基于Logistic回归麻雀算法的图像分割

陈刚; 林东; 陈飞; 陈祥宇

doi:10.13700/j.bh.1001-5965.2021.0268

基于Logistic回归麻雀算法的图像分割

doi: 10.13700/j.bh.1001-5965.2021.0268

陈刚¹,
林东^1, ,,
陈飞²,
陈祥宇¹

1.
福州大学物理与信息工程学院，福州 350108
2.
福州大学计算机与大数据学院/软件学院，福州 350108

详细信息

通讯作者:
E-mail：lindong@fzu.edu.cn

中图分类号: TP391.41
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- 被引次数: 0
出版历程
- 收稿日期: 2021-05-24
- 录用日期: 2021-08-27
- 网络出版日期: 2021-09-13
- 整期出版日期: 2023-03-30

Image segmentation based on Logistic regression sparrow algorithm

1.
College of Physics and Information Engineering，Fuzhou University，Fuzhou 350108，China
2.
College of Computer and Data Science/College of Software，Fuzhou University，Fuzhou 350108，China

More Information

Corresponding author: E-mail：lindong@fzu.edu.cn

摘要

摘要:
针对麻雀搜索算法后期种群多样性减少、易陷入局部最优解等问题，提出一种新的改进麻雀搜索算法。所提算法先引入小孔成像反向学习策略对发现者的位置进行更新，提升寻优位置的多样性；其次受Logistic模型的启发，提出一种新的自适应因子对安全阈值进行动态控制，平衡所提算法的全局搜索与局部开发的能力。通过与其他算法在6个基准函数上进行仿真对比，结果表明：所提算法的收敛精度与速度均优于其他算法。在工程应用上，用所提算法优化K-means聚类算法进行图像分割，峰值信噪比（PSNR）、结构相似性（SSIM）及特征相似性（FSIM）3种度量指标验证了其良好的分割性能。
- 麻雀搜索算法 /
- 图像分割 /
- 小孔成像反向学习 /
- Logistic模型 /
- K-means聚类算法
Abstract:
The sparrow search algorithm is improved to address its decrease of population diversity in the later stage and its easy fall into the local optimal solution. The improved algorithm introduces the oppositional learning strategy based small hole imaging to update the discoverer’s position, enhancing the diversity of the optimal position. Then, inspired by the Logistic model, a new adaptive factor is proposed to dynamically control the safety threshold, thus balancing the global search and local development capabilities of the algorithm. Simulations of comparison with other algorithms in six benchmark functions are conducted, and experimental results show higher convergence accuracy and speed of the improved algorithm than those of the other algorithms. In engineering applications, the proposed algorithm optimizes the K-means clustering algorithm for image segmentation with satisfactory segmentation performance in terms of peak signal to noise ratio (PSNR), structural similarity (SSIM) and feature similarity (FSIM).
- sparrow search algorithm /
- image segmentation /
- oppositional learning based small hole imaging /
- Logistic model /
- K-means clustering algorithm

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图 1 小孔成像反向学习原理

Figure 1. Principle of reverse learning for small hole imaging

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图 2 不同参数下对应的函数曲线

Figure 2. Curves of functions corresponding to different parameters

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图 3 基于MSSA的K-means图像分割

Figure 3. K-means image segmentation based on MSSA

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图 4 算法的收敛曲线对比

Figure 4. Comparison of convergence curves of algorithms

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图 5 分割结果对比

Figure 5. Comparison of segmentation results

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表 1 测试函数

Table 1. Test functions

编号	函数名	函数表达式	取值区间	最小值
F₁	Zakharov	$f(x) = \displaystyle\sum\limits_{i = 1}^d {x_i^2 + { {\left(\displaystyle\sum\limits_{i = 1}^d {0.5i{x_i} } \right)}^2} + { {\left(\displaystyle\sum\limits_{i = 1}^d {0.5i{x_i} } \right)}^4} }$	[−5,10]	0
F₂	Schwefel 2.22	$f(x) = \displaystyle\sum\limits_{i = 1}^d {\left\| { {x_i} } \right\|} + \prod\limits_{i = 1}^d {\left\| { {x_i} } \right\|}$	[−10,10]	0
F₃	Rotated Hyper- Ellipsoid	$f(x) = \displaystyle\sum\limits_{i = 1}^d { { {\left(\displaystyle\sum\limits_{j = 1}^i { {x_j} } \right)}^2} }$	[−100,100]	0
F₄	Rastrigin	$f(x) = \displaystyle\sum\limits_{i = 1}^d {\left[x_i^2 - 10\cos \;(2\text{π} {x_i}) + 10\right]}$	[−5.12,5.12]	0
F₅	Schaffer N.2	$f({x_1},{x_2}) = 0.5 + \dfrac{ { { {\sin }^2}(x_1^2 - x_2^2) - 0.5} }{ { { {[1 + 0.001(x_1^2 + x_2^2)]}^2} } }$	[−100,100]	0
F₆	Drop- Wave	$f({x_1},{x_2}) = - \dfrac{ {1 + \cos \;(12\sqrt {x_1^2 + x_2^2} )} }{ {0.5(x_1^2 + x_2^2) + 2} }$	[−5.12,5.12]	−1

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表 2 算法参数设置

Table 2. Parameter settings for algorithms

算法	参数设置
PSO	$ {w_{\max }} = 0.9,{w_{\min }} = 0.2,{c_1} = 2,{c_2} = 2 $
SCA	$a = 2,{r_2} \in [0,2\text{π} ],{r_3} \in [ - 2,2],{r_4} \in [0,1]$
ABC	L = round (0.6dP), a=1
SSA	$ {\rm{PD}} = 35,{\rm{ST}} = 0.6,{\rm{SD}} = 70 $
ISSA	${\rm{PD} } = 35,{\rm{ST}} = 0.6,{\rm{SD} } = 70$
MSSA	${\rm{PD} } = 35,{\rm{ST} } = 0.6\left(\dfrac{1}{ {1 + { {\rm{e} }^{t/10 - 20} } } }\right),{\rm{SD} } = 70$

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表 3 算法性能对比

Table 3. Performance comparison of algorithms

函数	维度	PSO		SCA		ABC		SSA		ISSA		MSSA
函数	维度	均值	标准差	均值	标准差	均值	标准差	均值	标准差	均值	标准差	均值	标准差
F₁	30	2.52×10²	9.35×10	4.19×10	1.40×10	1.34×10³	4.47×10²	4.23×10⁻⁴⁰	2.32×10⁻³⁹	5.36×10⁴	1.80×10³	5.07×10⁻⁴⁶	2.73×10⁻⁴⁵
F₂	30	1.29×10	2.23×10	6.22×10⁻¹	5.48×10⁻¹	8.58×10	1.58×10	1.83×10⁻³⁵	9.69×10⁻³⁵	1.32×10⁻⁵	1.21×10⁻⁵	2.71×10⁻³⁸	1.47×10⁻³⁷
F₃	30	6.11×10²	2.14×10²	1.18×10⁴	5.52×10³	6.32×10⁴	1.03×10⁴	6.68×10⁻⁴⁶	3.66×10⁻⁴⁵	2.97×10⁻⁴	7.07×10⁻⁴	9.46×10⁻⁶⁵	4.81×10⁻⁶⁴
F₄	30	2.17×10²	2.42×10	8.13×10	3.61×10	2.60×10²	1.27×10	0	0	1.02×10⁻⁷	2.15×10⁻⁷	0	0
F₅	2	3.36×10⁻¹	1.72×10⁻¹	0	0	3.61×10⁻⁸	7.15×10⁻⁸	0	0	0	0	0	0
F₆	2	−0.88	1.76×10⁻¹	−1	0	−0.99	1.57×10⁻⁵	−1	0	−1	0	−1	0

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表 4 时间复杂度对比

Table 4. Comparison of time complexity

算法	初始化种群阶段	发现者位置更新阶段	跟随者位置更新阶段	侦察预警机制阶段	全局最优位置更新阶段
SSA	O(d+f(d))	O(d)	O(d)	O(d)	O(d)
ISSA	O(d+f(d))	O(d)	O(d)	O(d)	O(d)
MSSA	O(d+f(d))	O(d)	O(d)	O(d)	O(d)

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表 5 实验1的分割结果评估

Table 5. Evaluation of segmentation results for experiment 1

算法	PSNR	SSIM	FSIM
K-means	4.59670	0.02719	0.64977
PSO	37.51920	0.56816	0.94510
SSA	38.36290	0.61893	0.92049
ISSA	39.62570	0.71613	0.93937
MSSA	39.62570	0.71613	0.93937

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表 6 实验 2的分割结果评估

Table 6. Evaluation of segmentation results for experiment 2

算法	PSNR	SSIM	FSIM
K-means	4.01260	0.02574	0.61662
PSO	36.23870	0.46239	0.93554
SSA	41.53260	0.75025	0.94916
ISSA	39.73070	0.65758	0.94255
MSSA	41.55340	0.75100	0.94976

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表 7 实验3的分割结果评估

Table 7. Evaluation of segmentation results for experiment 3

算法	PSNR	SSIM	FSIM
K-means	5.25340	0.00813	0.33502
PSO	39.31630	0.62781	0.97912
SSA	39.00710	0.64316	0.90803
ISSA	39.10880	0.64845	0.90652
MSSA	40.30030	0.68229	0.92895

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表 8 实验4的分割结果评估

Table 8. Evaluation of segmentation results for experiment 4

算法	PSNR	SSIM	FSIM
K-means	6.09730	0.10149	0.52270
PSO	37.96320	0.59825	0.93910
SSA	39.38630	0.68916	0.96929
ISSA	38.57120	0.62714	0.96676
MSSA	39.55090	0.69945	0.97200

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表 9 实验5的分割结果评估

Table 9. Evaluation of segmentation results for experiment 5

算法	PSNR	SSIM	FSIM
K-means	8.21190	0.04197	0.41687
PSO	38.80000	0.54837	0.96189
SSA	38.85060	0.58358	0.89783
ISSA	37.28800	0.45027	0.90825
MSSA	39.18070	0.60085	0.89722

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表 10 实验6的分割结果评估

Table 10. Evaluation of segmentation results for experiment 6

算法	PSNR	SSIM	FSIM
K-means	6.70790	0.02750	0.50615
PSO	39.11720	0.66199	0.94426
SSA	39.82990	0.62755	0.93491
ISSA	37.79500	0.54857	0.93213
MSSA	40.38320	0.67180	0.90882

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表 11 实验7的分割结果评估

Table 11. Evaluation of segmentation results for experiment 7

算法	PSNR	SSIM	FSIM
K-means	9.08630	0.05000	0.50498
PSO	39.30020	0.59669	0.93519
SSA	37.14440	0.43953	0.91722
ISSA	40.73710	0.68029	0.91686
MSSA	40.73710	0.68029	0.91686

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表 12 实验8的分割结果评估

Table 12. Evaluation of segmentation results for experiment 8

算法	PSNR	SSIM	FSIM
K-means	6.52240	0.01455	0.34518
PSO	36.68360	0.49072	0.96519
SSA	36.68360	0.49072	0.96519
ISSA	37.74220	0.55124	0.97844
MSSA	39.94510	0.64652	0.98883

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