-
这种BEMD和MPCM相结合的红外小目标检测算法,算法的核心思想是首先利用BEMD算法对图像进行分解得到若干满足条件的IMF分量和残差图像。为了能够准确的过滤掉均匀背景(低频),突出小目标(高频),需要去掉低频的内涵模态分量,将第一、二阶IMF分量和残差图像进行重构得到新的图像,同时作为MPCM红外小目标检测算法的输入图像进行小目标的识别。图1为BEMD-M算法的流程图。
将二维M×N图像信号
$ f(x,y) $ 使用BEMD算法分解过程描述如下:(1) 图像初始化,输入图像
$ f(x,y) $ ;(2) 将图像映射到XOY平面,图像对应像素点的灰度值作为Z坐标;
(3) 通过数学形态学方法找出图像的局部极大值点和极小值点;
(4) 对图像的局部极大值点和极小值点采用二维样条插值算法,得到上下包络面
${E_{\rm max }}(x,y)$ ,$ {E}_{\mathrm{min}}(x,y) $ ,并求其均值$ E(x,y) $ ;$$ E(x,y)=\frac{{E}_{\mathrm{max}}(x,y)+{E}_{\mathrm{min}}(x,y)}{2} $$ (1) (5) 从输入图像
$ f(x,y) $ 中减去包络均值$ E(x,y) $ 得到新的中间变量为:$$ {S_1}(x,y) = f(x,y) - E(x,y) $$ (2) (6) 验证
$ {S_1}(x,y) $ 是否满足BIMF筛选终止准则:$$ S D = \frac{{\displaystyle\sum _{x = 1}^M\displaystyle\sum _{y = 1}^N|{S_{m - 1}}(x,y) - {S_m}(x,y){|^2}}}{{\displaystyle\sum _{x = 1}^M\displaystyle\sum _{y = 1}^N|{S_{m - 1}}(x,y){|^2}}} $$ (3) 满足
$ {S_1}(x,y) = IM{F_1} $ ,则执行步骤(7) 得到残差图像,否则转步骤(3)重复过程;(7) 将经过分解得到的IMF分量之和从原图像中减去,得到两者之间的残差为:
$$ {R_m}(x,y) = f(x,y) - IM{F_{{m}}} $$ (4) (8) 输入图像f(x,y)经过BEMD分解可表示为:
$$f(x,y) = \sum\limits_{i = 1}^m {IM{F_i}(x,y) + {R_m}(x,y)} $$ (5) 将图像
$ f(x,y) $ 作为原始输入图像,经过m次循环满足终止条件,得到m个满足条件的IMF分量和最后的残差图像。最后的残差图像往往是一个单调图像,在实际应用中通常不能忽略残差图像,因为残差图像中包含了大量的灰度信息,表征了原始图像的趋势。经典MPCM红外小目标检测算法为了能够更好地突出小目标区域存在的局部差异性,将周围部分分成八个斑块
${B_{{i}}}(i = 1,2,\cdots,8$ ) 。将中心斑块与相邻八个斑块的区别定义为:$$ D(T) = \left( \begin{gathered} {{d}}(T,B_1) \\ {{d}}(T,B_2) \\ \begin{array}{*{20}{c}} {}& \vdots &{} \end{array} \\ {{d}}(T,B_8) \\ \end{gathered} \right) $$ (6) 式中:d表示中心斑块与相邻八个斑块的差异程度,即:
$$ {{d}}(T,B_i) = {m_T} - {m_{B_i}},(i = 1,2,\cdots ,8) $$ (7) 式中:mT,mBi
分别为中心斑块与相邻八个斑块的像素均值。 由于红外图像中,小目标的形状分布大致符合二维高斯函数分布,其形状一般呈现向四周发散的中心对称,因此,基于目标与背景的灰度差异程度,进一步提出:
$${{{\tilde d}}_i} = d(T,{B_i})\cdot d(T,{B_i} + 4),(i = 1,2,\cdots,4) $$ (8) $ {{{\tilde d}}_i} $ 表示在第i个方向上,中心斑块T与相邻八个斑块在不同方向上的灰度差异。中心斑块与相邻八个斑块的差异性可由公式(9)获得:$$ {C_{({x_{ii}},{y_{jj}})}} = \mathop {\min }\limits_{i = 1,2,3,4} {\tilde d_i} $$ (9) 式中:
$ ({x_{ii}},{y_{jj}}) $ 表示目标区域中心位置的坐标。当滑动窗口遍历整幅图像,得到给定比例尺上的斑块差异性测度图。为了使滑动窗口的大小更适合于目标,计算多个尺度下的局部对比度图
$ {C^l} $ ,以获得最大响应,其中l表示子窗口的不同尺度。$$ {\hat C_{p,q}} = \mathop {\max }\limits_{l = 1,2,\cdots L} {C^l}(p,q) $$ (10) 式中:p,q分别表示列号和行号。
当得到目标显著图后,很可能最显著的区域就是目标。为了区分目标和背景,采用自适应阈值分割进行真实目标的提取。
$$ Th = \mu + K\delta $$ (11) 式中:μ和δ表示MPCM得到的显著性图的均值和标准差;K是经验值。如果显著图的灰度值大于Th,确定为目标区域,否则,认定为背景。
-
为了评价文中提出的BEMD-M红外小目标检测算法在红外小目标图像上的有效性和可行性,将文中提出的算法与Top-Hat算法[2]、RLCM算法[6]、IPI算法[8]、Fast-Saliency算法[1]、MPCM算法[7]进行对比分析。此次实验采用六组不同场景(较弱云杂波多目标场景、白天较弱云杂波空天场景、傍晚较弱云杂波空天场景、较强云杂波复杂空天场景、目标淹没在较强云杂波空天场景、海天场景)的数据集来进行测试,所有测试结果取平均值,旨在减小实验误差,提高实验数据的准确性。红外图像数据集的详细说明如表1所示。
表 1 红外图像数据集详细说明
Table 1. Detail description of infrared image data set
Number of frames Background description Type of target Group 1 86 Weak cloud clutter multi-target scene Bird Group 2 57 Sky scene with weak cloud clutter in the daytime Bird Group 3 81 Daylight weaker cloudy clutter sky scene Bird Group 4 97 Stronger cloud clutter complex sky scene Bird Group 5 125 Target submerged in stronger cloud clutter sky scene Bird Group 6 92 Sea-sky scene Bird 主要通过以下两个指标进行算法性能分析,分别是检测率和虚警率。实验中,可对比分析不同算法在六组不同场景中计算得到的检测率和虚警率,验证文中算法的有效性和可行性。所有实验程序都是由MATLAB R2019 a软件编译,运行在英特尔i5 2.3 GHz处理器和8 GB运行内存的计算机上。
-
此次实验随机选择表1中每组数据集中的一帧图像,用不同算法分别进行处理,进行比较分析。图2为不同算法的测试结果图,红色方框表示真实目标,蓝色圆圈表示虚假目标,没有标注的表示没有检测到目标。从图2中可以看出,除BEMD-M算法外,其他五种算法在不同场景的检测中都出现了不同程度的虚警。因此,也可以出看出,BEMD-M算法在不同场景的红外小目标检测中均能达到较好的检测效果。
为了定量地评价不同算法的检测性能,采用检测率(Pd)和虚警率(Pf)两个指标来进行比较。Pd和Pf的定义如下:
$$ \left\{ \begin{gathered} {{{P}}_{\text{d}}} = \frac{1}{{{N_i}}}\cdot \frac{{{N_\text{d}}}}{{{N_\text{t}}}},(i = 1,2,\cdots,6) \\ {P_{\text{f}}} = \frac{1}{{{N_i}}}\cdot\frac{{{N_\text{f}}}}{M},(i = 1,2,\cdots,6) \\ \end{gathered} \right. $$ (18) 式中:
${N_\rm d}$ 为正确检测出小目标的个数;$ {N_{\text{t}}} $ 为真实小目标的数量总和;${N_\rm f}$ 为误检的小目标个数;M为完全检测到的目标数量;${N_{{i}}}(i = 1,2,\cdots,6)$ 为每组数据集的个数。表2和表3为六种算法在不同场景中的检测率和虚警率,黑色加粗字体表示其对应的算法性能最好。通过分析可得:BEMD-M算法在前四组数据集中检测率最高,其在傍晚较弱云杂波空天场景中的检测率最高达到了100%,传统的红外小目标检测方法在简单背景中具有较好的检测效果,但在复杂背景中虚警率较高。在第Group 2、Group 3、Group 4数据集中,文中算法检测率最高,虚警率最低。在Group 5和Group 6中,目标淹没在较强云杂波场景中,IPI、RLCM算法都取得了较好的检测结果。BEMD-M算法检测率最低、虚警率最高,这是由于目标淹没在背景中,在进行IMF分量重构时,去掉了低频的IMF分量,在减弱背景杂波影响的同时也减弱了小目标的特征。Top-hat、Fast-Saliency算法在复杂背景中不能很好地抑制背景噪声,造成虚警率较高。综上所述,BEMD-M算法在大多数场景中都能取得较高的检测性能。
表 2 六个真实场景数据集的平均检测率比较
Table 2. Comparison of the average detection rate of six real scene data sets
Algorithm Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Tophat 90.82% 94.74% 88.89% 97.94% 89.60% 93.33% Fast-Saliency 88.78% 95.76% 96.25% 95.88% 92% 91.11% RLCM 87.76% 96.76% 96.3% 96.91% 89.6% 95.56% IPI 94.9% 95.49% 97.53% 97.26% 96.8% 92.51% MPCM 93.88% 96.3% 96.29% 96.91% 88.8% 91.11% BEMD-M 96.94% 98.56% 100% 99.06% 82.4% 94.89% 表 3 六个真实场景数据集的平均虚警率比较
Table 3. Comparison of the average false alarm rate of six real scene data sets
Algorithm Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Tophat 14.29% 5.26% 7.41% 4.12% 12.8% 10.76% Fast-Saliency 12.24% 10.53% 8.64% 5.15% 15.2% 24.44% RLCM 16.32% 3.5% 5.83% 3.09% 12% 11.11% IPI 6.12% 7.02% 4.94% 2.06% 8% 10.31% MPCM 6.22% 8.77% 4.94% 7.22% 16.8% 9.46% BEMD-M 8.16% 2.11% 1.23% 1.56% 18.4% 11.56% -
此次实验是图2的三维灰度分布图,如图3所示。从图3中可以看出,Top-Hat算法、Fast-Saliency算法、RLCM算法处理后,背景杂波较多,有的杂波灰度值高于目标灰度值,肉眼难以区分目标位置。BEMD-M算法是BEMD和MCPM算法的结合,从图(f)MPCM和(g)BEMD-M中可以看出,BEMD-M算法经过BEMD分解重构后,去掉了低频IMF分量,有效抑制了背景,同时增强了目标。BEMD-M算法与其他算法相比,背景的灰度值更均匀,也更小,明显得到了抑制,同时目标的灰度值得到了增强,提高了小目标的检测性能。
-
表4为不同算法单帧的计算效率,其中Fast-Saliency方法具有最短的时间消耗,文中方法具有最大的时间消耗。由于文中方法需要对图像进行模态分解与重构,这是影响计算效率的一个重要因素。所有实验程序都是由MATLAB R2019 b软件编译,运行在英特尔i5 2.3 GHz处理器和8 G运行内存的计算机上。在未来,笔者将考虑提高文中方法的计算效率。
表 4 不同算法单帧的计算效率(Group 1)
Table 4. Computing efficiency of single frame with different algorithms (in Group 1)
Top-Hat Fast-Saliency RLCM IPI MPCM BEMD-M Time/s 0.498 0.009 4.022 6.719 0.072 31.595
Infrared small target detection algorithm based on two-dimensional modal decomposition combined with patch contrast
-
摘要: 红外小目标检测在红外目标搜索跟踪等应用中发挥着重要作用。文中提出一种二维经验模态分解与多尺度斑块对比度算法相结合的红外小目标检测算法。首先,利用二维经验模态分解将红外图像分解成不同尺度的模态分量,再将低频模态分量去掉进行图像重构,实现对背景杂波的抑制。然后,将重构图像做为多尺度斑块对比度算法的输入,生成目标结果图。最后,对目标结果图进行自适应阈值分割,检测出真实的红外小目标。实验仿真结果表明,该算法与现有算法相比,在不同背景下能够有效抑制背景对目标的干扰,具有较高的检测率,验证了该算法的有效性和鲁棒性。Abstract: Infrared small target detection plays an important role in applications such as infrared target search and tracking. In this paper, we propose an infrared small target detection algorithm combining two-dimensional empirical modal decomposition and multi-scale patch contrast algorithm. First, the infrared image is decomposed into modal components of different scales using two-dimensional empirical modal decomposition, and then the low-frequency modal components are removed for image reconstruction to achieve the suppression of background clutter. Then, the reconstructed image is used as the input of the multi-scale patch contrast algorithm to generate the target result map. Finally, adaptive threshold segmentation is performed on the target result map to detect the real infrared small targets. The experimental simulation results show that the algorithm can effectively suppress the background interference to the target with high detection rate under different backgrounds compared with the existing algorithms, which verifies the effectiveness and robustness of the algorithm.
-
表 1 红外图像数据集详细说明
Table 1. Detail description of infrared image data set
Number of frames Background description Type of target Group 1 86 Weak cloud clutter multi-target scene Bird Group 2 57 Sky scene with weak cloud clutter in the daytime Bird Group 3 81 Daylight weaker cloudy clutter sky scene Bird Group 4 97 Stronger cloud clutter complex sky scene Bird Group 5 125 Target submerged in stronger cloud clutter sky scene Bird Group 6 92 Sea-sky scene Bird 表 2 六个真实场景数据集的平均检测率比较
Table 2. Comparison of the average detection rate of six real scene data sets
Algorithm Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Tophat 90.82% 94.74% 88.89% 97.94% 89.60% 93.33% Fast-Saliency 88.78% 95.76% 96.25% 95.88% 92% 91.11% RLCM 87.76% 96.76% 96.3% 96.91% 89.6% 95.56% IPI 94.9% 95.49% 97.53% 97.26% 96.8% 92.51% MPCM 93.88% 96.3% 96.29% 96.91% 88.8% 91.11% BEMD-M 96.94% 98.56% 100% 99.06% 82.4% 94.89% 表 3 六个真实场景数据集的平均虚警率比较
Table 3. Comparison of the average false alarm rate of six real scene data sets
Algorithm Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Tophat 14.29% 5.26% 7.41% 4.12% 12.8% 10.76% Fast-Saliency 12.24% 10.53% 8.64% 5.15% 15.2% 24.44% RLCM 16.32% 3.5% 5.83% 3.09% 12% 11.11% IPI 6.12% 7.02% 4.94% 2.06% 8% 10.31% MPCM 6.22% 8.77% 4.94% 7.22% 16.8% 9.46% BEMD-M 8.16% 2.11% 1.23% 1.56% 18.4% 11.56% 表 4 不同算法单帧的计算效率(Group 1)
Table 4. Computing efficiency of single frame with different algorithms (in Group 1)
Top-Hat Fast-Saliency RLCM IPI MPCM BEMD-M Time/s 0.498 0.009 4.022 6.719 0.072 31.595 -
[1] Qi Shengxiang, Xu Guojing, Mou Zhiying, et al. A fast-saliency method for real-time infrared small target detection [J]. Infrared Physics & Technology, 2016, 77: 440-450. [2] Zhou J, Lv H, Zhou F. Infrared small target enhancement by using sequential top-hat filters[C]//International Society for Optics and Photonics, SPIE, 2014, 9301: 93011L. [3] Chen C L P, Li H, Wei Y T, et al. A local contrast method for small infrared target detection [J]. IEEE Transactions on Geoscience & Remote Sensing, 2013, 52(1): 574-581. [4] Han J, Yong M, Bo Z, et al. A robust infrared small target detection algorithm based on human visual system [J]. IEEE Geoscience & Remote Sensing Letters, 2014, 11(12): 2168-2172. [5] Du P, Hamdulla A. Infrared small target detection using homogeneity-weighted local contrast measure [J]. IEEE Geoscience and Remote Sensing Letters, 2020, 17(3): 514-518. doi: 10.1109/LGRS.2019.2922347 [6] Han J, Liang K, Zhou B, et al. Infrared small target detection utilizing the multiscale relative local contrast measure [J]. IEEE Geoscience and Remote Sensing Letters, 2018, 15(4): 612-616. doi: 10.1109/LGRS.2018.2790909 [7] Wei Yantao, You Xinge, Li Hong. Multiscale patch-based contrast measure for small infrared target detection [J]. Pattern Recognition, 2016, 58: 216-226. doi: https://doi.org/10.1016/j.patcog.2016.04.002 [8] Gao Chenqiang, Meng Deyu, Yang Yi, et al. Infrared patch-image model for small target detection in a single image [J]. IEEE Transactions on Image Processing, 2013, 22(12): 4996-5009. doi: 10.1109/TIP.2013.2281420 [9] Qin Y, Bruzzone L, Gao C, et al. Infrared small target detection based on facet kernel and random walker [J]. IEEE Transactions on Geoscience and Remote Sensing, 2019, 57(9): 7104-7118. doi: 10.1109/TGRS.2019.2911513 [10] Redmon J, Divvala S, Girshick R, et al. You only look once: Unified, real-time object detection[C]//IEEE Conference on Computer Vision and Pattern Recognition, 2015: 779-788. [11] Redmon J, Farhadi A. YOLO9000: Better, faster, stronger[C]//IEEE Conference on Computer Vision and Pattern Recognition, 2017: 6517-6525. [12] Redmon J, Farhadi A. YOLOv3: An incremental improvement[C]//IEEE Conference on Computer Vision and Pattern Recognition, 2018: 89-95. [13] Liu W, Anguelov D, Erhan D, et al. SSD: Single shot multiBox detector[C]//European Conference on Computer Vision, 2016: 21-37. [14] Lin T, Goyal P, Grishick R., et al. Focal loss for dense object detection[C]//IEEE International Conference on Computer Vision, 2017: 2999-3007. [15] He K, Gkioxari G, Dollár P, et al. Mask R-CNN[C]//IEEE International Conference on Computer Vision, 2017: 2980-2988. [16] Zhang Ruzhen, Zhang Jianlin, Qi Xiaoping, et al. Infrared target detection in complex scenes [J]. Photoelectric Engineering, 2020, 47(10): 10. (in Chinese) [17] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis [J]. Proceedings Mathematical Physical & Engineering Sciences, 1998, 454(1971): 903-995. [18] Nunes J C, Bouaoune Y, ric Deléchelle, et al. Image analysis by bidimensional empirical mode decomposition [J]. Image & Vision Computing, 2003, 21: 1019-1026.