Infrared small target detection based on clustering idea

Fig. 3. Graph of density peak clustering results，Note：(a) images of density peak clustering results for raw IR, (b) images of density peak clustering results for pre-processed

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Fig. 4. IFCM Stage Graph：（a）comparison graph of segmentation results，（b）enhanced template map

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Fig. 5. Samples of the 4 real IR sequences，Note：(a) –(d) Seq. 1-4

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Fig. 6. Probability that candidate targets contain the real target

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Fig. 7. Saliency maps of different methods

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Fig. 8. ROC curves of different methods，Note：(a) –(d) Seq.1-4

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Table 0. [in Chinese]

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Table 0. [in Chinese]

Algorithm 1IFCM

输入：候选目标局部图像块 $Ω_{i}; i = 1, . . ., n$

输出：局部图像块像素c类标签（目标类像素与背景类像素）

1：初始化参数：聚类中心个数c=2，模糊值q=2，迭代停止阈值，最大迭代次数

2：初始化隶属度矩阵，初始化目标类初始值，以候选目标为目标类初始值

3：利用式（12）计算空间权重因子 $w_{j k}$

4：更新隶属度矩阵 $μ_{j k}^{}$ ，更新聚类中心 $v_{k}$

5：利用式（11）计算目标函数 $J_{F C M}$

6：如果相邻两次目标函数值误差小于迭代收敛阈值或迭代次数超过最大迭代次数，则退出迭代循环。否则返回步骤3继续迭代。

Table 1. Number of iterations of the segmentation graph of FCM and IFCM
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Table 1. Number of iterations of the segmentation graph of FCM and IFCM
类型 FCM迭代次数 IFCM迭代次数
目标 23 13
噪声 16 7
杂波 31 20

Table 2. Details of the four IR sequences
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Table 2. Details of the four IR sequences
序列帧数图像大小目标大小背景情况
1 200 256*256 $2 \times 1$ 复杂地面背景
2 200 320*256 $2 \times 2$ - $6 \times 2$ 高亮云层背景
3 399 256*256 $4 \times 4$ 复杂地面背景
4 500 256*256 $3 \times 3$ - $6 \times 7$ 复杂地面背景

Table 3. Details of parameter settings for the different methods

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Table 3. Details of parameter settings for the different methods

No.	Methods	Acronyms	Parameter settings
1	New White Top-Hat	NWTH	$Δ B = 4, B_{i} = 7$
2	Partial Sum of the Tensor Nuclear Norm	PSTNN	$\begin{array}{l} P a t c h s i z e : 40 \times 40, s l i d i n g s t e p : 40, \\ λ = \frac{0.6}{\sqrt[]{m a x (n_{1}, n_{2}) * n_{3}}}, ε = 10^{- 7} \end{array}$
3	Variance Difference	VARD	$D = 3, L o c a l w i n d o w s i z e : 15 \times 15$
4	Multiscale Relative Local Contrast Measure	RLCM	$C e l l s i z e : 9 \times 9, K_{1} \in \{2,5, 9\}, K_{2} \in \{4,9, 16\}$
5	Multiscale Patch-based Contrast Measure	MPCM	$C e l l s i z e : 3 \times 3,5 \times 5,7 \times 7,9 \times 9$
6	Density Peaks Searching and Maximum-Gray Region Growing	DPS-MRG	$n_{p} = 20$
7	Facet Kernel and Random Walker	FKRW	$K = 4, p = 6, β = 200, w i n d o w s i z e : 11 \times 11$
8	Based on Clustering Idea	Ours	$n = 10, S = 22, k = 2$

Table 4. Average running time for a frame (256×256) in different methods
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Table 4. Average running time for a frame (256×256) in different methods
Methods NWTH PSTNN VARD RLCM MPCM DPS-MRG FKRW Ours
Times（s） 0.008 6 0.127 8 0.005 8 1.675 0 0.037 6 0.448 0 0.069 3 0.307 6

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Jun-Min RAO, Jing MU, Shi-Jian LIU, Jin-Fu GONG, Fan-Ming LI. Infrared small target detection based on clustering idea[J]. Journal of Infrared and Millimeter Waves, 2023, 42(4): 527

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