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利用惯导信息对摄像机的运动进行建模。目前基于惯导信息的预测算法大都利用当前帧的惯导数据与目标点之间的空间关系。惯导系统的输出误差会随时间累计,时间越长,惯导系统的漂移越大,利用惯导信息进行位置预测的误差就越大。但是,惯导系统漂移的方向具有一致性,惯导信息的增量漂移误差很小,因此,利用连续帧之间的增量惯导信息建立模型便可以有效地消除漂移误差。
为此,文中提出了增量惯导信息概念,设计了一种基于增量惯导信息的位置预测模型(Location Prediction based on the Incremental INS,LPI)。利用两帧图像之间的姿态信息和位置信息,将两帧图像之间相同目标点的对应像素关系通过比例变化、姿态变化和视角变化建模,有效消除了惯导偏移引起的误差。
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对于捷联成像飞行系统,摄像机与飞行器固连,飞行器的运动会直接引起图像中场景的运动。如图1所示,若空间中目标点
$p$ 的位置为$p{o_t} = \left[ {{\lambda _t},{L_t},{h_t}} \right]$ 。设${t_1}$ 时刻摄像机坐标系的原点为摄像机的光心${O_{c1}}$ ,捷联后与飞行器重合,其${x_{c1}},{y_{c1}},{z_{c1}}$ 轴分别为滚动轴、偏航轴和俯仰轴。为避免姿态角奇点对余弦矩阵的影响,${t_1}$ 时刻飞行器的姿态用四元素表示为${q^1} = \left[ {q_0^1,q_1^1,q_2^1,q_3^1} \right]$ ,飞行器的位置表示为$p{o_1} = \left[ {{\lambda _1},{L_1},{h_1}} \right]$ 。同样的,${t_2}$ 时刻飞行器的位置信息为$p{o_2} = \left[ {{\lambda _2},{L_2},{h_2}} \right]$ ,姿态信息为${q^2} = \left[ {q_0^2,q_1^2,q_2^2,q_3^2} \right]$ 。由于连续帧之间的时间间隔较短,可以假设两帧图像具有相同的地理系。因此,对于目标点
$p$ ,可根据在${t_1}$ 时刻的摄像机坐标系的成像位置$\left( {{u_1},{v_1}} \right)$ 经过相同的地理系转换,准确地计算出在${t_2}$ 时刻摄像机坐标系下的成像位置$\left( {{u_2},{v_2}} \right)$ 。 -
基于以上分析,将两帧中飞行器运动所引起图像目标点的变化模型转化为比例变化模型、姿态变化模型和视角变化模型三个部分。
(1)比例变化模型
飞行器和目标之间距离的变化反映着图像上尺度的缩放。因此,可以通过飞行器与目标的距离来对图像的比例参数进行建模。首先计算
${t_1}$ 时刻飞行器$p{o_1}$ 和目标点$p{o_t}$ 对应的卯酉圈和子午圈半径:$$ \left\{ {\begin{array}{*{20}{c}} {{R_{{W_1}}} = \dfrac{{a_e^2}}{{{{(a_e^2{{\cos }^2}{L_1} + b_e^2{{\sin }^2}{L_1})}^{\text{}\tfrac{1}{2}}}}}} \\ {{R_{{N_1}}} = {R_{{W_1}}}\dfrac{{b_e^2}}{{a_e^2}}} \end{array}} \right. $$ (1) $$ \left\{ {\begin{array}{*{20}{c}} {{R_{{W_t}}} = \dfrac{{a_e^2}}{{{{(a_e^2{{\cos }^2}{L_t} + b_e^2{{\sin }^2}{L_t})}^{\tfrac{1}{2}}}}}} \\ {{R_{{N_t}}} = {R_{{W_t}}}\dfrac{{b_e^2}}{{a_e^2}}} \end{array}} \right. $$ (2) 式中:
${a_e}$ 、${b_e}$ 分别为地球椭球半径。那么$p{o_1}$ 和$p{o_t}$ 在地心系下的坐标为$E\left( {p{o_1}} \right)$ 和$E\left( {p{o_t}} \right)$ ,计算公式为:$$ E\left( {p{o_1}} \right) = \left[ {\begin{array}{*{20}{c}} {{E_x}\left( {p{o_1}} \right)} \\ {{E_y}\left( {p{o_1}} \right)} \\ {{E_z}\left( {p{o_1}} \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\left( {{R_{{W_1}}} + {h_1}} \right)\cos {L_1}\cos {\lambda _1}} \\ {\left( {{R_{{W_1}}} + {h_1}} \right)\cos {L_1}\sin {\lambda _1}} \\ {\left( {{R_{{N_1}}} + {h_1}} \right)\sin {L_1}} \end{array}} \right] $$ (3) $$ E\left( {p{o_t}} \right) = \left[ {\begin{array}{*{20}{c}} {{E_x}\left( {p{o_t}} \right)} \\ {{E_y}\left( {p{o_t}} \right)} \\ {{E_z}\left( {p{o_t}} \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\left( {{R_{{W_t}}} + {h_t}} \right)\cos {L_t}\cos {\lambda _t}} \\ {\left( {{R_{{W_t}}} + {h_t}} \right)\cos {L_t}\sin {\lambda _t}} \\ {\left( {{R_{{N_t}}} + {h_t}} \right)\sin {L_t}} \end{array}} \right] $$ (4) 两者相减得到对应的视线方向
$\overrightarrow {p{o_t}p{o_1}} $ 的投影:$$ \Delta E\left( {p{o_1},p{o_t}} \right) = \left[ {E\left( {p{o_1}} \right) - E\left( {p{o_t}} \right)} \right] $$ (5) 则
$p{o_1}$ 和$p{o_t}$ 的空间距离可以表示为:$$ dis\left( {p{o_1},p{o_t}} \right) = norm\left( {\Delta E\left( {p{o_1},p{o_t}} \right),2} \right) $$ (6) 同理,可以得到
$p{o_2}$ 和$p{o_t}$ 的空间距离:$$ dis\left( {p{o_2},p{o_t}} \right) = norm\left( {\Delta E\left( {p{o_2},p{o_t}} \right),2} \right) $$ (7) 则
${t_2}$ 时刻图像相比${t_1}$ 时刻图像的比例变化为:$$ k = \frac{{dis\left( {p{o_1},p{o_t}} \right)}}{{dis\left( {p{o_2},p{o_t}} \right)}} $$ (8) (2)姿态变化模型
目标点的成像位置会随着飞行器姿态的改变而对应改变,因此,在假设两帧图像具有相同地理系的条件下,可以通过空间坐标系的转换建立姿态变化模型。根据
${t_1}$ 时刻图像坐标系下的位置$\left( {{u_1},{v_1}} \right)$ ,得到成像平面坐标系的坐标$\left( { - {u_1} + {U_0},{v_1} - {V_0}} \right)$ ,其中$\left( {{U_0},{V_0}} \right)$ 为成像平面坐标系的原点$O$ 在图像坐标系下的坐标。根据摄像机的焦距$f$ (或者称为空间分辨率,单位:pixel)可以得到视线在摄像机系(飞行器系)下的坐标为:$$ {m_b} = \left[ {\begin{array}{*{20}{c}} f \\ { - {u_1} + {U_0}} \\ {{v_1} - {V_0}} \end{array}} \right] $$ (9) 考虑到摄像机在水平方向焦距
${f_v}$ 与垂直方向焦距${f_u}$ 一般大小不同,统一换算到${f_v}$ 分辨率下飞行器系坐标,记为:$$ {m_{{b_1}}} = \left[ {\begin{array}{*{20}{c}} {{f_v}} \\ {\left( { - {u_1} + {U_0}} \right){f_v}/{f_u}} \\ {{v_1} - {V_0}} \end{array}} \right] $$ (10) 同理,根据坐标转换,
${t_2}$ 时刻待求的位置$\left( {{u_2},{v_2}} \right)$ 在飞行器系下的坐标为:$$ {m_{{b_2}}} = \left[ {\begin{array}{*{20}{c}} {{f_v}} \\ {\left( { - {u_2} + {U_0}} \right){f_v}/{f_u}} \\ {{v_2} - {V_0}} \end{array}} \right] $$ (11) 根据
${t_1}$ 时刻的四元素${q^1} = \left[ {q_0^1,q_1^1,q_2^1,q_3^1} \right]$ ,可以计算飞行器系到地理系的转换矩阵:$$ R_{({b_1})}^n = \left[ {\begin{array}{*{20}{c}} {q_0^1q_0^1 + q_1^1q_1^1 - q_2^1q_2^1 - q_3^1q_3^1}&{2(q_1^1q_2^1 + q_0^1q_3^1)}&{2(q_1^1q_3^1 - q_0^1q_2^1)} \\ {2(q_1^1q_2^1 - q_0^1q_3^1)}&{q_0^1q_0^1 - q_1^1q_1^1 + q_2^1q_2^1 - q_3^1q_3^1}&{2(q_2^1q_3^1 + q_0^1q_1^1)} \\ {2(q_1^1q_3^1 + q_0^1q_2^1)}&{2(q_2^1q_3^1 - q_0^1q_1^1)}&{q_0^1q_0^1 - q_1^1q_1^1 - q_2^1q_2^1 + q_3^1q_3^1} \end{array}} \right] $$ (12) 根据
${t_2}$ 时刻的四元素${q^2} = \left[ {q_0^2,q_1^2,q_2^2,q_3^2} \right]$ ,可以计算地理系到${t_2}$ 时刻飞行器系的转换矩阵:$$ R_n^{({b_2})} = \left[ {\begin{array}{*{20}{c}} {q_0^2q_0^2 + q_1^2q_1^2 - q_2^2q_2^2 - q_3^2q_3^2}&{2(q_1^2q_2^2 - q_0^2q_3^2)}&{2(q_1^2q_3^2 + q_0^2q_2^2)} \\ {2(q_1^2q_2^2 + q_0^2q_3^2)}&{q_0^2q_0^2 - q_1^2q_1^2 + q_2^2q_2^2 - q_3^2q_3^2}&{2(q_2^2q_3^2 - q_0^2q_1^2)} \\ {2(q_1^2q_3^2 - q_0^2q_2^2)}&{2(q_2^2q_3^2 + q_0^2q_1^2)}&{q_0^2q_0^2 - q_1^2q_1^2 - q_2^2q_2^2 + q_3^2q_3^2} \end{array}} \right] $$ (13) 那么,可以得到视线在
${t_2}$ 时刻飞行器系的三个分量:$$ \left[ {\begin{array}{*{20}{c}} {{s_x}\left( {{u_1},{v_1}} \right)} \\ {{s_y}\left( {{u_1},{v_1}} \right)} \\ {{s_z}\left( {{u_1},{v_1}} \right)} \end{array}} \right] = R_n^{{b_2}}R_{{b_1}}^n{m_{{b_1}}} $$ (14) 根据飞行器系坐标系和焦距的定义,这三个分量与
${t_2}$ 时刻待求位置$\left( {{u_2},{v_2}} \right)$ 的飞行器系下的坐标成比例:$$ \left[ {\begin{array}{*{20}{c}} {{s_x}\left( {{u_1},{v_1}} \right)} \\ {{s_y}\left( {{u_1},{v_1}} \right)} \\ {{s_z}\left( {{u_1},{v_1}} \right)} \end{array}} \right] = K{m_{{b_2}}} = K\left[ {\begin{array}{*{20}{c}} {{f_v}} \\ {\left( { - {u_2} + {U_0}} \right){f_v}/{f_u}} \\ {{v_2} - {V_0}} \end{array}} \right] $$ (15) 上式的解可写为:
$$ \left\{ {\begin{array}{*{20}{c}} {K = \dfrac{{{s_x}\left( {{u_1},{v_1}} \right)}}{{{f_v}}}} \\ { - {u_2} + {U_0} = \dfrac{{{s_y}\left( {{u_1},{v_1}} \right){f_u}}}{{K{f_v}}}} \\ {{v_2} - {V_0} = \dfrac{{{s_z}\left( {{u_1},{v_1}} \right)}}{K}} \end{array}} \right. $$ (16) 由于比例模型为成像平面坐标系下图像的比例参数,为此,在成像平面下定义两帧之间像素点的姿态模型为:
$$ \begin{split} \\ \left[ {\begin{array}{*{20}{c}} { - {u_2} + {U_0}} \\ {{v_2} - {V_0}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{F_u}\left( {{u_1},{v_1}} \right)} \\ {{F_v}\left( {{u_1},{v_1}} \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\dfrac{{{s_y}\left( {{u_1},{v_1}} \right){f_u}}}{{{s_x}\left( {{u_1},{v_1}} \right)}}} \\ {\dfrac{{{s_z}\left( {{u_1},{v_1}} \right){f_v}}}{{{s_x}\left( {{u_1},{v_1}} \right)}}} \end{array}} \right] \end{split} $$ (17) (3)视角变化模型
飞行器位置的变化还体现了两帧之间飞行器和目标视角的变化。为此,可以根据飞行器之间的空间位置关系建立视角变化模型。根据公式(3)可以得出
$p{o_1}$ 和$p{o_2}$ 在地心系下的坐标为$E\left( {p{o_1}} \right)$ 和$E\left( {p{o_2}} \right)$ ,两者相减得到对应的视角变化矢量$\overrightarrow {p{o_1}p{o_2}} $ 的投影:$$ \Delta E\left( {p{o_2},p{o_1}} \right) = \left[ {E\left( {p{o_2}} \right) - E\left( {p{o_1}} \right)} \right] $$ (18) 从地心系到地理系的转换矩阵可以表示为:
$$ R_o^n = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} { - \sin {L_2}\cos {\lambda _2}} \\ {\cos {L_2}\cos {\lambda _2}} \\ { - \sin {L_2}} \end{array}}&{\begin{array}{*{20}{c}} { - \sin {L_2}\sin {\lambda _2}} \\ {\cos {L_2}\sin {\lambda _2}} \\ {\cos {\lambda _2}} \end{array}}&{\begin{array}{*{20}{c}} {\cos {L_2}} \\ {\sin {L_2}} \\ 0 \end{array}} \end{array}} \right] $$ (19) 根据公式(13)中从地理系到
${t_2}$ 时刻飞行器系的转换矩阵$R_n^{{b_2}}$ ,可以得到视角变化矢量在飞行器系下的三个分量:$$ \left[ {\begin{array}{*{20}{c}} {\Delta {t_x}} \\ {\Delta {t_y}} \\ {\Delta {t_z}} \end{array}} \right] = R_n^{{b_2}}R_o^n\Delta E\left( {p{o_2},p{o_1}} \right) $$ (20) 式中:
$\Delta {t_y}$ 和$\Delta {t_z}$ 分别表示在飞行器坐标系下垂直方向和水平方向的增量,m。由于$\Delta {t_x}$ 表示景深的变化量,无法与成像平面坐标系像素进行对应。用${t_2}$ 时刻的弹目距离$dis\left( {p{o_2},p{o_t}} \right)$ 进行替代,则焦距和像素的对应关系为:$$ \left[ {\begin{array}{*{20}{c}} {dis\left( {p{o_2},p{o_t}} \right)} \\ {\Delta {t_y}} \\ {\Delta {t_z}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{f_v}} \\ {\Delta {u_v}\dfrac{{{f_v}}}{{{f_u}}}} \\ {\Delta v} \end{array}} \right] $$ (21) 可以得出视角变化模型为:
$$ \left[ {\begin{array}{*{20}{c}} {\Delta u} \\ {\Delta v} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\dfrac{{\Delta {t_y}{f_u}}}{{dis\left( {p{o_2},p{o_t}} \right)}}} \\ {\dfrac{{\Delta {t_z}{f_v}}}{{dis\left( {p{o_2},p{o_t}} \right)}}} \end{array}} \right] $$ (22) (4) LPI模型
综上所述,可以得到最终的变化模型为:
$$ \left[ {\begin{array}{*{20}{c}} { - {u_2} + {U_0}} \\ {{v_2} - {V_0}} \end{array}} \right] = k\left[ {\begin{array}{*{20}{c}} {{F_u}\left( {{u_1},{v_1}} \right)} \\ {{F_v}\left( {{u_1},{v_1}} \right)} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} {\Delta u} \\ {\Delta v} \end{array}} \right] $$ (23) 化简可以得到:
$$ \left\{ {\begin{array}{*{20}{l}} {{u_2} = - k{F_u}\left( {{u_1},{v_1}} \right) + \Delta u + {U_0}} \\ {{v_2} = k{F_v}\left( {{u_1},{v_1}} \right) - \Delta v + {V_0}} \end{array}} \right. $$ (24) -
基于增量惯导信息的位置预测模型可实现对场景变化的准确建模,结合弱小目标的灰度奇异性和时间运动性,文中提出了一种增量惯导信息辅助的空地红外弱小移动目标检测算法,实现了对高动态条件下目标的可靠检测,算法的步骤包括:(1)利用增量惯导信息把相关历史图像校正到当前帧对应飞行器位姿下的成像;(2)利用相关算法计算历史图像与当前帧的平移参数;(3)通过高斯加权对校正后的图像背景建模;(4)采用最大类间方差法对差值图像进行阈值分割,检测移动目标。
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假设当前帧为图像的第
$n$ 帧,利用增量惯导信息的预测模型对前$m$ 帧图像的每个像素进行预测,校正到当前帧姿态下的成像,然后再通过计算平移参数得到精确的图像配准信息,为后续的背景估计提供基准。图2为校正某一帧实时图的结果,图2(a)为当前时刻(第10帧)的实时图,图2(b)为第8帧的图像,图2(c)为将第8帧图像校正到当前帧飞行器姿态下的图像。 -
通过选择兴趣区域,采用归一化积相关算法计算平移参数,实现两帧图像的精确配准。根据跟踪波门的限制,选择的兴趣区域R应该同样存在于前9帧的绝大多数帧中。如图3所示,图3(a)为当前帧,选择在中心区域截取一个101×101的区域作为兴趣区域(红色边框内区域)。对于第n帧兴趣区域与校正后的第n−1帧相关匹配,对n−1帧的搜索区域选择为第n帧兴趣区域中心点周围33×33的范围内。如图3(a)所示,蓝色边框内区域表示搜索范围,而红色边框内为兴趣区域。图3(b)表示所有33×33次相关运算的相关系数曲面,通过求解最大值便可得到平移参数。
如果整视场搜索,会有1089次的相关计算,计算量相对较大。为了尽可能缩短匹配时间,文中采用爬山法的搜索策略,等间隔设置爬山者的起始点,爬山方向为上、下、左、右四个方向,如图3(c)所示,在搜索区域等间距的设置了9个爬山者,并通过不同的表示方式显示了9个爬山者的爬行轨迹,红色的五角星表示最终计算得到的匹配位置。可以看出,爬山法大幅提升了搜索速度,只进行了137次相关运算就找到了局部极值。由于感兴趣区域显著大于爬山间隔,爬山法得到的局部极值就是全局最优值。
通过基于爬山的互相关匹配算法找到了n−1帧和n帧的平移参数,那么对于n−2帧的互相关匹配运算,其搜索范围中心就设定n−1帧的匹配位置,然后在周围选择33×33作为搜索范围。依此类推,通过爬山法的互相关匹配算法便可以得到前m帧相对于当前帧的平移参数。
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为解决飞行器运动带来构建背景模型困难的问题,文中将实时对背景进行估计和建模。一般利用前m(m=9)帧来估计当前帧的背景。如果以当前帧的左上角为坐标原点,按照平移参数将前m帧转换至当前帧的坐标,并截取当前帧相同大小的区域来进行背景估计。图4列出了其中3帧的结果。可以看出,图像中的每个像素位置都是一一对应的,可以通过这些图像准确地估计背景。
图5为(87,68)和(200,180)两点(位置在图4中用十字标出)在前9帧和当前帧的灰度值分布。可以看出,如果有弱小移动目标经过该像素点,该像素点的灰度有较大的变化。文中采用一种高斯加权的方法来进行背景估计。若某帧的
$\left| {I\left( {x,y} \right) - average} \right| \gt T$ ,表明目标经过了该像素点,就用均值average来替代这帧中该像素点的灰度值。考虑到飞行器运动过程中整个图像的灰度值会发生变化,设计的高斯加权策略为越靠近当前帧,其权值越大。图6给出了高斯加权曲线和最后估计的背景图像。 -
对当前帧与估计背景的差分图像进行阈值分割,便可以有效检测出弱小移动目标。采用经典的OSTU算法,阈值可表示为:
$$ {d_B}\left( t \right) = {\omega _0}{\left| {{\mu _0} - \mu } \right|^2} + {\omega _1}{\left| {{\mu _1} - \mu } \right|^2} $$ (25) 取
${d_B}$ 最大时对应的阈值$u$ 便为最优的分割阈值。
Infrared dim moving target detection algorithm assisted by incremental inertial navigation information in highdynamic air to ground background (Invited)
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摘要: 红外弱小移动目标检测技术是计算机视觉的研究热点和难点。针对机载高动态条件下的空地目标检测存在的场景变化动态、背景干扰强度大、目标运动规律未知等挑战,提出了一种新型的基于增量惯导信息辅助的空地红外弱小移动目标检测算法。为了解决传统惯导信息预测的漂移误差问题,提出了增量惯导信息概念,设计了增量惯导信息的位置预测模型,实现了对目标点的准确预测。构建了基于增量惯导信息辅助与背景差分的移动目标检测框架,通过增量惯导信息对不同位姿下的成像进行校正,引入基于爬山法互相关匹配算法计算校正后图像的平移参数,采用高斯加权对背景图像进行估计,最后通过图像分割检测弱小移动目标。仿真实验验证了文中设计检测算法的有效性和精确性。Abstract: Infrared dim moving target detection technology is a hot and difficult research area in computer vision. To deal with the challenges of target detection with airborne in high dynamic air to ground background, such as dynamic scene change, large background interference intensity and unknown target motion law, a novel incremental inertial navigation information assisted air to ground infrared dim moving target detection algorithm was proposed. To solve the drift error problem of traditional inertial navigation information prediction, the concept of incremental inertial navigation information was put forward. The location prediction model of incremental inertial navigation information (LPI) was designed and the accurate prediction of the target point was achieved. A moving target detection framework was constructed based on inertial navigation information assistance and background difference, which corrected the images under different positions and attitudes by LPI. The cross correlation matching algorithm based on mountain climbing method was introduced to calculate the translation parameters, and Gaussian weighting was used to estimate the background. The dim moving target could be detected by adaptive threshold segmentation. The simulation experiments verified the effectiveness and accuracy of the proposed detection algorithm.
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