Research Article
Image Multithreshold Segmentation Method Based on Improved Harris Hawk Optimization
Table 3
Comparative results of benchmark functions.
| | Function | Metric | SFO | BOA | EO | PFA | HHO | HHO-DE | IMHHO | | F1 | MEAN | 2.6227 × 10−9 | 8.8775 × 10−12 | 1.3923 × 10−55 | 29.8548 | 3.4255 × 10−104 | 0.0000 | 0.0000 | | STD | 6.5148 × 10−9 | 8.1105 × 10−13 | 1.6100 × 10−55 | 12.5124 | 1.3627 × 10−103 | 0.0000 | 0.0000 |
| | F2 | MEAN | 0.0002 | 1.1158 × 109 | 5.2573 × 10−32 | 7.7397 | 3.2577 × 10−56 | 1.3535 × 10−178 | 0.0000 | | STD | 0.0002 | 4.8639 × 109 | 3.3334 × 10−32 | 2.2920 | 6.7993 × 10−56 | 8.7013 × 10−177 | 0.0000 |
| | F3 | MEAN | 2.8761 × 10−6 | 7.6887 × 10−12 | 7.4146 × 10−16 | 4966.4513 | 4.1087 × 10−83 | 4.7360 × 10−134 | 0.0000 | | STD | 7.3530 × 10−6 | 5.4763 × 10−13 | 2.3678 × 10−15 | 1188.92113 | 1.7909 × 10−82 | 3.5249 × 10−133 | 0.0000 |
| | F4 | MEAN | 1.5905 × 10−5 | 5.1159 × 10−9 | 8.8904 × 10−16 | 18.1415 | 8.3787 × 10−54 | 1.0293 × 10−87 | 0.0000 | | STD | 3.2407 × 10−5 | 3.9235 × 10−10 | 1.0528 × 10−15 | 3.9004 | 1.8989 × 10−53 | 8.7706 × 10−88 | 0.0000 |
| | F5 | MEAN | 0.0002 | 0.0007 | 0.0007 | 0.1832 | 5.2533 × 10−5 | 0.0002 | 4.9783 × 10−5 | | STD | 0.0002 | 0.0003 | 0.0002 | 0.0762 | 4.4012 × 10−5 | 8.0900 × 10−5 | 3.4536 × 10−5 |
| | F6 | MEAN | −4117.4347 | −4189.3318 | −9086.4271 | −12449.3729 | −12569.4582 | −12564.3968 | −12569.4448 | | STD | 604.8037 | 271.5672 | 540.5657 | 102.7128 | 0.0498 | 0.0612 | 0.0427 |
| | F7 | MEAN | 3.4191 × 10−8 | 1.7087 × 10−5 | 0.0000 | 90.9641 | 0.0000 | 0.0000 | 0.0000 | | STD | 1.0698 × 10−7 | 7.3987 × 10−5 | 0.0000 | 15.0725 | 0.0000 | 0.0000 | 0.0000 |
| | F8 | MEAN | −39.9999 | −39.9999 | −39.9999 | −37.9329 | −39.9999 | −39.9999 | −39.9999 | | STD | 2.3730 × 10−5 | 0.0000 | 0.0000 | 1.0928 | 0.0000 | 0.0000 | 0.0000 |
| | F9 | MEAN | 1.1396 × 10−9 | 3.2007 × 10−13 | 0.0000 | 1.3382 | 0.0000 | 0.0000 | 0.0000 | | STD | 4.1928 × 10−9 | 2.3100 × 10−13 | 0.0000 | 0.1605 | 0.0000 | 0.0000 | 0.0000 |
| | F10 | MEAN | −1.0294 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | | STD | 0.0051 | 1.7233 × 10−5 | 2.2204 × 10−15 | 1.9229 × 10−15 | 4.5405 × 10−13 | 7.3205 × 10−15 | 3.5108 × 10−16 |
| | F11 | MEAN | 0.3978 | 0.3983 | 0.3978 | 0.3978 | 0.3981 | 0.3978 | 0.3978 | | Q STD | 4.9156 × 10−8 | 0.0005 | 0.0000 | 1.2402 × 10−15 | 4.7046 × 10−7 | 0.0000 | 0.0000 |
| | F12 | MEAN | −2.5964 | −3.1492 | −3.2236 | −3.2625 | −3.2444 | −3.3219 | −3.1043 | | STD | 0.3503 | 0.0627 | 0.0511 | 0.0594 | 0.0567 | 2.2598 × 10−13 | 3.1401 × 10−16 |
| | F13 | MEAN | 5.3106 | 3.0082 | 2.9999 | 2.9999 | 3.0000 | 2.9999 | 3.0000 | | STD | 6.7269 | 0.0083 | 7.1607 × 10−10 | 9.0989 × 10−13 | 5.7284 × 10−9 | 3.1401 × 10−14 | 5.2471 × 10−15 |
| | F14 | MEAN | 2.9675 | 0.0006 | 0.0000 | 4.8495 × 10−28 | 0.0998 | 0.0000 | 0.9934 | | STD | 3.9806 | 0.0025 | 0.0000 | 2.0796 × 10−27 | 0.2994 | 0.0000 | 0.9060 |
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