Group Intelligent Hybrid Optimization Algorithm for Image Segmentation of Deep Space Exploration

Qiying Nie; Zhencai Zhu; Yonghe Zhang; Yamin Wang

doi:10.3788/LOP202158.0210002

Laser & Optoelectronics Progress, Volume. 58, Issue 2, 0210002(2021)

Group Intelligent Hybrid Optimization Algorithm for Image Segmentation of Deep Space Exploration

Qiying Nie^1,2,3, Zhencai Zhu^1,3、*, Yonghe Zhang^1,3, and Yamin Wang^1,3

Author Affiliations

¹Innovation Academy for Microsatellites of CAS, Shanghai 201203, China

²University of Chinese Academy of Sciences, Beijing 100049, China

³Key Laboratory of Microsatellites, Shanghai 201203, China

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Figures & Tables(13)

Fig. 1. Wolves algorithm hierarchy model

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Fig. 2. Segmentation process of proposed algorithm

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Fig. 3. Segmentation results of single threshold segmentation method. (a) Original images; (b) segmentation results

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Fig. 4. Segmentation results of Otsu algorithm. (a) Original images; (b) segmentation results; (c) gray histograms

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Fig. 5. Segmentation results of proposed algorithm. (a) Image 1; (b) image 2; (c) image 3

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Fig. 6. Segmentation detail diagram of different algorithms. (a) Original image; (b) single threshold segmentation; (c) Otsu algorithm; (d) proposed algorithm

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Table 1. Unimodal benchmark functions
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Table 1. Unimodal benchmark functions
Name Function n Range Min
F1 f₁(x)= $\overset{n}{\sum_{i = 1}} x_{i}^{2}$ 30 [-100,100] 0
F2 f₂(x)= $\overset{n}{\sum_{i = 1}}$ |x_i|+ $\overset{n}{\prod_{i = 1}}$ |x_i| 30 [-10,10] 0
F3 f₃(x)= $\max_{i} [|x_{i}|, 1 \leq i \leq n]$ 30 [-100,100] 0

Table 2. Multimodal benchmark functions
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Table 2. Multimodal benchmark functions
Name Function n Range Min
F4 $\begin{matrix} f_{4} (x) = - 20 \exp (- 0.2 \sqrt[]{\frac{1}{n} \overset{n}{\sum_{i = 1}} x_{i}^{2}}) - \exp [\frac{1}{n} \overset{n}{\sum_{i = 1}} \cos (2 π x_{i})] + 20 + e \end{matrix}$ 30 [-32,32] 0
F5 f₅ $(x)$ = $\frac{1}{4000} \overset{n}{\sum_{i = 1}} x_{i}^{2}$ - $\overset{n}{\prod_{i = 1}}$ cos $(x_{i} / \sqrt[]{i})$ +1 30 [-600,600] 0
F6 f₆ $(x)$ = $\overset{n}{\sum_{i = 1}} x_{i}^{2}$ -10cos $(2 π x_{i})$ +10 30 [-5.12,5.12] 0

Table 3. Fixed-dimension multimodal benchmark functions

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Table 3. Fixed-dimension multimodal benchmark functions

Name	Function	n	Range	Min
F7	f₇ $(x)$ = $\overset{11}{\sum_{c = 1}} {[a_{c} - \frac{x_{1} (b_{c}^{2} + b_{c} x_{2})}{b_{c}^{2} + b_{c} x_{3} + x_{4}}]}^{2}$	4	[-5,5]	0.00030
F8	f₈ $(x)$ = ${(x_{2} - \frac{5.1}{4 π^{2}} x_{1}^{2} + \frac{5}{π} x_{1} - 6)}^{2}$ +10 $(1 - \frac{1}{8 π})$ cos x₁+10	2	[-5,5]	0.398
F9	$\begin{array}{l} f_{9} (x) = [1 + {(x_{1} + x_{2} + 1)}^{2} (19 - 14 x_{1} + 3 x_{1}^{2} - 14 x_{2} + 6 x_{1} x_{2} + 3 x_{2}^{2})] \times \\ [30 + {(2 x_{1} - 3 x_{2})}^{2} \times (18 - 32 x_{1} + 12 x_{1}^{2} + 48 x_{2} - 36 x_{1} x_{2} + 27 x_{2}^{2})] \end{array}$	2	[-2,2]	3

Table 4. Average of different algorithms under different functions

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Table 4. Average of different algorithms under different functions

Functions	Proposed algorithm	GWO	PSO	DE	GSA
F1	5.18887×10^-49	2.80179×10^-27	0.000237219	0.00314	2.37×10^-16
F2	2.7456×10^-25	9.93897×10^-17	0.04260275	0.00339	1.08782
F3	1.9321×10^-15	6.53673×10^-7	1.120836	0.00334	43.30114
F4	4.3668×10^-15	1.10667×10^-13	0.07106	0.000275933	8.71582
F5	0	0.003175	0.016024	0.1462	335.2185875
F6	0	0.293711	66.0182	786.4320	13.13346
F7	0.0014554	0.010344514	0.000938607	1.50073×10^-7	0.00536
F8	0.398652	0.397891	0.3979	0.39771	0.3979
F9	3.00071	3.00733	3	3	3

Table 5. Standard deviation of different algorithm under different functions

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Table 5. Standard deviation of different algorithm under different functions

Functions	Proposed method	GWO	PSO	DE	GSA
F1	2.83492×10^-49	4.09404×10^-27	0.000207836	0.000685079	9.74×10^-17
F2	2.18425×10^-25	8.07479×10^-17	0.067624678	0.000860814	0.980801962
F3	6.10984×10^-15	4.7406×10^-7	0.278588176	0.001478137	1.147027104
F4	4.3668×10^-15	6.19657×10^-16	0.20023266	5.5731×10^-5	1.479301656
F5	0	0	0.012184864	0.08498613	180.0696952
F6	0	49.4631	20.8949	0	3.24273875
F7	3.40825×10^-5	0.01056044	0.00012533	1.44066×10^-7	0.004790778
F8	0.001191216	3.16228×10^-6	0	9.21×10^-8	0
F9	0.001747029	0.008511176	0	0	0

Table 6. Threshold comparison of different algorithms
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Table 6. Threshold comparison of different algorithms
Image Single threshold Otsu Proposed algorithm
Logarithmic entropy Exponential entropy T entropy
1 110 65, 109 76, 155 74, 148 78, 149
2 127 80, 120 74, 154 78, 153 78, 152
3 135 80, 123 74, 150 74, 153 71, 149

Table 7. Results of multi-level threshold search

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Table 7. Results of multi-level threshold search

Image	Number of thresholds is 2	Number of thresholds is 3	Number of thresholds is 4	Number of thresholds is 5
1	75, 153	74, 123, 211	67, 74, 153, 186	74, 77, 153, 207, 243
2	78, 149	74, 92, 153	74, 153, 202, 230	74, 82, 114, 153, 188
3	72, 154	74, 131, 153	74, 119, 127, 153	74, 127, 153, 185, 208

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Qiying Nie, Zhencai Zhu, Yonghe Zhang, Yamin Wang. Group Intelligent Hybrid Optimization Algorithm for Image Segmentation of Deep Space Exploration[J]. Laser & Optoelectronics Progress, 2021, 58(2): 0210002

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