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峰值搜索算法[16]假设:中心点被局部密度较低的近邻数据点包围,且任意中心点与比它密度更高的数据点间的距离都较远。
对于任意像素点m, 需要计算m的局部密度ρm和最临近相关距离δm:
$ {\rho _m} = {g_m} $
(1) 式中,gm代表图像中像素点的灰度值。最临近相关距离δm则是通过计算点m与其它密度更高的点n之间的最小距离来测量:
$ {\delta _m} = \mathop {\min }\limits_{m:{\rho _n} > {\rho _m}} \left( {{d_{mn}}} \right) $
(2) 对于密度最高的点, ${\delta _m} = \mathop {\max }\limits_n \left( {{d_{mn}}} \right)$。
$ {d_{mn}} = \left| {{x_m} - {x_n}} \right| + \left| {{y_m} - {y_n}} \right| $
(3) $ {\gamma _m} = {\rho _m} \times {\delta _m} $
(4) 式中,dmn是Manhattan距离,逐个像素计算联合特征因子γm,并按照降序排列把它们放到队列Q中,这里提取前12个像素点作为候选目标点; xm和ym代表点m的横坐标和纵坐标; xn和yn代表点n的横坐标和纵坐标。
目标点在图像中具有局部差异性,即目标点的灰度值通常要高于局部相邻像素的灰度值。提取候选目标可以减小搜索目标的范围,减少算法计算时间。
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传统的局部对比度方法(LCM)、改进的LCM(ILCM)、相对LCM(RLCM)和基于差分的局部对比测量方法(difference local contrast measurement, DLCM)[17]采用多尺度技术检测1×2像素~9×9像素的小目标。对于红外图像中尺寸小于9×9像素的小目标,采用的多尺度技术将增强目标周围的背景面积,导致检测到的目标的大小扩大到9×9像素,即“扩张效应”,如图 1所示。“扩张效应”使两个目标重叠,不能精确地检测目标。因此,处理“扩张效应”的关键是找到一种非多尺度的方法,可以自适应地检测不同大小的目标。
为了在固定尺度下检测从2×1像素~9×9像素的小目标,设计了一个3层双邻域窗口,共包含25个单元,每个单元大小为3×3像素。如图 2所示,将整个窗口划分为3个区域,其中单元T是目标单元,单元T周围的8个单元Mi(i=1~8)代表中间单元,其余16个单元Bjk(j, k=1~4)表示背景单元。将候选目标置于3层双邻域窗口的中心时,小目标的灰度和梯度差异都会反映在3个区域中,用来检测不同大小的目标。同时3层双邻域窗口形状接近目标轮廓,可以准确逼近目标的真实分布。
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小目标检测通过增强目标对比度,有效地突出小目标。根据3层双邻域窗口,充分利用3个区域之间的差异来测量对比度。中心单元和背景单元之间的最小灰度对比度d(T, Bjk)、中心单元和中间单元之间的梯度对比度d(T, Mi)分别表示为:
$ \begin{array}{*{20}{c}} {d\left( {T, {B_{jk}}} \right) = }\\ {\left\{ {\begin{array}{*{20}{l}} {{g_T} - \max \left( {{g_{{B_{jk}}}}} \right), \left( {{g_T} > \max \left( {{g_{{B_{jk}}}}} \right)} \right)}\\ {0, ({\rm{ else }})} \end{array}} \right.} \end{array} $
(5) $ d\left( {T, {M_i}} \right) = \left\{ {\begin{array}{*{20}{l}} {{G_T} - {G_{{M_i}}}, \left( {{G_T} > {G_{{M_i}}}} \right)}\\ {0, ({\rm{ else }})} \end{array}} \right. $
(6) 式中,gT和gBjk分别代表中心单元和背景单元的灰度均值,GT和GMi分别代表中心单元和中间单元的梯度均值,其中i=1, 2, …, 8;j, k=1, 2, …, 4。为了进一步凸显目标和抑制杂波,采用中间区域梯度对比度对角相乘作为加权因子W,即:
$ \begin{array}{*{20}{c}} {W = \min \left[ {d\left( {T, {M_i}} \right) \times d\left( {T, {M_{9 - i}}} \right)} \right], }\\ {(i = 1, 2, 3, 4)} \end{array} $
(7) 在局部区域内,真实目标强度通常高于局域背景强度,而虚假目标强度与局域背景强度相当,所以真实目标的d(T, Bjk)值较大;真实目标通常是中心对称,向四周辐射的圆点状,高亮杂波则普遍是不规则形状,所以虚假目标的对角梯度乘积通常为0。根据上述特征,候选目标位置的对比度信息为:
$ {C_{{\rm{DNCM}}}} = d\left( {T, {B_{jk}}} \right) \times W $
(8) 对所有候选目标进行窗口遍历,真实目标区域对比度得到增强,背景杂波得到有效抑制,最终得到双邻域对比测量方法(double neighborhood contrast measurement, DNCM)目标映射图。
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根据DNCM的计算,可以得到图像的DNCM目标映射图。考虑到目标映射图具有不同层次的杂波背景,采用自适应阈值法对目标和背景进行分割。
$ {T_{{\rm{th }}}} = {\mu _{{\rm{DNCM }}}} + k{\sigma _{{\rm{DNCM }}}} $
(9) 式中, μDNCM是DNCM目标映射图的均值,σDNCM是DNCM目标映射图的标准差,k是阈值系数,一般取30~50。经过阈值Tth分割得到真实目标。
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本文中采用天空背景、云层背景和海天背景等5组单一目标或多目标的红外图像进行实验,并用本方法与顶帽变换[18]、方差差异方法(variance difference, VARD)[9]、LCM[6]、基于多尺度补丁的对比测量方法(multiscale patch-based contrast measurement,MPCM)[19]和RLCM[7]方法进行对比实验,图 4为实验结果,每张图像用矩形框显示真实目标区域。使用背景抑制因子(background suppression factor, BSF)、对比度增益(contrast gain, CG)和平均运行时间对所有算法进行评估,BSF可以全局评价算法的杂波抑制能力,其值与杂波抑制效果成正比;CG则可以评估目标的增强效果,其值与目标增强效果成正比。实验计算环境是3.40GHz Intel i7-3770 CPU处理器,8GB内存,所使用的测试软件是MATLAB 2018b。
Figure 4. Frame 1, 2, 3, 4, 5 five original image sequences and detection results under different methods
很明显,图 4中采用多尺度技术的LCM和RLCM方法在5个图像序列中都出现了“扩张效应”,在frame 5检测结果中,邻近的两个目标发生重叠;顶帽变换和MPCM方法在背景抑制方面效果较差,检测结果有大量杂波;RLCM和VARD方法在frame 5中漏检目标;总体而言,本方法有效地解决了“扩张效应”并抑制了背景杂波。
为了进一步量化分析,表 1中(加黑数字是最优结果)给出了5个图像序列经过6种不同检测算法处理后的BSF, CG和时间值。本方法的BSF和CG值在6种不同检测算法中均为最优,分别平均提高4.7倍和1.8倍,说明本方法背景抑制和目标增强能力高于基线水平;VARD和RLCM方法平均运行时间分别为最短和最长,本方法兼顾了检测精度和运算效率。
表 1 BSF, CG and average running time of different algorithms under each image sequence
methods top-hat VARD LCM MPCM RLCM proposed BSF frame 1 3.754 8.718 1.356 5.947 3.562 10.029 frame 2 2.423 9.154 2.450 11.366 2.869 12.263 frame 3 1.648 5.634 1.339 2.514 2.939 9.937 frame 4 9.436 21.198 1.730 7.819 7.820 23.075 frame 5 3.104 2.438 12.480 1.628 4.388 12.751 CG frame 1 2.385 2.483 1.914 1.634 2.396 2.484 frame 2 1.691 1.743 1.507 1.595 1.339 1.758 frame 3 2.473 2.325 1.588 0.479 2.448 2.681 frame 4 0.998 2.131 1.409 1.695 1.515 2.233 frame 5 0.996 1.426 0.954 1.426 0.631 1.431 time frame 1 0.570 0.067 0.116 0.103 1.049 0.336 frame 2 0.380 0.066 0.135 0.118 2.650 0.815 frame 3 0.430 0.069 0.150 0.126 3.553 1.023 frame 4 0.470 0.082 0.167 0.153 4.553 1.200 frame 5 0.732 0.102 0.131 0.076 3.358 0.873
基于双邻域对比度的红外小目标检测算法
Infrared small target detection algorithm based on double neighborhood contrast measure
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摘要: 为了解决密集多目标检测中易造成的漏检问题,提出一种基于双邻域对比度的红外小目标检测算法。首先利用峰值搜索算法筛选出候选目标;再通过单尺度3层双邻域窗口遍历候选目标; 最后利用双邻域对比度模型计算候选目标区域的最小灰度对比度,并用对角梯度因子增强对比度和抑制杂波。结果表明,与5种对比方法相比,该方法的背景抑制因子和对比度增益分别平均提高4.7倍和1.8倍,有效地抑制了杂波,增强了目标。该研究能够准确地检测到相互接近的多个目标,对提高复杂背景下的多目标检测精度是有帮助的。Abstract: In order to solve the problem of missed detection easily caused in dense multi-target detection, an infrared small target detection algorithm based on double neighborhood contrast measure was proposed. First, the peak search algorithm was used to screen out the candidate targets; then the candidate targets were traversed through a single-scale three-layer double neighborhood window; finally the dual-neighbor contrast model was used to calculate the minimum gray contrast of the candidate target area, and the contrast and suppresses clutter were enhanced by the diagonal gradient. The results show that compared with the five comparison methods, the background suppression factor and contrast gain of this method are increased by 4.7 times and 1.8 times on average, respectively, which effectively suppresses clutter and enhances the target. This research can accurately detect multiple targets that are close to each other, which is helpful to improve the accuracy of multi-target detection in complex backgrounds.
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表 1 BSF, CG and average running time of different algorithms under each image sequence
methods top-hat VARD LCM MPCM RLCM proposed BSF frame 1 3.754 8.718 1.356 5.947 3.562 10.029 frame 2 2.423 9.154 2.450 11.366 2.869 12.263 frame 3 1.648 5.634 1.339 2.514 2.939 9.937 frame 4 9.436 21.198 1.730 7.819 7.820 23.075 frame 5 3.104 2.438 12.480 1.628 4.388 12.751 CG frame 1 2.385 2.483 1.914 1.634 2.396 2.484 frame 2 1.691 1.743 1.507 1.595 1.339 1.758 frame 3 2.473 2.325 1.588 0.479 2.448 2.681 frame 4 0.998 2.131 1.409 1.695 1.515 2.233 frame 5 0.996 1.426 0.954 1.426 0.631 1.431 time frame 1 0.570 0.067 0.116 0.103 1.049 0.336 frame 2 0.380 0.066 0.135 0.118 2.650 0.815 frame 3 0.430 0.069 0.150 0.126 3.553 1.023 frame 4 0.470 0.082 0.167 0.153 4.553 1.200 frame 5 0.732 0.102 0.131 0.076 3.358 0.873 -
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