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根据遥感成像原理,可以建立起植被覆盖情况下传感器接收的像元线性光谱混合模型:
$ \begin{array}{*{20}{c}} {X(\lambda ) = K{L_j}(\lambda ) = }\\ {K\left\{ {\sum\limits_{j = 1}^m {{F_j}} {L_j}(\lambda ) + {L_{{\rm{veg}}}}(\lambda ){r_{{\rm{veg}}}}} \right\}} \end{array} $
(1) 式中, Lj(λ)表示第j种物质在波长λ上的辐射亮度;Lveg(λ)为植被端元在波长λ上的辐射亮度;Fj为第j种物质在像元中所占的面积比,且$\sum\limits_{j=1}^{m} F_{j}=1$;m为端元数目;tj为不同端元物质辐射的大气透射率;K为仪器和大气参量;rveg为植被丰度,亦即植被密度。
将植被看作一种端元,混合像元光谱率反射信号X(λ)可以表示为:
$ X(\lambda)=\sum\limits_{j=1}^{m} \alpha_{j} e_{j}(\lambda)+r_{\mathrm{veg}} e_{\mathrm{veg}}(\lambda)+\varepsilon=\\ \sum\limits_{j=1}^{m+1} \alpha_{j}^{\prime} e_{j}^{\prime}(\lambda)+\varepsilon, \left(\sum\limits_{j=1}^{m+1} \alpha_{j}^{\prime}=1, 0 \leqslant \alpha_{j}^{\prime} \leqslant 1\right) $
(2) 式中, ej(λ)为其它地物光谱的辐射亮度,eveg(λ)为植被光谱的辐射亮度,αj为第j种端元的丰度,且有所有端元丰度均大于0且和为1,ε为噪声影响, ej′(λ)是将植被端元看作一个普通端元后的每一个地物光谱的辐射亮度,αj′代表其中每一个地物端元的丰度,且1≤j≤m+1。将光谱信号写成矩阵形式,有:
$ \boldsymbol{X}_{p \times N}=\boldsymbol{E}_{p \times(m+1)} \boldsymbol{A}_{(m+1) \times N}+\boldsymbol{e}_{p \times N} $
(3) 式中, Xp×N是包含p个波段、N个像元的图像矩阵,Ep×(m+1)和A(m+1)×N分别为包含植被端元的端元矩阵和丰度矩阵,ep×N为误差矩阵。通过以上表达式即可对高光谱图像进行线性解混[11]。
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植被对观测光谱的影响主要体现在两个方面:(1)太阳光经植被反射后,进入到传感器,成为植被端元反射光谱;(2)地物的反射光谱经植被衰减后到达传感器,形成地物的透射光谱。这里假设植被覆盖区域变化缓慢,且透射率恒定;忽略地物反射光在植被间多次散射和吸收的情况[12-13]。
基于以上分析作出两点基本假设:(1)植被自身所产生的反射光谱通过反射率加以表达;对植被覆盖下区域地物反射光谱所产生的衰减效应通过透射率加以表达[14], 对于给定像元,植被的反射率与该像元中植被所占比例即植被端元的丰度值成正相关,植被的透射率与该像元中植被所占比例即植被端元的丰度值成负相关; (2)植被的反射率和透射率均非负,且两者之和为定值。若植被稀疏,则反射率较低,而对其它地物反射光谱的透射率较高; 反之若植被茂密,则植被的反射率较高,而对其它地物反射光谱的透射率较低。
在此基础上,令植被区域透射率为tveg,成像模型可改进为:
$ \begin{array}{c} X(\lambda)=K L_{j}(\lambda)= \\ K\left\{\left[\sum\limits_{j=1}^{m} F_{j} L_{j}(\lambda)\right] t_{\mathrm{veg}}+L_{\mathrm{veg}}(\lambda) r_{\mathrm{veg}}\right\} \end{array} $
(4) 式中,tveg+rveg=1,且均为非负。
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根据提出的植被覆盖区域的光谱混合模型,即可对图像进行植被端元去除实验,流程如图 1所示。
对于获取的一幅去除条带等噪声后的高光谱图像,为了去除植被端元,就要先从图像中提取出植被端元。
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在确定图像端元后,就可以提取植被和其它地物的端元。为提高复杂背景的检测效率,避免过多端元对于背景简化效果的影响,直接在影像数据中分离出几个分别包含主要地物的窗格,进而采用端元提取算法,基于几何学的顶点成分分析(vertex component analysis,VCA)算法来进行端元矩阵Ep×(m+1)的计算[8]。
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获取了端元矩阵Ep×(m+1)后,通过丰度反演的方法求解出光谱图像Xp×N中每个像素中各个端元所占的比例。为简化模型,选择忽略(3)式中的误差项,得到如下式子:
$ \boldsymbol{X}_{p \times N}=\boldsymbol{E}_{p \times(m+1)} \boldsymbol{A}_{(m+1) \times N} $
(5) 用全约束最小二乘法求解(5)式中的丰度矩阵A(m+1)×N。
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此时可去除植被端元的成分,为避免去除端元后导致图像亮度整体下降,对其它地物端元进行调整:
$ \tilde{\alpha}_{j}=\frac{\alpha_{j}}{\sum\limits_{j=1}^{m} \alpha_{j}} $
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去端元效果的好坏,主要体现在图像亮度的变化和图像细节的丰富程度,本文中选取标准差[16]和全变分[17]的方法对3幅图像目标区域进行定量分析。定义图像中每一个像元的辐射度为u(i, k),图像大小为W×H,两个评价指标可以如下表示。
标准差:
$ S=\sqrt{\frac{1}{W \times H} \sum\limits_{k=1}^{n} \sum\limits_{i=1}^{n}[u(i, k)-\bar{u}]^{2}} $
(7) 式中, $\bar{u}$代表整个图像辐射度的平均值。
全变分:
$ \begin{aligned} T=& \sum\limits_{k=1}^{H} \sum\limits_{i=1}^{W}[|u(i+1, k)-u(i, k)|+\\ &|u(i, k+1)-u(i, k)|] \end{aligned} $
(8) 图像的标准差和全变分值越大,表明图像对比度越高,即检测效果越好。
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在原始野外驻训地图像、第54波段图像、第14波段图像、去端元图像以及多次去端元图像的目标区域分别选取10×10大小的窗格作为评价对象,通过标准差及全变分计算得到结果, 如表 1所示。
Table 1. Comparison of mixing accuracy
S T original field resident image 461.3 14804 image at 54th band 2219.4 202215 image at 14th band 2867.6 301862 remove end member image 3324.3 373388 remove end member image multiple times 3908.4 479536 由表 1可知,去端元图像对于目标的检测效果较原始图像提升10倍以上,单独选取第54波段、第14波段图像进行检测也能取得较好的结果,但是去端元图像、多次去端元图像相对于与两个波段图像相比,检测效果仍然有很大程度的提升。
在复杂背景条件下,端元去除的方法不考虑所有端元的丰度信息,而是通过去除主要端元丰度的方法实现背景简化的效果[18]。实验表明,该方法能够增强地物间的差异性,将目标从背景环境中分离出来,从而达到目标检测的目的。为了进一步说明本文中算法在目标检测方面的检测性能,接下来绘制接收者操作特性(receiver operating characteristic,ROC)曲线进行比较。ROC曲线能够观察算法正确地识别正例的比例与模型错误地把负例识别成正例的比例之间的权衡,曲线越接近左上角,算法的性能越好。
由图 7可以明显看出,本文中提出方法的检测性能要优于传统的RX算法。目前高光谱图像在揭露伪装方面的研究大都利用光谱匹配方法,但该方法需要大量的先验知识,应用于作战时,需要大量的敌目标及伪装网等的表面光谱数据[19],在当前的技术条件下实现难度较大, 且该方法不适用于复杂背景环境下搜寻目标,工作量大且检测结果不完全精确。本文中提出的基于解混技术的端元去除方法,技术路线简单明了、适用性强,对于模拟战场环境的目标检测有很强的实践意义。
基于线性解混的高光谱图像目标检测研究
Research of target detection of hyperspectral images in complex background based on linear unmixing
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摘要: 高光谱图像的空间分辨率普遍较低,导致混合像元大量存在,为目标检测带来了一定困难。为了实现复杂背景下的高光谱图像目标检测,提出了一种去端元的目标检测方法。在光谱解混技术的基础上,建立了复杂背景下的光谱混合模型并加以改进,采用多次去端元的方法,取得了简化背景之后的高光谱图像。结果表明,与传统的RX目标检测算法相比,所提出的算法能够显著提升目标检测效果。在实际的军事运用中,为大尺幅图像的目标识别和揭露伪装提供了思路。Abstract: The spatial resolution of hyperspectral images was generally low. As a result, a large number of mixed pixels existed. It brought some difficulties to target detection. In order to realize target detection in hyperspectral images under complex background, a target detection method based on de-endmember was proposed. On the basis of spectral de-mixing technology, the spectral mixing model under complex background was established and improved. The method of removing endpoints many times was adopted. The hyperspectral image after simplified background was obtained. The results show that, compared with the traditional RX target detection algorithm, the proposed algorithm can significantly improve the performance of target detection. In practical military applications, it provides a train of thought for target recognition and camouflage exposure of large-scale images.
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Key words:
- spectroscopy /
- hyperspectral images /
- remove end members /
- target detection
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Table 1. Comparison of mixing accuracy
S T original field resident image 461.3 14804 image at 54th band 2219.4 202215 image at 14th band 2867.6 301862 remove end member image 3324.3 373388 remove end member image multiple times 3908.4 479536 -
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