Levy Flight Trajectory-based Salp Swarm Algorithm for Multilevel Thresholding Image Segmentation
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摘要: 针对Otsu算法用于多阈值图像分割中存在运算时间长和精度低的不足, 利用群智能优化算法对图像分割算法进行优化.本文首先应用莱维飞行算法对樽海鞘群优化算法进行改进, 将多阈值Otsu函数作为优化算法的适应度函数, 利用改进后的LSSA寻找适应度函数的最大值, 同时获得相对应的多阈值.其次, 通过对几幅基本图像、伯克利大学图像分割库中的图像和实际污油图像进行多阈值Otsu分割研究, 在最佳适应度值、PSNR、SSIM指标以及算法耗时方面进行对比分析.实验结果表明本文提出的算法可以获得更为准确的分割阈值和更高的分割效率.Abstract: Aiming at the shortcoming of long operation time and low precision in multi-threshold image segmentation using Otsu algorithm, image segmentation algorithm is optimized by using group intelligent optimization algorithm. In this paper, firstly, the optimized algorithm of thaliacea scabbard group is improved by using the Levy flight algorithm. The multi-threshold Otsu function is taken as the fitness function of the optimized algorithm, and the improved LSSA is used to find the maximum fitness function, and the corresponding multi-threshold value is obtained. Secondly, the multi-threshold Otsu segmentation study was conducted on several basic images, images in Berkeley university image segmentation database and actual images of pollution oil, and the comparative analysis was conducted on the optimal fitness value, PSNR, SSIM index and algorithm time. Experimental results show that the proposed algorithm can obtain more accurate segmentation thresholds and higher segmentation efficiency.
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Key words:
- Multi-threshold image segmentation /
- Otsu method /
- salp swarm optimization /
- Levy flight
1) 本文责任编委 左旺孟 -
表 1 元启发式算法的参数
Table 1 Parameter of the heuristic algorithm
算法 参数 取值 WOA $a$ [0, 2] $b$ 1 $l$ $[-1, 1]$ SSA ${{{c}}_2}$ rand ${{{c}}_3}$ rand PSO ${{{c}}_1}$ 1.5 $V$ $[0, 1]$ HSA $HMCR$ 0.7 $PAR$ 0.3 $PAR_{\min}$ 0.3 $PAR_{\max}$ 0.9 $bw_{\min}$ 0.2 $bw_{\max}$ 0.5 FPA $P$ 0.5 LSSA 莱维参数 1.5 
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表 2 各算法所用时间(s)
Table 2 The time of each algorithm (s)
图像 $K$ WOA SSA PSO HSA FPA LSSA Lena 2 2.0194 1.1280 2.3447 2.151 2.2726 1.2192 3 2.1376 1.3220 2.5441 3.5147 3.6616 1.4381 4 2.3473 1.5417 2.7315 5.4181 5.4681 1.6668 5 2.5166 1.7181 3.0027 7.5123 7.8495 1.9037 Moon 2 1.8974 1.3124 2.2654 2.1011 2.1043 1.1867 3 1.9821 1.5134 2.5297 3.5741 3.6502 1.4522 4 2.0864 1.8076 2.8298 5.1547 5.5808 1.6469 5 2.1856 2.0871 3.9691 7.7145 7.9073 1.8979 Baboon 2 1.6136 1.3094 2.3135 2.1421 2.1442 1.1925 3 1.8123 1.5775 2.5898 3.5741 3.7015 1.4971 4 2.0219 1.7995 2.7694 5.6241 5.6584 1.7795 5 2.2238 2.0742 3.0042 7.8145 7.9067 2.0095 Camera 2 1.5753 1.0552 2.0963 1.4321 1.5753 1.2465 3 1.7649 1.2233 2.2171 1.9451 1.7649 1.4252 4 2.3980 1.4006 3.4061 2.5124 2.3980 1.6983 5 2.4131 1.5882 3.6251 2.6412 2.4131 1.8411 Plane 2 2.3117 1.6997 2.5147 2.5421 2.5117 1.6197 3 2.4719 1.6959 2.8412 3.1741 2.8749 1.6759 4 2.6711 1.7831 3.2145 4.1241 2.9711 1.7731 5 2.9613 2.1693 3.8417 5.1145 3.1633 1.9693 Tank 2 2.1714 1.8784 2.6415 2.4321 2.2714 1.5784 3 2.3113 1.9103 2.9451 2.9451 2.6123 1.7103 4 2.4024 2.1094 3.3171 3.5124 2.9024 1.8094 5 2.8117 2.3817 3.9541 4.6412 3.2117 1.8817
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表 3 各优化算法的最佳分割阈值
Table 3 Optimal segmentation threshold of each optimization algorithm
图像 $K$ WOA SSA PSO HSA FPA LSSA Lena 2 93 151 93 151 94 152 94 152 93 151 93 151 3 80 126 171 80 126 171 84 128 168 84 128 168 80 138 168 80 126 171 4 75 114 146 181 75 114 146 181 67 113 142 191 69 110 143 193 73 113 142 179 75 114 146 181 5 73 109 136 160 188 6 593 121 149 182 55 102 143 173 205 59 107 140 179 205 72 111 139 163 182 65 93 120 148 182 Moon 2 57 152 57 152 57 152 57 152 56 151 57 152 3 41 110 178 41 110 178 42 111 178 42 111 178 39 112 174 41 110 178 4 3 493 142 198 3 492 141 198 34 103 146 198 39 105 142 198 33 116 140 175 34 93 142 198 5 2 878 117 153 204 2 877 116 153 204 2 162 104 138 205 2 064 101 138 205 30 78 120 146 207 2 876 115 152 204 Baboon 2 98 150 98 150 97 149 97 149 97 150 98 150 3 85 125 161 85 125 161 67 108 160 67 108 160 84 124 160 85 125 161 4 72 106 137 168 72 106 137 168 61 105 132 161 69 102 132 161 69 107 138 166 72 106 137 168 5 6 799 125 150 175 6 697 123 148 174 64 102 126 156 184 66 104 124 156 184 70 102 128 149 174 6 799 125 150 175 Camera 2 70 144 70 144 70 144 70 144 70 144 70 144 3 59 119 156 59 119 156 59 119 156 59 119 156 54 109 152 59 119 156 4 4 396 140 170 4 295 140 170 41 92 140 170 4 295 140 170 47 106 140 170 4 293 140 170 5 3 683 122 149 173 3 682 122 149 173 35 83 122 149 173 3 683 122 149 173 3 885 103 141 171 3 683 122 149 173 Plane 2 26 179 126 179 126 179 126 179 126 179 126 179 3 85 142 174 84 141 178 85 143 175 85 144 175 85 141 173 85 145 178 4 82 144 171 183 81 142 171 182 79 138 171 182 84 141 174 185 84 141 174 185 84 141 174 185 5 81 132 163 171 181 83 132 163 171 183 81 130 156 172 181 77 122 151 161 185 82 131 160 174 185 82 131 160 174 185 Tank 2 96 134 96 134 96 134 96 134 96 134 96 134 3 82 121 142 87 121 144 81 102 134 89 112 134 88 129 154 88 122 144 4 71 102 138 138 76 106 131 148 76 118 152 189 78 108 132 149 98 109 142 159 78 108 132 149 5 6 593 119 137 143 6 592 116 132 146 6 791 107 114 138 6 693 117 134 148 4 673 127 154 188 6 693 117 134 148
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表 4 各优化算法的最佳适应度值
Table 4 Optimum fltness value of each optimization algorithm
图像 $K$ WOA SSA PSO HSA FPA LSSA Lena 2 1 962.9788 1 962.9788 1 962.7213 1 962.7841 1 962.9788 1 962.9788 3 2 129.5118 2 129.5118 2 121.1345 2 127.0668 2 107.4125 2 129.5118 4 2 193.1658 2 193.1658 2 175.0012 2 176.0021 2 192.0198 2 193.1658 5 2 219.0787 2 217.7731 2 175.9015 2 184.9068 2 215.3949 2 219.0787 Moon 2 4 488.1684 4 488.1684 4 488.1684 4 488.1684 4 487.9365 4 488.1684 3 4 635.5642 4 635.5642 4 631.1234 4 635.5614 4 633.7889 4 636.7907 4 4 705.9054 4 705.8884 4 688.5124 4 699.5635 4 655.2737 4 705.9054 5 4 736.3511 4 736.3721 4 710.0314 4 727.0397 4 731.9581 4 736.3277 Baboon 2 1 559.9789 1 559.9789 1 559.8912 1 559.8972 1 559.9723 1 559.9789 3 1 651.5989 1 651.5989 1 613.8143 1 631.8262 1 651.5354 1 651.3989 4 1 705.5302 1 725.5302 1 701.3112 1 701.3283 1 704.0964 1 705.5302 5 1 731.7870 1 731.6784 1 712.5131 1 722.5437 1 730.9155 1 731.7877 Camera 2 3 651.5573 3 651.5573 3 651.5573 3 651.5573 3 651.5573 3 651.5573 3 3 726.9841 3 726.9841 3 726.9841 3 726.9841 3 724.7608 3 726.9841 4 3 782.0173 3 872.0395 3 781.0311 3 782.0391 3 778.4987 3 782.0395 5 3 813.3775 3 813.3769 3 813.3775 3 813.3775 3 799.5781 3 813.3775 Plane 2 408.3514 411.1475 416.1014 411.0124 400.1204 416.3834 3 427.5317 437.2471 457.2478 447.2474 424.1478 457.5537 4 438.5733 459.2357 469.3457 457.1247 438.2044 469.5933 5 454.8162 464.1789 474.6457 469.8751 475.5751 474.8202 Tank 2 611.4421 611.1247 631.1240 611.2407 601.2104 631.4447 3 641.2147 652.5789 671.3745 641.3047 641.3578 671.2437 4 680.4747 671.5478 690.4577 680.4701 670.4528 690.4043 5 690.1457 693.0124 703.1045 691.1023 693.9014 703.1382
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表 5 各优化算法的最佳适应度值
Table 5 Optimum fltness value of each optimization algorithm
图像 $K$ WOA SSA PSO HSA FPA LSSA Test1 2 7 891.2936 7 891.2936 7 891.2936 7 891.2936 7 891.2936 7 891.2936 3 8 087.8384 8 087.8384 8 014.3372 8 024.3372 8 084.3372 8 087.8384 4 8 172.9962 8 172.9962 8 072.9653 8 122.9653 8 172.9653 8 172.9962 5 8 215.5841 8 215.5841 8 005.2923 8 139.8311 8 199.8311 8 215.4419 Test2 2 326.2732 326.2732 326.1873 321.1873 326.1873 326.2732 3 375.7722 375.7722 365.6812 370.6812 375.6812 375.7722 4 408.6649 408.6993 398.2891 401.2891 408.2891 408.6945 5 422.1188 407.3658 404.9742 414.9742 424.9742 425.8495 Test3 2 1 437.6581 1 437.6581 1 437.5427 1 437.5427 1 437.5427 1 437.6581 3 1 562.7039 1 562.7039 1 460.9753 1 510.9753 1 550.9753 1 562.7039 4 1 627.4583 1 627.456 1 525.0731 1 585.0731 1 625.0731 1 627.4273 5 1 664.2046 1 664.1218 1 521.0817 1 619.2961 1 649.2961 1 664.0444 Test4 2 1 355.9394 1 355.9394 1 355.9394 1 355.9394 1 355.9394 1 355.9394 3 1 448.3263 1 448.3263 1 397.9881 1 407.9881 1 447.9881 1 448.3263 4 1 491.6077 1 491.6077 1 427.9804 1 437.9804 1 487.9804 1 491.5784 5 1 492.1746 1 478.1969 1 483.6063 1 493.6063 1 513.6063 1 483.8625 Test5 2 3 102.2450 3 122.2145 3 022.1045 3 012.0124 3 112.2748 3 122.2871 3 3 209.2104 3 249.1245 3 149.2786 3 149.4577 3 189.2741 3 249.0745 4 3 287.1247 3 297.8161 3 217.2014 3 247.2547 3 207.3045 3 317.8161 5 3 312.1274 3 312.5482 3 252.5758 3 302.7885 3 302.1278 3 352.5482 Test6 2 821.1024 831.1042 801.2371 801.3457 831.0245 831.8096 3 905.2785 935.5921 905.0543 915.0214 915.5781 955.5921 4 985.7852 1 001.2456 927.0578 987.2787 997.3857 1 007.4113 5 1 001.2457 1 018.4278 948.3542 1 018.0122 1 008.4527 1 028.6463 Test7 2 515.3857 565.4257 505.0248 505.2788 525.0245 565.1769 3 587.0245 608.0125 571.2578 578.3942 575.6781 608.1853 4 606.5728 616.1410 595.2452 606.2015 606.2015 626.7067 5 616.4527 626.4527 601.0276 616.3782 616.4578 636.4758 Test8 2 704.3458 716.6664 684.1275 701.0217 671.2573 716.6664 3 718.9524 768.4527 715.3857 748.8377 718.0214 768.3891 4 751.4205 781.0124 752.7821 771.0215 751.5789 791.4562 5 795.4527 800.1045 783.0274 795.3781 795.2452 805.5394
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表 6 各算法的香农熵值
Table 6 The Shannon entropy of each algorithm
图像 FCM Otsu 模糊熵 MSRG RC LSSA Lena 0.8157 0.8021 0.8112 0.8524 0.8614 0.9514 Baboon 0.8251 0.8154 0.8354 0.8414 0.8517 0.9317 Test6 0.8314 0.8231 0.8047 0.8358 0.8421 0.8821 Test7 0.8318 0.8057 0.8012 0.8304 0.8407 0.8907
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表 7 各算法区域一致性值
Table 7 The regional consistency value of each algorithm
图像 FCM Otsu 模糊熵 MSRG RC LSSA Lena 0.8325 0.8514 0.8654 0.8514 0.8681 0.9414 Baboon 0.8258 0.8412 0.8517 0.8415 0.8631 0.9217 Test6 0.8197 0.8357 0.8481 0.8517 0.8758 0.8921 Test7 0.8314 0.8341 0.8617 0.8718 0.8811 0.8907
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表 8 各算法区域对比值
Table 8 Ratio of each algorithm region
图像 FCM Otsu 模糊熵 MSRG RC LSSA Lena 0.4024 0.4024 0.4131 0.4021 0.4231 0.4214 Baboon 0.4124 0.4124 0.4258 0.4317 0.4428 0.4117 Test6 0.4258 0.4025 0.4189 0.4257 0.4527 0.4421 Test7 0.4028 0.4157 0.4358 0.4318 0.4612 0.4707
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表 9 各算法所用时间
Table 9 The time of each algorithm
图像 FCM Otsu 模糊熵 MSRG RC LSSA Lena 3.5166 17.5778 3.6457 3.8457 4.1266 1.9037 Baboon 4.2238 17.0147 3.4527 3.7527 5.3438 2.0095 Test6 5.9131 15.4457 3.8131 5.1131 6.9671 1.8411 Test7 4.5613 15.5789 3.4527 5.4517 6.5613 1.9693
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表 10 各算法所用时间
Table 10 The time of each algorithm
图像 $K$ WOA SSA PSO HSA FPA LSSA Oil1 2 1.5813 1.3501 10.8044 1.4131 1.5813 1.2690 3 1.8284 1.4181 11.0703 1.8145 1.8284 1.4165 4 1.9591 1.6535 11.5977 1.9874 1.9591 1.6501 5 2.1831 1.8763 12.0414 2.2514 2.1831 1.8584 Oil2 2 1.6183 1.2056 11.0774 1.6124 1.6183 1.2093 3 1.8057 1.4853 11.2452 1.8421 1.8057 1.5087 4 1.9716 1.7181 11.5426 1.9587 1.9716 1.6898 5 2.1823 1.9337 11.9453 2.2151 2.1823 1.9916 Oil3 2 1.5915 1.1830 14.4043 1.5467 1.5915 1.2289 3 1.7729 1.4196 14.3581 1.7951 1.7729 1.4492 4 1.9602 1.7168 14.8511 1.9641 1.9602 1.6507 5 2.1482 1.9474 15.0878 2.1054 2.1482 1.9004 Oil4 2 1.6269 1.2696 1.7499 1.6844 1.6269 1.1873 3 1.8117 1.5481 2.0056 1.9541 1.8117 1.4476 4 2.0206 1.8283 2.2152 2.1547 2.0206 1.8023 5 2.2196 2.0961 2.4264 2.5123 2.2196 1.9617
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表 11 各算法的PSNR值
Table 11 PSNR value of each algorithm
图像 $K$ WOA SSA PSO HSA FPA LSSA Oil1 2 15.4928 15.4928 15.4129 15.7529 15.492 15.4928 3 17.8281 17.828 13.6561 17.7283 17.8926 17.8281 4 19.5611 19.5811 18.8672 19.8867 19.4862 19.5651 5 20.8643 21.0431 16.6292 21.3415 20.7961 20.9544 Oil2 2 12.2654 12.2654 12.2654 13.3473 12.0936 12.2654 3 16.7488 16.7488 18.7909 16.9435 16.7466 16.7488 4 18.6808 18.9998 16.2054 20.9003 18.0668 18.9129 5 21.4732 21.6717 19.7711 23.0068 21.4817 21.4732 Oil3 2 15.1441 15.1441 15.8394 15.1441 15.1441 15.1441 3 18.1237 18.1237 10.5491 18.1456 18.1606 18.1237 4 20.1087 20.1087 14.6293 19.8004 19.6802 20.1087 5 22.2648 22.4092 9.6173 20.2118 22.0937 22.2648 Oil4 2 15.6292 15.6292 15.5639 15.6292 15.6292 15.6292 3 17.9204 17.9204 14.8809 18.2441 18.0359 17.9204 4 19.6612 19.6612 15.4654 18.9829 19.8258 19.6612 5 20.7293 20.8209 13.4597 20.6193 20.5241 20.9209
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表 12 各算法的SSIM值
Table 12 SSIM value of each algorithm
图像 $K$ WOA SSA PSO HSA FPA LSSA Oil1 2 0.4492 0.5529 0.4492 0.4492 0.4492 0.5529 3 0.6019 0.6441 0.6019 0.6019 0.6016 0.6741 4 0.6927 0.7389 0.6927 0.6927 0.6617 0.7489 5 0.7518 0.7786 0.7516 0.7518 0.7526 0.7986 Oil2 2 0.3241 0.5608 0.3241 0.3241 0.3241 0.5608 3 0.4888 0.7191 0.4888 0.4888 0.5073 0.7291 4 0.5903 0.7455 0.5903 0.5945 0.5945 0.7755 5 0.6491 0.8292 0.6559 0.6683 0.6616 0.8492 Oil3 2 0.3349 0.4455 0.3349 0.3349 0.3393 0.4655 3 0.4831 0.6082 0.4831 0.4831 0.4884 0.6182 4 0.5868 0.7036 0.5868 0.5868 0.5602 0.7036 5 0.6701 0.7677 0.6701 0.6701 0.6663 0.7777 Oil4 2 0.3924 0.4759 0.3924 0.3924 0.3924 0.4759 3 0.5412 0.6061 0.5412 0.5412 0.5139 0.6061 4 0.6389 0.6586 0.6389 0.6389 0.6287 0.6886 5 0.6974 0.7302 0.6974 0.6995 0.6907 0.7402
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