Research Article
A Comparative Study of Improved Artificial Bee Colony Algorithms Applied to Multilevel Image Thresholding
Table 4
The successful performance (SP) and ranks of the nine methods.
| | Image | | PSO | DPSO | FODPSO | ABC | ABC/best/1 | ABC/best/2 | IABC/best/1 | IABC/rand/1 | CABC | | SP | Rank | SP | Rank | SP | Rank | SP | Rank | SP | Rank | SP | Rank | SP | Rank | SP | Rank | SP | Rank |
| | Starfish | 2 | 1350 | 7 | 3200 | 8 | 4200 | 9 | 1150 | 6 | 520.83 | 2 | 650 | 3 | 450 | 1 | 1000 | 5 | 851.06 | 4 | | 3 | 2050 | 7 | 5600 | 8 | 9347.83 | 9 | 1900 | 6 | 850 | 2 | 950 | 3 | 800 | 1 | 1250 | 5 | 1000 | 4 | | 4 | 4550 | 5 | 11326.53 | 8 | 24500 | 9 | 6500 | 7 | 2000 | 1 | 3350 | 3 | 2200 | 2 | 3900 | 4 | 5572.92 | 6 | | 5 | 10347.22 | 6 | 26785.71 | 8 | 49615.38 | 9 | 10984.85 | 7 | 5852.27 | 2 | 8333.33 | 3 | 4600 | 1 | 9605.26 | 5 | 8750 | 4 |
| | Snow | 2 | 1150 | 6 | 3500 | 8 | 6700 | 9 | 1500 | 7 | 700 | 2 | 950 | 3 | 550 | 1 | 1100 | 5 | 1020.41 | 4 | | 3 | 2150 | 6.5 | 8800 | 9 | 7021.28 | 8 | 2150 | 6.5 | 750 | 1.5 | 900 | 3 | 750 | 1.5 | 1150 | 4 | 1223.40 | 5 | | 4 | 4234.69 | 6 | 12244.90 | 8 | 22058.82 | 9 | 3500 | 4 | 1550 | 1 | 2150 | 2 | 2250 | 3 | 4050 | 5 | 4250 | 7 | | 5 | 12241.38 | 7 | 24833.33 | 8 | 124166.70 | 9 | 7346.94 | 5 | 2700 | 2 | 3900 | 3 | 2550 | 1 | 6550 | 4 | 7608.70 | 6 |
| | Fox | 2 | 550 | 6 | 2200 | 8 | 3100 | 9 | 650 | 7 | 300 | 1 | 400 | 3 | 350 | 2 | 500 | 5 | 450 | 4 | | 3 | 1200 | 4 | 4500 | 8 | 7244.89 | 9 | 2050 | 7 | 700 | 1 | 1100 | 3 | 850 | 2 | 1750 | 5 | 1842.11 | 6 | | 4 | 2604.17 | 5 | 9534.88 | 8 | 13833.33 | 9 | 3150 | 7 | 1420.46 | 2 | 1950 | 3 | 1350 | 1 | 2400 | 4 | 2987.81 | 6 | | 5 | 3622.45 | 4 | 615000 | 8 | 9204.55 | 9 | 5612.25 | 5 | 2450 | 2 | 3300 | 3 | 2200 | 1 | 6530.61 | 6 | 7062.50 | 7 |
| | Human | 2 | 1350 | 7 | 3300 | 8 | 4200 | 9 | 1050 | 6 | 350 | 1 | 650 | 3 | 550 | 2 | 750 | 4 | 989.58 | 5 | | 3 | 2650 | 7 | 4700 | 8 | 10106.38 | 9 | 2250 | 6 | 750 | 1 | 1000 | 3 | 800 | 2 | 1100 | 5 | 1032.61 | 4 | | 4 | 4285.71 | 3 | 12444.44 | 7 | 37500 | 9 | 6326.53 | 4 | 7653.06 | 5 | 4000 | 2 | 3800 | 1 | 9459.46 | 6 | 13303.57 | 8 | | 5 | 10071.43 | 5 | 29791.67 | 8 | 60833.33 | 9 | 11136.36 | 6 | 4285.71 | 1 | 5100 | 4 | 4600 | 2 | 4836.96 | 3 | 17000 | 7 |
| | Burro | 2 | 1400 | 4.5 | 3100 | 8 | 5918.37 | 9 | 1750 | 6 | 468.75 | 1 | 1100 | 3 | 850 | 2 | 1400 | 4.5 | 1836.74 | 7 | | 3 | 3150 | 7 | 6400 | 8 | 8979.59 | 9 | 2100 | 6 | 850 | 1 | 1200 | 4 | 1050 | 2 | 1400 | 5 | 1150 | 3 | | 4 | 3958.33 | 7 | 14772.73 | 8 | 44117.65 | 9 | 3850 | 6 | 1944.44 | 2 | 2291.67 | 3 | 1700 | 1 | 2650 | 4 | 2959.18 | 5 | | 5 | 10909.09 | 4 | 18846.15 | 7 | 18939.39 | 8 | 17045.45 | 6 | 7833.33 | 3 | 7621.95 | 2 | 7608.70 | 1 | 15520.83 | 5 | 34750 | 9 |
| | Mountain | 2 | 1750 | 7 | 2800 | 8 | 5400 | 9 | 1100 | 6 | 364.58 | 1 | 650 | 5 | 450 | 2 | 600 | 4 | 585.11 | 3 | | 3 | 2150 | 6 | 6300 | 8 | 9687.50 | 9 | 2400 | 7 | 1000 | 2 | 1250 | 3 | 800 | 1 | 1950 | 5 | 1800 | 4 | | 4 | 5867.35 | 7 | 14375 | 8 | 38055.56 | 9 | 4600 | 5 | 3125 | 4 | 2650 | 2 | 2000 | 1 | 2800 | 3 | 4787.23 | 6 | | 5 | 10285.71 | 7 | 22424.24 | 8 | 52500 | 9 | 6500 | 5 | 1989.80 | 1 | 3200 | 3 | 2050 | 2 | 4300 | 4 | 8958.33 | 6 |
| | Girl | 2 | 1350 | 6 | 3200 | 8 | 4900 | 9 | 1400 | 7 | 500 | 1.5 | 700 | 3 | 500 | 1.5 | 900 | 5 | 765.31 | 4 | | 3 | 1900 | 5 | 6300 | 8 | 11363.64 | 9 | 2250 | 6 | 800 | 1.5 | 1200 | 3 | 800 | 1.5 | 1650 | 4 | 2368.42 | 7 | | 4 | 7239.58 | 7 | 15319.15 | 8 | 28653.85 | 9 | 4050 | 5 | 2500 | 3 | 2350 | 2 | 1900 | 1 | 2600 | 4 | 4946.81 | 6 | | 5 | 10067.57 | 6 | 18589.74 | 8 | 22424.24 | 9 | 8963.42 | 5 | 2908.16 | 1 | 6900 | 3 | 4700 | 2 | 8869.05 | 4 | 13541.67 | 7 |
| | Scenery | 2 | 1150 | 4 | 4100 | 8 | 6900 | 9 | 2150 | 6 | 750 | 1 | 1050 | 3 | 800 | 2 | 1550 | 5 | 3958.33 | 7 | | 3 | 3500 | 4 | 8200 | 8 | 11547.62 | 9 | 4081.63 | 5 | 1377.55 | 1 | 3150 | 3 | 1450 | 2 | 5156.25 | 7 | 4402.17 | 6 | | 4 | 5153.06 | 7 | 11666.67 | 8 | 25833.33 | 9 | 3050 | 6 | 1836.74 | 3 | 1800 | 2 | 1300 | 1 | 2100 | 4 | 2244.90 | 5 | | 5 | 8333.33 | 4 | 24827.59 | 8 | 62727.27 | 9 | 9375 | 5 | 7244.90 | 2 | 7604.17 | 3 | 4846.94 | 1 | 12857.14 | 7 | 12586.21 | 6 |
| | Penguin | 2 | 1200 | 7 | 3100 | 8 | 3400 | 9 | 800 | 6 | 350 | 1.5 | 450 | 3 | 350 | 1.5 | 550 | 5 | 500 | 4 | | 3 | 2200 | 7 | 4700 | 8 | 6086.96 | 9 | 1850 | 6 | 714.29 | 1 | 900 | 3 | 800 | 2 | 1100 | 5 | 1071.43 | 4 | | 4 | 7962.96 | 4 | 24193.55 | 8 | 62727.27 | 9 | 12053.57 | 7 | 7142.86 | 2 | 6607.14 | 1 | 7215.91 | 3 | 9125 | 5 | 9736.84 | 6 | | 5 | 8841.46 | 7 | 22321.43 | 8 | 66000 | 9 | 7000 | 6 | 2291.67 | 2 | 3200 | 3 | 2150 | 1 | 3250 | 4 | 3829.79 | 5 |
| | Pillar | 2 | 1050 | 4 | 3700 | 8 | 4700 | 9 | 1400 | 6 | 612.25 | 2 | 850 | 3 | 550 | 1 | 1200 | 5 | 1542.55 | 7 | | 3 | 2450 | 6 | 5900 | 8 | 12162.16 | 9 | 4350 | 7 | 1600 | 2 | 2000 | 3 | 1300 | 1 | 2050 | 5 | 2040.82 | 4 | | 4 | 5212.77 | 5 | 10937.50 | 8 | 21212.12 | 9 | 7440.48 | 7 | 5051.02 | 4 | 3571.43 | 1 | 4050 | 2 | 4387.76 | 3 | 5243.90 | 6 | | 5 | 8625 | 6 | 17875 | 8 | 21481.48 | 9 | 12096.77 | 7 | 6500 | 2 | 6614.58 | 3 | 5765.31 | 1 | 7944.44 | 5 | 7380.95 | 4 |
| | Waterfall | 2 | 1050 | 7 | 3100 | 8 | 4000 | 9 | 1000 | 6 | 400 | 1 | 600 | 3 | 500 | 2 | 700 | 4.5 | 700 | 4.5 | | 3 | 4850 | 7 | 7600 | 8 | 11666.67 | 9 | 2650 | 6 | 1000 | 1 | 1300 | 3 | 1200 | 2 | 1950 | 5 | 1902.17 | 4 | | 4 | 7336.96 | 7 | 15444.44 | 8 | 25357.14 | 9 | 5350 | 5 | 4555.56 | 4 | 2700 | 2 | 2350 | 1 | 3750 | 3 | 7021.28 | 6 | | 5 | 11333.33 | 5 | 21875 | 8 | 22586.21 | 9 | 15543.48 | 7 | 3437.50 | 1 | 6276.60 | 3 | 4450 | 2 | 8618.42 | 4 | 11785.71 | 6 |
| | Bridge | 2 | 1400 | 7 | 2500 | 8 | 5000 | 9 | 900 | 6 | 459.18 | 3 | 450 | 1.5 | 450 | 1.5 | 700 | 4 | 714.29 | 5 | | 3 | 3650 | 7 | 6428.57 | 8 | 13285.71 | 9 | 2150 | 6 | 918.37 | 2 | 1550 | 3 | 900 | 1 | 1800 | 5 | 1650 | 4 | | 4 | 5677.08 | 6 | 14239.13 | 8 | 21875 | 9 | 8750 | 7 | 5217.39 | 3 | 4200 | 2 | 3400 | 1 | 5277.78 | 4 | 5285.71 | 5 | | 5 | 8571.43 | 5 | 22575.76 | 8 | 20735.29 | 7 | 7393.62 | 4 | 3776.60 | 1 | 5208.33 | 3 | 3906.25 | 2 | 9423.08 | 6 | 31590.91 | 9 |
| | Average rank (lower is better) | 5.85 | | 7.98 | | 8.9167 | | 5.99 | | 1.85 | | 2.802 | | 1.53 | | 4.625 | | 5.45 |
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