.136 × 10−11 | 6.136 × 10−11 | |
4 | 0.000 | 9.009 × 102 | 1.732 × 104 | 2.368 × 10−10 | 2.368 × 10−10 | 2.368 × 10−10 | 0.000 | 0.000 | |
5 | 1.778 × 102 | 2.201 × 103 | 2.626 × 104 | 1.920 × 103 | 1.892 × 103 | 1.935 × 103 | 1.875 × 103 | 1.232 × 103 | |
Butterfly | 2 | 1.227 × 10−10 | 2.230 × 102 | 1.323 × 102 | 3.552 × 10−10 | 3.552 × 10−10 | 3.552 × 10−10 | 1.227 × 10−10 | 1.227 × 10−10 |
3 | 6.136 × 10−11 | 2.518 × 102 | 1.034 × 104 | 1.206 × 10 | 1.776 × 10−10 | 1.400 × 10 | 6.136 × 10−11 | 6.136 × 10−11 | |
4 | 6.136 × 10−11 | 1.030 × 103 | 5.854 × 104 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 6.136 × 10−11 | 6.136 × 10−11 | |
5 | 4.658 × 10 | 2.343 × 103 | 4.496 × 104 | 6.780 × 10 | 4.936 × 10 | 1.159 × 102 | 8.012 × 10 | 5.252 × 10 | |
Lake | 2 | 0.000 | 1.377 × 102 | 9.821 | 3.552 × 10−10 | 3.552 × 10−10 | 3.552 × 10−10 | 3.552 × 10−10 | 0.000 |
3 | 1.227 × 10−10 | 1.119 × 103 | 9.698 × 103 | 1.776 × 10−10 | 1.776 × 10−10 | 1.776 × 10−10 | 1.227 × 10−10 | 1.227 × 10−10 | |
4 | 0.000 | 5.207 × 103 | 4.114 × 104 | 2.960 × 10−10 | 2.960 × 10−10 | 2.960 × 10−10 | 0.000 | 0.000 | |
5 | 1.121 × 102 | 2.058 × 103 | 4.480 × 104 | 1.181 × 102 | 4.672 × 10 | 1.192 × 102 | 9.631 × 10 | 1.125 × 102 | |
Barbara | 2 | 0.000 | 1.184 × 10−10 | 5.490 × 102 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 0.000 | 0.000 |
3 | 0.000 | 6.443 × 102 | 1.810 × 103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |
4 | 0.000 | 1.028 × 103 | 3.237 × 103 | 0.000 | 0.000 | 0.000 | 6.136 × 10−11 | 6.136 × 10−11 | |
5 | 1.214 × 102 | 2.636 × 103 | 1.967 × 104 | 1.710 × 102 | 2.856 × 102 | 2.376 × 102 | 3.143 × 102 | 2.982 × 102 | |
Columbia | 2 | 1.184 × 10−10 | 1.184 × 10−10 | 2.308 × 102 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 1.227 × 10−10 | 1.227 × 10−10 |
3 | 0.000 | 1.956 × 102 | 9.040 × 102 | 2.960 × 10−10 | 2.960 × 10−10 | 2.960 × 10−10 | 0.000 | 0.000 | |
4 | 0.000 | 2.857 × 102 | 3.020 × 104 | 2.368 × 10−10 | 3.086 × 10 | 3.086 × 10 | 0.000 | 0.000 | |
5 | 4.182 × 10 | 2.346 × 103 | 3.366 × 104 | 4.204 × 102 | 4.182 × 10 | 6.908 × 102 | 4.372 × 102 | 4.372 × 102 | |
Milkdrop | 2 | 0.000 | 0.000 | 6.849 × 102 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
3 | 0.000 | 1.458 × 102 | 6.801 × 102 | 0.000 | 0.000 | 0.000 | 1.227 × 10−10 | 1.227 × 10−10 | |
4 | 4.747 × 10 | 3.207 × 103 | 3.095 × 103 | 1.567 × 103 | 1.261 × 103 | 1.429 × 103 | 1.997 × 103 | 1.307 × 103 | |
5 | 0.000 | 4.512 × 103 | 3.620 × 104 | 2.960 × 10−11 | 2.810 | 2.960 × 10−11 | 0.000 | 0.000 | |
Man | 2 | 1.184 × 10−10 | 1.184 × 10−10 | 3.175 × 102 | 1.184 × 10−10 | 1.184 × 10−10 | 1.184 × 10−10 | 1.227 × 10−10 | 1.227 × 10−10 |
3 | 0.000 | 4.403 × 102 | 2.117 × 103 | 6.882 | 7.798 | 7.798 | 7.132 | 6.136 × 10−11 | |
4 | 6.136 × 10−11 | 2.104 × 103 | 2.069 × 104 | 8.880 × 10−11 | 8.880 × 10−11 | 1.128 × 103 | 6.136 × 10−11 | 6.136 × 10−11 | |
5 | 0.000 | 3.379 × 103 | 2.601 × 104 | 4.448 × 102 | 1.268 × 102 | 1.151 × 103 | 3.122 × 102 | 4.851 × 102 |
Images | d | ISMA | GWO | SOA | SMA | POA | MFO | × 10SMA | DFSMA |
---|---|---|---|---|---|---|---|---|---|
Lena | 2 | 9.432 × 10−1 | 1.083 | 9.310 × 10−1 | 9.043 × 10−1 | 1.845 | 9.212 × 10−1 | 1.052 | 9.714 × 10−1 |
3 | 9.787 × 10−1 | 1.010 | 9.458 × 10−1 | 9.425 × 10−1 | 1.884 | 9.226 × 10−1 | 1.065 | 9.793 × 10−1 | |
4 | 9.818 × 10−1 | 1.014 | 9.555 × 10−1 | 9.513 × 10−1 | 1.930 | 9.239 × 10−1 | 1.065 | 9.885 × 10−1 | |
5 | 9.949 × 10−1 | 1.035 | 9.718 × 10−1 | 9.809 × 10−1 | 1.935 | 9.467 × 10−1 | 1.083 | 9.954 × 10−1 | |
Cameraman | 2 | 9.312 × 10−1 | 9.974 × 10−1 | 9.064 × 10−1 | 9.085 × 10−1 | 1.809 | 9.038 × 10−1 | 1.021 | 9.622 × 10−1 |
3 | 9.609 × 10−1 | 9.979 × 10−1 | 9.065 × 10−1 | 9.306 × 10−1 | 1.810 | 9.296 × 10−1 | 1.050 | 9.714 × 10−1 | |
4 | 9.830 × 10−1 | 1.019 | 9.275 × 10−1 | 9.616 × 10−1 | 1.821 | 9.818 × 10−1 | 1.099 | 1.005 | |
5 | 9.993 × 10−1 | 1.106 | 9.597 × 10−1 | 9.735 × 10−1 | 1.885 | 1.049 | 1.108 × 10 | 1.008 | |
Butterfly | 2 | 9.292 × 10−1 | 9.722 × 10−1 | 8.903 × 10−1 | 9.061 × 10−1 | 1.824 | 9.025 × 10−1 | 1.019 | 9.628 × 10−1 |
3 | 9.725 × 10−1 | 1.010 | 9.337 × 10−1 | 9.457 × 10−1 | 1.894 | 9.186 × 10−1 | 1.061 | 9.794 × 10−1 | |
4 | 9.738 × 10−1 | 1.040 | 9.438 × 10−1 | 9.513 × 10−1 | 1.899 | 9.296 × 10−1 | 1.081 | 9.913 × 10−1 | |
5 | 9.874 × 10−1 | 1.054 | 9.387 × 10−1 | 9.785 × 10−1 | 1.954 | 9.739 × 10−1 | 1.110 | 1.022 | |
Lake | 2 | 9.374 × 10−1 | 9.805 × 10−1 | 9.026 × 10−1 | 9.165 × 10−1 | 1.761 | 8.677 × 10−1 | 1.021 | 9.617 × 10−1 |
3 | 9.579 × 10−1 | 1.008 | 9.268 × 10−1 | 9.344 × 10−1 | 1.853 | 9.102 × 10−1 | 1.066 | 9.665 × 10−1 | |
4 | 9.754 × 10−1 | 1.037 | 9.450 × 10−1 | 9.683 × 10−1 | 1.935 | 9.566 × 10−1 | 1.076 | 1.004 | |
5 | 1.012 | 1.082 | 9.520 × 10−1 | 9.858 × 10−1 | 2.038969 | 1.116 | 1.095 | 1.012 | |
Barbara | 2 | 9.268 × 10−1 | 9.912 × 10−1 | 9.002 × 10−1 | 9.151 × 10−1 | 1.795 | 9.267 × 10−1 | 1.012 | 9.666 × 10−1 |
3 | 9.520 × 10−1 | 9.994 × 10−1 | 9.110 × 10−1 | 9.322 × 10−1 | 1.825 | 9.289 × 10−1 | 1.043 | 9.723 × 10−1 | |
4 | 9.670 × 10−1 | 1.060 | 9.269 × 10−1 | 9.410 × 10−1 | 1.874 | 9.637 × 10−1 | 1.077 | 9.737 × 10−1 | |
5 | 9.669 × 10−1 | 1.067 | 1.008 | 9.658 × 10−1 | 1.958 | 1.014 | 1.078 | 9.918 × 10−1 | |
Columbia | 2 | 8.669 × 10−1 | 9.080 × 10−1 | 8.273 × 10−1 | 8.429 × 10−1 | 1.695 | 8.309 × 10−1 | 9.612 × 10−1 | 9.019 × 10−1 |
3 | 8.855 × 10−1 | 9.397 × 10−1 | 8.683 × 10−1 | 8.592 × 10−1 | 1.724 | 8.453 × 10−1 | 9.789 × 10−1 | 9.080 × 10−1 | |
4 | 9.148 × 10−1 | 9.905 × 10−1 | 8.813 × 10−1 | 8.814 × 10−1 | 1.784 | 8.741 × 10−1 | 1.000 | 9.177 × 10−1 | |
5 | 9.216 × 10−1 | 1.004 | 8.819 × 10−1 | 9.072 × 10−1 | 1.791 | 8.966 × 10−1 | 1.034 | 9.359 × 10−1 | |
Milkdrop | 2 | 9.327 × 10−1 | 9.947 × 10−1 | 9.239 × 10−1 | 9.098 × 10−1 | 1.852 | 9.218 × 10−1 | 1.034 | 9.662 × 10−1 |
3 | 9.550 × 10−1 | 1.028 | 9.331 × 10−1 | 9.259 × 10−1 | 1.882 | 9.569 × 10−1 | 1.031 | 9.668 × 10−1 | |
4 | 9.775 × 10−1 | 1.077 | 9.535 × 10−1 | 9.528 × 10−1 | 1.888 | 9.570 × 10−1 | 1.065 | 9.830 × 10−1 | |
5 | 1.005 | 1.064 | 9.572 × 10−1 | 9.829 × 10−1 | 1.964 | 9.628 × 10−1 | 1.081 | 1.007 | |
Man | 2 | 9.250 × 10−1 | 9.722 × 10−1 | 8.956 × 10−1 | 9.013 × 10−1 | 1.798 | 8.896 × 10−1 | 1.003 | 9.502 × 10−1 |
3 | 9.755 × 10−1 | 1.028 | 9.231 × 10−1 | 9.396 × 10−1 | 1.876 | 9.378 × 10−1 | 1.052 | 9.905 × 10−1 | |
4 | 9.901 × 10−1 | 1.059 | 9.410 × 10−1 | 9.682 × 10−1 | 1.904 | 9.531 × 10−1 | 1.086 | 1.002 | |
5 | 9.974 × 10−1 | 1.163 | 9.548 × 10−1 | 9.836 × 10−1 | 1.942 | 9.572 × 10−1 | 1.097 | 1.012 |
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Jiang, Y.; Zhang, D.; Zhu, W.; Wang, L. Multi-Level Thresholding Image Segmentation Based on Improved Slime Mould Algorithm and Symmetric Cross-Entropy. Entropy 2023, 25, 178. https://doi.org/10.3390/e25010178
Jiang Y, Zhang D, Zhu W, Wang L. Multi-Level Thresholding Image Segmentation Based on Improved Slime Mould Algorithm and Symmetric Cross-Entropy. Entropy. 2023; 25(1):178. https://doi.org/10.3390/e25010178
Chicago/Turabian StyleJiang, Yuanyuan, Dong Zhang, Wenchang Zhu, and Li Wang. 2023. "Multi-Level Thresholding Image Segmentation Based on Improved Slime Mould Algorithm and Symmetric Cross-Entropy" Entropy 25, no. 1: 178. https://doi.org/10.3390/e25010178
APA StyleJiang, Y., Zhang, D., Zhu, W., & Wang, L. (2023). Multi-Level Thresholding Image Segmentation Based on Improved Slime Mould Algorithm and Symmetric Cross-Entropy. Entropy, 25(1), 178. https://doi.org/10.3390/e25010178