基于改进麻雀搜索算法的多阈值图像分割

doi:10.12305/j.issn.1001-506X.2021.02.05

Abstract

Abstract:

To solve the problems of low segmentation accuracy, large calculation amount and slow segmentation speed in the traditional multi-threshold image segmentation methods, a multi-threshold image segmentation method based on improved sparrow search algorithm (ISSA) is proposed. First, the sparrow search algorithm (SSA) is optimized based on the flight behavior in the bird swarm algorithm (BSA), and four types of benchmark functions are used to evaluate the optimization performance of ISSA. Then, the between-class variance and Kapur entropy are used to perform the multi-threshold image segmentation, and the segmentation results of the two methods are compared. Finally, using PSNR, objective function value and standard deviation as evaluation criteria, ISSA is compared with the existing segmentation algorithms. The results show that ISSA has better search ability and development ability, and it has a significant improvement in terms of segmentation speed and accuracy.

Key words: image segmentation, improved sparrow search algorithm (ISSA), multi-threshold, Otsu, Kapur entropy

CLC Number:

TP391.41

Xin LYU, Xiaodong MU, Jun ZHANG. Multi-threshold image segmentation based on improved sparrow search algorithm[J]. Systems Engineering and Electronics, 2021, 43(2): 318-327.

Figures/Tables 13

Fig.1

Fig.2

Table 1

Fig.3

Table 2

Table 3

Table 4

Fig.4

Fig.5

Table 5

Table 6

Table 7

Comparisons results among the four algorithms based on Kapur method"

图像	n	ISSA			GWO			SSA1			ABC
图像	n	PSNR	MEAN	STD	PSNR	MEAN	STD	PSNR	MEAN	STD	PSNR	MEAN	STD
Cameraman	2	13.647 5	17.555 7	0.000 4	13.635 4	17.552 9	0.043 1	13.635 4	17.531 1	0.164 7	13.671 0	16.752 4	0.396 1
	3	14.609 5	21.957 4	0.032 2	14.116 6	21.939 3	0.116 7	15.222 1	21.855 4	0.213 8	16.951 4	21.117 1	0.334 5
	4	20.209 0	26.538 2	0.001 7	20.153 8	26.447 2	0.206 0	18.323 6	26.212 7	0.399 0	17.463 6	25.197 8	0.441 5
	5	20.806 9	30.453 3	0.062 9	20.614 5	30.314 7	0.261 4	19.077 0	30.128 2	0.410 3	19.306 9	28.911 7	0.439 8
Lena	2	14.580 6	17.818 5	0	14.553 5	17.816 3	0.044 8	14.596 0	17.803 5	0.121 1	14.564 1	17.659 2	0.108 8
	3	16.226 1	22.206 4	0.139 4	16.074 6	22.361 8	0.192 3	16.060 3	22.247 4	0.279 6	16.140 3	21.710 6	0.187 3
	4	19.276 6	26.621 9	0.206 0	19.174 0	26.610 7	0.212 4	18.913 3	26.487 1	0.365 6	17.702 6	25.543 9	0.270 2
	5	20.938 7	30.450 6	0.241 4	20.227 1	30.436 0	0.278 3	20.881 5	30.307 1	0.372 7	19.393 2	29.038 7	0.480 0
Butterfly	2	14.522 4	17.748 5	7.105 4E-15	13.648 5	17.747 3	0.024 2	13.200 4	17.740 4	0.076 0	13.650 9	17.666 9	0.046 5
	3	15.017 6	22.200 1	0.000 1	15.290 5	22.172 0	0.133 5	14.999 0	22.108 2	0.243 5	16.286 6	21.773 8	0.183 9
	4	17.408 2	26.412 3	0.000 4	17.337 2	26.316 8	0.218 5	16.592 6	26.108 4	0.314 4	16.877 5	25.341 2	0.254 8
	5	18.861 0	30.197 7	0.040 7	17.162 0	30.109 8	0.302 3	20.444 7	29.873 6	0.460 7	17.585 0	28.784 1	0.336 4
Baboon	2	16.018 3	17.628 7	1.065 8E-14	16.018 3	17.628 1	0.000 5	16.018 3	17.622 5	0.009 9	15.829 4	17.574 9	0.035 8
	3	18.604 7	22.045 9	0.000 7	18.631 3	22.039 5	0.004 6	18.649 0	22.010 5	0.030 4	17.891 1	21.929 4	0.122 0
	4	20.501 8	26.156 3	0.002 3	20.353 9	26.126 1	0.015 3	20.632 4	26.070 7	0.063 7	19.974 7	25.954 7	0.123 6
	5	22.371 0	29.992 0	0.004 9	22.013 2	29.901 8	0.048 0	21.955 4	29.846 8	0.082 8	20.680 6	29.458 1	0.213 0

Table 7

Fig.6

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函数	特征	函数表达式	上下界	维数
F1	US	$f_{1}(x)=\sum\limits_{i=1}^{n} x_{i}^{2}$	[-100, 100]	30
F2	UN	$f_{2}(x)=\sum\limits_{i=1}^{n-1}\left[100\left(x_{i+1}-x_{i}^{2}\right)+\left(x_{i}-1\right)^{2}\right]$	[-30, 30]	30
F3	MS	$\begin{aligned} f_{3}(x)=& 0.1\left\{\sin ^{2}\left(3 \pi x_{1}\right)+\sum\limits_{i=1}^{n}\left(x_{i}-1\right)^{2}\left[1+\sin ^{2}\left(3 \pi x_{i}+1\right)\right]+\right.\\ &\left.\left(x_{n}-1\right)^{2}\left[1+\sin ^{2}\left(2 \pi x_{n}\right)\right]\right\}+\sum\limits_{i=1}^{n} u\left(x_{i}, 5, 100, 4\right) \end{aligned}$	[-50, 50]	30
F4	MN	$f_{4}(x)=-\sum\limits_{i=1}^{n} \sin \left(x_{i}\right)\left(\sin \left(i x_{i}^{2} \div \pi\right)\right)^{20}$	[0, π]	10

函数	算法	最劣值	最优值	平均值	标准差	平均运行时间
F1	SSA	5.377 9E-39	0	2.423 6E-40	1.029 6E-39	0.351 0
F1	ISSA	7.114 7E-47	1.673 9E-56	3.284 1E-48	1.323 9E-47	0.308 3
F2	SSA	0.022 9	1.051 4E-07	0.003 0	0.006 0	0.442 2
F2	ISSA	0.022 6	2.521 3E-09	0.002 4	0.004 7	0.402 6
F3	SSA	1.657 7E-04	3.172 8E-08	1.506 2E-05	3.243 6E-05	0.849 5
F3	ISSA	4.757 6E-05	3.120 1E-11	7.826 6E-06	1.160 2E-05	0.827 1
F4	SSA	-5.516 0	-9.339 3	-7.456 0	0.850 0	0.378 1
F4	ISSA	-5.923 3	-9.483 9	-8.109 9	0.819 5	0.348 4

图像	n	阈值	PSNR	STD
Cameraman	2	70 144	17.249 1	1.348 7E-06
	3	59 119 156	20.216 5	0.033 9
	4	4 295 140 170	21.526 1	0.120 6
	5	3 682 122 149 173	23.286 2	0.112 9
Lena	2	92 151	15.458 5	0
	3	80 126 170	17.490 5	0
	4	74 113 145 180	18.883 7	1.168 0E-06
	5	73 109 136 160 188	20.267 2	0.791 6
Butterfly	2	85 148	14.726 2	0
	3	74 120 171	16.994 1	1.168 0E-06
	4	6 698 134 176	18.705 8	0.016 6
	5	6 288 113 143 180	19.747 3	0.097 1
Baboon	2	97 149	15.425 3	0
	3	85 125 161	17.718 0	0.032 3
	4	72 106 137 168	20.707 5	0.042 0
	5	68 100 126 150 175	21.438 9	0.063 8

图像	n	P-value Otsu versus Kapur
Cameraman	2	6.115 1E-14
	3	8.467 6E-13
	4	3.038 0E-12
	5	1.959 6E-11
Lena	2	1.685 3E-14
	3	5.297 9E-13
	4	2.270 6E-11
	5	1.251 3E-07
Butterfly	2	1.685 3E-14
	3	1.333 4E-13
	4	1.570 2E-13
	5	7.290 6E-12
Baboon	2	1.685 3E-14
	3	7.544 2E-13
	4	1.385 6E-12
	5	2.036 8E-12

图像	n	ISSA			GWO			SSA1			ABC
图像	n	PSNR	MEAN	STD	PSNR	MEAN	STD	PSNR	MEAN	STD	PSNR	MEAN	STD
Cameraman	2	17.249 1	3 650.3	1.348 7E-06	17.249 1	3 650.3	0.173 3	17.249 1	3 650.2	0.438 6	17.159 4	3 649.0	0.804 9
	3	20.216 5	3 725.7	0.033 9	20.214 0	3 725.4	0.364 5	20.128 7	3 722.7	1.407 3	19.641 3	3 720.3	1.298 0
	4	21.526 1	3 780.7	0.120 6	20.998 7	3 779.3	0.880 6	21.853 1	3 773.9	2.149 9	21.057 6	3 763.9	2.677 0
	5	23.286 2	3 812.0	0.112 9	23.125 1	3 809.6	1.072 2	21.276 0	3 801.3	1.954 4	22.041 9	3 793.6	2.365 3
Lena	2	15.458 5	1 969.0	0	15.328 1	1 969.0	0.205 8	15.367 4	1 968.6	0.634 6	15.328 1	1 967.2	1.057 2
	3	17.490 5	2 135.8	0	17.239 9	2 135.3	0.530 3	17.229 7	2 131.8	1.844 0	17.357 1	2 130.3	1.576 0
	4	18.883 7	2 199.5	1.168 0E-06	18.510 8	2 197.5	0.993 4	18.855 9	2 189.4	2.177 3	18.675 6	2 175.6	2.944 8
	5	20.267 2	2 224.6	0.791 6	19.260 7	2 221.0	1.508 0	19.450 9	2 207.6	2.822 5	19.280 4	2 203.3	2.662 8
Butterfly	2	14.726 2	2 508.5	0	14.641 8	2508.4	0.242 8	14.658 4	2 508.1	0.6414	14.560 8	2 507.5	0.666 3
	3	16.994 1	2 656.3	1.1 680E-06	16.887 7	2 655.7	0.663 1	16.978 7	2 652.0	1.967 7	16.237 2	2 649.4	1.758 8
	4	18.705 8	2 720.4	0.016 6	18.608 4	2 718.4	0.979 6	18.611 1	2 712.1	2.164 5	18.419 6	2 697.4	3.442 2
	5	19.747 3	2 747.7	0.097 1	19.781 9	2 744.4	1.078 6	19.637 1	2 731.6	2.342 4	20.059 1	2 724.4	2.428 5
Baboon	2	15.425 3	1 547.9	0	15.353 0	1 547.7	0.347 6	15.378 4	1 546.2	1.210 4	15.408 7	1 546.5	0.727 4
	3	17.718 0	1 638.1	0.032 3	17.539 6	1 637.0	0.740 0	18.722 5	1 628.9	2.331 7	18.542 2	1 631.9	1.556 8
	4	20.707 5	1 692.0	0.042 0	20.204 2	1 688.3	1.282 3	19.829 5	1 675.3	3.108 8	20.139 4	1 671.9	2.657 1
	5	21.438 9	1 717.8	0.063 8	20.156 3	1 712.8	1.288 6	20.637 5	1 695.4	3.172 9	20.882 6	1 691.6	3.037 7

Multi-threshold image segmentation based on improved sparrow search algorithm

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