CN102708544A

CN102708544A - Spectral angle mapping method used for correcting negative correlation of hyperspectral remote sensing image by wavebands

Info

Publication number: CN102708544A
Application number: CN2012101183640A
Authority: CN
Inventors: 郭雷; 王瀛; 梁楠
Original assignee: Northwestern Polytechnical University
Current assignee: Nantong Jiumao Clothing Co Ltd; Northwestern Polytechnical University
Priority date: 2012-04-21
Filing date: 2012-04-21
Publication date: 2012-10-03
Anticipated expiration: 2032-04-21
Also published as: CN102708544B

Abstract

The present invention proposes a spectral angle mapping method for correcting negative correlation band by band. The technical features are as follows: firstly, the calculation of the traditional spectral angle is carried out, and the value of the newly added spectral band is used as an independent variable, and it is judged band by band whether there is Negative correlation, and give correction parameters for the bands that produce negative correlation. This method mainly focuses on solving the phenomenon that the traditional spectral angle mapping method cannot distinguish the negative correlation between the spectra, which leads to the phenomenon that the spectral curves with different characteristics are equivalent to the same type when compared to a certain reference spectrum. The experiment of this method proves that the method proposed by the present invention can effectively increase the separability between the spectra. For the spectral vectors that cannot be separated by the traditional spectral angle mapping method, they can be separated in stages according to the different negative correlation bands, which is the follow-up high-quality method. The basis for applications such as spectral remote sensing image classification and object recognition.

Description

Spectral Angle Mapping Method for Band-by-Band Correction of Negative Correlation in Hyperspectral Remote Sensing Images

技术领域 technical field

本发明涉及一种用于高光谱遥感图像逐波段修正负相关的光谱角填图方法，用于高光谱遥感图像的光谱相似性度量，属于高光谱遥感数字图像处理和模式识别领域。逐波段修正负相关后的光谱角可以更好的反映相近光谱间的相似关系，增强光谱间的可分性，是更精细的光谱相似性度量手段，可以用于高光谱遥感图像中分类、目标识别等应用领域。The invention relates to a spectral angle mapping method for correcting negative correlation band by band of hyperspectral remote sensing images, which is used for spectral similarity measurement of hyperspectral remote sensing images, and belongs to the field of hyperspectral remote sensing digital image processing and pattern recognition. The spectral angle after correcting the negative correlation band by band can better reflect the similarity relationship between similar spectra and enhance the separability between spectra. applications such as recognition.

背景技术 Background technique

高光谱成像仪可以获取的某一地域高光谱数据包含空间、光谱、辐射等多重信息，是遥感领域的前沿技术。分类是高光谱图像处理领域中一个重要的研究方向，在地物识别、对某地区地物分布进行精确划分以及对某地区地物改变进行探测等方面都有广泛的应用。高光谱图像传感器可以提供更广泛的光谱波段范围和更为细致的光谱特性，是高光谱遥感图像分类具有良好应用前景的保障，同时也是设计分类算法的难点所在。在对高光谱遥感图像进行分类时，主要涉及两方面的问题：一是选用何种光谱相似性度量方法，二是基于特定光谱相似性度量方法的分类策略。由此可以看出，如何判断两条光谱曲线的相似性，即光谱相似性度量方法，在高光谱遥感图像分类中占有举足轻重的地位。The hyperspectral data of a certain region that can be acquired by hyperspectral imagers contains multiple information such as space, spectrum, and radiation, and is a cutting-edge technology in the field of remote sensing. Classification is an important research direction in the field of hyperspectral image processing, and it has a wide range of applications in the recognition of ground features, the precise division of the distribution of ground features in a certain area, and the detection of changes in ground features in a certain area. The hyperspectral image sensor can provide a wider range of spectral bands and more detailed spectral characteristics, which is a guarantee for the good application prospects of hyperspectral remote sensing image classification, and it is also the difficulty of designing classification algorithms. When classifying hyperspectral remote sensing images, it mainly involves two aspects: one is which spectral similarity measurement method to choose, and the other is the classification strategy based on a specific spectral similarity measurement method. It can be seen from this that how to judge the similarity of two spectral curves, that is, the spectral similarity measurement method, plays an important role in the classification of hyperspectral remote sensing images.

目前存在的光谱相似性度量方法可以根据其侧重点分为以下几类：以光谱信号协方差矩阵为基础计算两个光谱样本相似度的马氏距离(Mahalanobis Distance，MD)；以信息论为基础衡量两个光谱样本相对熵值的光谱信息散度(Spectral InformationDivergence，SID)；在光谱特征空间中衡量两个光谱向量空间距离的最小欧式距离(Euclidean Minimum Distance，EMD)以及衡量两个光谱向量夹角的光谱角填图(Spectral Angle Mapper，SAM)等。其中SAM采用特征空间中两个光谱向量间的夹角作为光谱相似性度量，角度越小，表明两条光谱越相似。自SAM算法提出以来，因其简单高效、标量乘不变性等优点在地物标定、植被研究、高光谱图像压缩、地物光谱变化检测等方面得到了广泛的应用。The existing spectral similarity measurement methods can be divided into the following categories according to their focus: calculate the Mahalanobis distance (Mahalanobis Distance, MD) of the similarity between two spectral samples based on the spectral signal covariance matrix; The spectral information divergence (Spectral Information Divergence, SID) of the relative entropy value of two spectral samples; the minimum Euclidean distance (Euclidean Minimum Distance, EMD) to measure the spatial distance of two spectral vectors in the spectral feature space and the angle between two spectral vectors Spectral Angle Mapper (SAM) etc. Among them, SAM uses the angle between two spectral vectors in the feature space as the measure of spectral similarity, and the smaller the angle, the more similar the two spectra are. Since the SAM algorithm was proposed, it has been widely used in ground object calibration, vegetation research, hyperspectral image compression, and ground object spectral change detection due to its advantages of simplicity, efficiency, and scalar multiplication invariance.

然而SAM最终用一个标量来表示几十甚至上百波段光谱向量间的相似性，有着如下几点局限性：SAM中全部光谱都参与运算，大部分次要光谱的相似性会压制少数特征光谱之间的差异而造成SAM最终输出结果整体偏小，给后续的分类以及类间阈值的设定带来困难；SAM对每个光谱的加性因子敏感，这会给最终的输出带来不确定性；SAM无法分辨两个光谱向量间的正负相关，这使得相对于某一参考光谱，不同的光谱可能得到相同的角度值，最终造成误分、虚警率过高等现象。目前针对SAM内在的缺陷，一些改进的算法相继出现，BAO-SAM(Band add-on SAM)对光谱向量中的分量进行选择，用产生最大光谱角的分量代表整个光谱，增大了光谱间和类间的可分性；SCM(Spectral Correlation Mapper)和RAF-SAM(Removed Additive Factor SAM)都考虑了SAM对加性因子敏感的特点，前者用光谱向量减去均值向量，后者寻找产生最大光谱角的加性因子，两种算法在一定程度上都降低了虚警率；KSAC(KernelSpectralAngel Cosine)和NSAM(Nonlinear SAM)通过核函数将光谱向量非线性映射到高维特征空间再求光谱角，可以增大角度值，从而达到增大分类阈值可选择范围的效果。However, SAM finally uses a scalar to represent the similarity between dozens or even hundreds of band spectral vectors, which has the following limitations: all spectra in SAM are involved in the calculation, and the similarity of most secondary spectra will suppress the difference between a few characteristic spectra. The final output of SAM is relatively small due to the difference between them, which brings difficulties to the subsequent classification and the setting of the threshold between classes; SAM is sensitive to the additive factor of each spectrum, which will bring uncertainty to the final output ; SAM cannot distinguish the positive and negative correlation between two spectral vectors, which makes it possible for different spectra to obtain the same angle value relative to a certain reference spectrum, which eventually leads to misclassification and high false alarm rate. At present, in view of the inherent defects of SAM, some improved algorithms have emerged one after another. BAO-SAM (Band add-on SAM) selects the components in the spectral vector, and uses the component that produces the largest spectral angle to represent the entire spectrum, which increases the inter-spectral sum. Separability between classes; SCM (Spectral Correlation Mapper) and RAF-SAM (Removed Additive Factor SAM) both consider the characteristics of SAM's sensitivity to additive factors. The former uses the spectral vector to subtract the mean vector, and the latter seeks to generate the maximum spectrum. The additive factor of the angle, both algorithms reduce the false alarm rate to a certain extent; KSAC (KernelSpectralAngel Cosine) and NSAM (Nonlinear SAM) use the kernel function to nonlinearly map the spectral vector to the high-dimensional feature space and then calculate the spectral angle. The angle value can be increased to achieve the effect of increasing the selectable range of the classification threshold.

上述改进算法均能在一定程度上优化SMA算法的性能，同时也各有不足，BAO-SAM选取的波段子集，未必是表征整个光谱的最佳子集；而SCM和RAF-SAM在一定程度上改变了光谱数值，破坏了光谱与实际地物的对应关系；KSAC和NSAM通过非线性映射放大了光谱角度值，同时也放大了负相关的影响。The above-mentioned improved algorithms can optimize the performance of the SMA algorithm to a certain extent, but they also have their own shortcomings. The subset of bands selected by BAO-SAM may not be the best subset to characterize the entire spectrum; The spectral value is changed on the surface, which destroys the corresponding relationship between the spectrum and the actual ground objects; KSAC and NSAM amplify the spectral angle value through nonlinear mapping, and also amplify the influence of negative correlation.

所谓SAM算法中的负相关，指用光谱向量夹角表征全光谱相似度时，因最终角度值和每一波段的光谱数值呈非线性相关，而由此造成的不同光谱产生同一角度值的现象。The so-called negative correlation in the SAM algorithm refers to the phenomenon that different spectra produce the same angle value due to the nonlinear correlation between the final angle value and the spectral value of each band when the spectral vector angle is used to represent the full spectrum similarity .

发明内容 Contents of the invention

要解决的技术问题technical problem to be solved

为了避免现有技术的不足之处，本发明提出一种用于高光谱遥感图像逐波段修正负相关的光谱角填图方法，针对传统SAM算法负相关造成的光谱相似性误判问题，对SAM公式进行分析，将SAM求出的光谱角作为原始光谱角，给出公式逐波段展开形式，并根据每一波段对光谱角造成的影响判断该波段是否为负相关，然后对造成负相关的波段加以修正，最终达到去除负相关的效果。本发明提出的MNC-SAM可以有效地分离传统SAM算法错误等同的光谱向量，较之SAM算法，是更精确的光谱相似性度量手段，是后续分类、目标识别的基础。In order to avoid the deficiencies of the prior art, the present invention proposes a spectral angle mapping method for correcting negative correlation of hyperspectral remote sensing images band by band, aiming at the problem of misjudgment of spectral similarity caused by negative correlation of traditional SAM algorithm. Analyze the formula, take the spectral angle obtained by SAM as the original spectral angle, give the formula band-by-band expansion form, and judge whether the band is negatively correlated according to the impact of each band on the spectral angle, and then determine the negatively correlated band It is corrected to finally achieve the effect of removing negative correlation. The MNC-SAM proposed by the invention can effectively separate the wrongly equivalent spectral vectors of the traditional SAM algorithm. Compared with the SAM algorithm, it is a more accurate measure of spectral similarity and is the basis for subsequent classification and target recognition.

技术方案Technical solutions

一种用于高光谱遥感图像逐波段修正负相关的光谱角填图方法，其特征在于步骤如下：A spectral angle mapping method for correcting negative correlation band by band of hyperspectral remote sensing images, characterized in that the steps are as follows:

步骤1：对于一幅高光谱遥感图像I＝f(x，y，n)，(x，y)∈Z²为空间分辨率，n为光谱波段数。针对图像中待判定光谱向量x_n和已知参考光谱向量r_n，根据SAM算法定义，得出两个光谱向量之间的原始光谱角

Step 1: For a hyperspectral remote sensing image I = f(x, y, n), (x, y) ∈ Z ² is the spatial resolution, and n is the number of spectral bands. According to the spectral vector x _n to be determined and the known reference spectral vector r _n in the image, according to the definition of the SAM algorithm, the original spectral angle between the two spectral vectors is obtained

${θ θ}_{{r r}_{n no},, {x x}_{n no}} = = {cos cos}^{- - 11} \frac{< < {r r}_{n no},, {x x}_{n no} > >}{| | | | {r r}_{n no} | | | | | | | | {x x}_{n no} | | | |}$

步骤2：展开步骤1的公式，得出原始光谱角的分波段形式

Step 2: Expand the formula in step 1 to obtain the sub-band form of the original spectral angle

${θ θ}_{{r r}_{m m + + 11},, {x x}_{m m + + 11}} = = {cos cos}^{- - 11} [[cos cos {θ θ}_{{r r}_{m m},, {x x}_{m m}} \frac{< < {r r}_{m m + + 11},, {r r}_{m m} > >}{| | | | {r r}_{m m + + 11} | | | | | | | | {r r}_{m m} | | | |} \frac{< < {x x}_{m m + + 11},, {x x}_{m m} > >}{| | | | {x x}_{m m + + 11} | | | | | | | | {x x}_{m m} | | | |} ((11 + + \frac{< < {r r}_{+ + 11},, {x x}_{+ + 11} > >}{< < {r r}_{m m},, {x x}_{m m} > >}))]]$

其中m∈[1，n-1]为光谱向量下标，初始值为1，代表逐个递增的光谱波段数，r₊₁和x₊₁是波段数由m变为m+1时两个光谱向量相对应增加的分量；Where m ∈ [1, n-1] is the subscript of the spectral vector, the initial value is 1, representing the number of spectral bands increasing one by one, r _{+ 1} and x _{+ 1} are the two spectra when the number of bands changes from m to m+1 The corresponding increased component of the vector;

步骤3：将步骤2公式中的x₊₁作为自变量x，生成以x₊₁为自变量的函数，得出

和x₊₁之间的函数关系式：Step 3: Take x ₊₁ in the formula of step 2 as the independent variable x, generate a function with x ₊₁ as the independent variable, and obtain

The functional relationship between and x ₊₁ :

${θ θ}_{{r r}_{m m + + 11},, {x x}_{m m + + 11}} = = f f ((x x))$

$= = {cos cos}^{- - 11} [[cos cos {θ θ}_{{r r}_{m m},, {x x}_{m m}} \frac{< < {r r}_{m m + + 11},, {r r}_{m m} > >}{| | | | {r r}_{m m + + 11} | | | | | | | | {r r}_{m m} | | | |} \frac{< < {x x}_{m m + + 11},, {x x}_{m m} > >}{\sqrt{{| | | | {x x}_{m m} | | | |}^{22} + + {x x}^{22}} | | | | {x x}_{m m} | | | |} ((11 + + \frac{< < {r r}_{+ + 11},, x x > >}{< < {r r}_{m m},, {x x}_{m m} > >}))]]$

令方程形式 $f (x) - θ_{r_{m + 1}, x_{m + 1}} = 0;$ Let the equation form $f (x) - θ_{r_{m + 1}, x_{m + 1}} = 0;$

步骤4：对步骤3的方程式进行求解得出近似解x₀、x₁，规定x₀＜x₁，x₀和x₁为造成相同光谱角

数值的光谱波段分量；Step 4: Solve the equation in step 3 to obtain approximate solutions x ₀ , x ₁ , specify x ₀ < x ₁ , x ₀ and x ₁ are to cause the same spectral angle

numerical spectral band components;

步骤5：根据步骤4得出的近似解，对x₊₁进行负相关判断，记为x_-，同时得出修正量α：Step 5: According to the approximate solution obtained in step 4, judge the negative correlation of x ₊₁ , record it as x _- , and obtain the correction amount α at the same time:

$\{\begin{matrix} {x x}_{- -} = = {x x}_{00},, & α α = = | | \frac{{f f}^{' '} (({x x}_{00}))}{{f f}^{' '} (({x x}_{11}))} | | < < 11 \\ {x x}_{- -} = = {x x}_{11},, & α α = = | | \frac{{f f}^{' '} (({x x}_{00}))}{{f f}^{' '} (({x x}_{11}))} | | > > 11 \end{matrix};;$

步骤6：根据步骤5的判定结果及修正量，对原始光谱角的分波段形式

进行负相关修正，得

Step 6: According to the judgment result and correction amount of step 5, the sub-band form of the original spectral angle

Corrected for negative correlation, we get

$\{\begin{matrix} {θ θ}_{{r r}_{m m + + 11},, {x x}_{m m + + 11}}^{MNC MNC - - SAM SAM} = = \frac{11}{α α} {θ θ}_{{r r}_{m m + + 11},, {x x}_{m m + + 11}},, & {x x}_{+ + 11} = = {x x}_{- -} = = {x x}_{00} \\ {θ θ}_{{r r}_{m m + + 11},, {x x}_{m m + + 11}}^{MNC MNC - - SAM SAM} = = α α {θ θ}_{{r r}_{m m + + 11},, {x x}_{m m + + 11}},, & {x x}_{+ + 11} = = {x x}_{- -} = = {x x}_{11} \end{matrix}$

步骤7：如果m＝n-1，原始光谱角

修正完毕，得到最终全波段修正的光谱角

否则，m＝m+1，从步骤2开始重复。Step 7: If m=n-1, raw spectral angle

After the correction is completed, the final full-band corrected spectral angle is obtained

Otherwise, m=m+1, repeat from step 2.

有益效果Beneficial effect

本发明提出的一种用于高光谱遥感图像逐波段修正负相关的光谱角填图方法，通过逐波段判定、修正的方式消除传统SAM算法中负相关对光谱角产生的影响。对于任一波段数值，光谱角负相关的判定和修正都是基于当前光谱角度值对光谱相似性的表征能力。通过修正量α增大对当前部分光谱向量相似性表征能力差的光谱角。所有波段依次完成判定修正过程后，最终的光谱角

可以正确反映光谱间的相似关系，有效拉伸不同光谱间的可分离性，能够将传统SAM算法无法区分的光谱正确分离出来，可以用于后续的高光谱遥感图像分类、目标探测等应用场合，能够提高分类精度，有效地压制误分率。The present invention proposes a spectral angle mapping method for hyperspectral remote sensing images to correct negative correlation band by band, and eliminates the influence of negative correlation on spectral angle in traditional SAM algorithms through band-by-band determination and correction. For any band value, the judgment and correction of the negative correlation of spectral angle are based on the ability of the current spectral angle value to represent spectral similarity. The spectral angle with poor ability to characterize the similarity of the current part of the spectral vectors is increased by the correction amount α. After all bands complete the determination and correction process in turn, the final spectral angle

It can correctly reflect the similarity relationship between spectra, effectively stretch the separability between different spectra, and can correctly separate the spectra that cannot be distinguished by traditional SAM algorithms. It can be used in subsequent hyperspectral remote sensing image classification, target detection and other applications. It can improve the classification accuracy and effectively suppress the misclassification rate.

本发明提出一种逐波段修正负相关影响的光谱角填图算法MNC-SAM(ModifiedNegative Correlation SAM)，考察每个参与SAM运算的波段出现负相关的情况，同时对由负相关波段生成的光谱角加以修正，经过负相关修正的全波段光谱角克服了不同光谱产生相同光谱角的问题。试验表明，以MNC-SAM作为光谱相似性度量可以有效地降低误分率，提高分类精度。The present invention proposes a spectral angle mapping algorithm MNC-SAM (Modified Negative Correlation SAM) that corrects the influence of negative correlation band by band. After being corrected, the full-band spectral angle corrected by negative correlation overcomes the problem that different spectra produce the same spectral angle. Experiments show that using MNC-SAM as a measure of spectral similarity can effectively reduce the misclassification rate and improve classification accuracy.

附图说明 Description of drawings

图1：本发明算法MNC-SAM的基本流程图。Fig. 1: The basic flowchart of the algorithm MNC-SAM of the present invention.

图2：一个通过负相关修正，增大模拟光谱可分离性的实例。图中实线代表参考光谱RefSp，不同虚线型代表待分光谱Sp0～Sp4，可以看出Sp0～Sp4的波形曲线在不同波段有明显的不同。SAM计算的Sp0～Sp4和RefSp间的光谱角均约为0.17980604(弧度)，各角度之间差异小于10^-6弧度，因此以SAM的结果，Sp0～Sp4完全不可分，将归为同一类。本发明提出的MNC-SAM计算的消除负相关影响的光谱角，将各角度之间差异提高至10^-2弧度至10^-1弧度之间，并且对不同波段出现负相关的情况，得到的光谱角度值不同，角度值随包含负相关波段数的增加而增大，使得光谱间的可分度性具有阶梯性。Figure 2: An example of increasing the separability of simulated spectra through negative correlation correction. The solid line in the figure represents the reference spectrum RefSp, and the different dotted lines represent the spectra to be divided Sp0-Sp4. It can be seen that the waveform curves of Sp0-Sp4 are obviously different in different bands. The spectral angles between Sp0~Sp4 and RefSp calculated by SAM are all about 0.17980604 (radian), and the difference between each angle is less than 10 ^-6 radian. Therefore, based on the results of SAM, Sp0~Sp4 are completely inseparable and will be classified into the same category. The spectral angle calculated by the MNC-SAM proposed by the present invention to eliminate the negative correlation influence increases the difference between the angles to between 10 ^-2 radians and 10 ^-1 radians, and when negative correlations occur in different wave bands, the obtained spectrum The angle values are different, and the angle value increases with the increase of the number of negatively correlated bands, which makes the separability between the spectra have a stepwise nature.

图3：MNC-SAM应用于实际高光谱遥感图像目标探测的结果，并与ENVI自带方法BandMax+SAM进行比较。实验采用ENVI软件自带的AVIRIS于美国加利福尼亚州圣地亚哥海军机场获取的图像，空间分辨率为400×400，光谱分辨率为10nm，共有224个波段的数据，为便于显示，选取原图左上200×200空间区域用于实验。试验目的是以(89，11)处像素点的光谱作为参考光谱，试图将左上角坐标(89，11)附近的三架飞机与指定的背景分离，ENVI提供了BandMax算法结合SAM用于该目标探测试验。图3(a)为实验图第122波段灰度拉伸图，图3(b)～(c)为以SAM算法为基础的BandMax的目标探测结果，由图可见随着阈值的微小增大，误分率明显增高(如图像右方的建筑物群)，而目标本身的增强并不明显。而使用本发明提出的MNC-SAM算法修正了负相关后，拉伸了光谱间的可分度，通过设置不同的阈值，可以增强目标探测的效果，而不同地物被误分为目标的概率明显降低了。如图3(d)～(f)所示，随着阈值较大幅度的增加，属于目标的像素被正确探测到，而误分率得到了很好的控制。Figure 3: The results of MNC-SAM applied to the actual hyperspectral remote sensing image target detection, and compared with ENVI's own method BandMax+SAM. The experiment adopts the image acquired by AVIRIS which comes with ENVI software at the Naval Airfield in San Diego, California, USA. The spatial resolution is 400×400, the spectral resolution is 10nm, and there are 224 bands of data. For the convenience of display, the upper left 200× 200 spatial regions are used for experiments. The purpose of the test is to use the spectrum of the pixel point at (89, 11) as the reference spectrum, and try to separate the three aircraft near the coordinates (89, 11) in the upper left corner from the specified background. ENVI provides the BandMax algorithm combined with SAM for this target Probe test. Figure 3(a) is the grayscale stretching diagram of the 122nd band of the experimental image, and Figure 3(b)~(c) are the target detection results of BandMax based on the SAM algorithm. It can be seen from the figure that with the slight increase of the threshold, The misclassification rate is significantly increased (such as the building group on the right of the image), but the enhancement of the target itself is not obvious. However, after using the MNC-SAM algorithm proposed by the present invention to correct the negative correlation, the separability between the spectra is stretched, and by setting different thresholds, the effect of target detection can be enhanced, and the probability of different ground objects being misclassified as targets Significantly reduced. As shown in Fig. 3(d)~(f), as the threshold value increases significantly, the pixels belonging to the target are detected correctly, and the misclassification rate is well controlled.

具体实施方式 Detailed ways

现结合实施例、附图对本发明作进一步描述：Now in conjunction with embodiment, accompanying drawing, the present invention will be further described:

用于实施的硬件环境是：Pentium-43.0G计算机、1G内存、128M显卡；运行的软件环境是：Window XP操作系统，用IDL7.0程序设计语言结合ENVI实现了本发明提出的方法。The hardware environment that is used for implementing is: Pentium-43.0G computer, 1G memory, 128M graphics card; The software environment of operation is: Window XP operating system, has realized the method that the present invention proposes with IDL7.0 programming language in conjunction with ENVI.

1.对于一幅高光谱遥感图像原始高光谱遥感图像I＝f(x，y，n)，(x，y)∈Z²为空间分辨率，n为光谱波段数。针对图像中待判定光谱向量x_n和已知参考光谱向量r_n，根据SAM算法定义，得出两个光谱向量之间的原始光谱角

1. For a hyperspectral remote sensing image, the original hyperspectral remote sensing image I = f(x, y, n), (x, y) ∈ Z ² is the spatial resolution, and n is the number of spectral bands. According to the spectral vector x _n to be determined and the known reference spectral vector r _n in the image, according to the definition of the SAM algorithm, the original spectral angle between the two spectral vectors is obtained

2.针对步骤1的公式进行分解，

由参与运算的两个光谱向量的所有波段数据计算得到，因此产生负相关的波段数据隐性影响着最终的光谱角数值，造成误判现象。为了检测和判定每个光谱波段出现负相关的情况，最终去除负相关对光谱角的影响，写出SAM分波段的公式，得出分波段光谱角

如下：2. Decompose the formula in step 1,

It is calculated from all the band data of the two spectral vectors participating in the operation, so the negatively correlated band data implicitly affects the final spectral angle value, resulting in misjudgment. In order to detect and determine the occurrence of negative correlation in each spectral band, and finally remove the influence of negative correlation on the spectral angle, write the formula of SAM sub-band, and obtain the sub-band spectral angle

as follows:

${θ θ}_{{r r}_{m m + + 11},, {x x}_{m m + + 11}} = = {cos cos}^{- - 11} ((\frac{< < {r r}_{m m + + 11},, {x x}_{m m + + 11} > >}{| | | | {r r}_{m m + + 11} | | | | | | | | {x x}_{m m + + 11} | | | |}))$

$= = {cos cos}^{- - 11} ((\frac{< < {r r}_{m m},, {x x}_{m m} > > + + < < {r r}_{+ + 11},, {x x}_{+ + 11} > >}{\sqrt{{| | | | {r r}_{m m} | | | |}^{22} + + {| | | | {r r}_{+ + 11} | | | |}^{22}} \sqrt{{| | | | {x x}_{m m} | | | |}^{22} + + {| | | | {x x}_{+ + 11} | | | |}^{22}}}))$

$= = {cos cos}^{- - 11} ((cos cos {θ θ}_{{r r}_{m m},, {x x}_{m m}} \frac{11 + + \frac{< < {r r}_{+ + 11},, {x x}_{+ + 11} > >}{< < {r r}_{m m},, {x x}_{m m} > >}}{\sqrt{11 + + \frac{{| | | | {r r}_{+ + 11} | | | |}^{22}}{{| | | | {r r}_{m m} | | | |}^{22}}} \sqrt{11 + + \frac{{| | | | {x x}_{+ + 11} | | | |}^{22}}{{| | | | {x x}_{m m} | | | |}^{22}}}}))$

$= = {cos cos}^{- - 11} [[cos cos {θ θ}_{{r r}_{m m},, {x x}_{m m}} \frac{< < {r r}_{m m + + 11},, {r r}_{m m} > >}{| | | | {r r}_{m m + + 11} | | | | | | | | {r r}_{m m} | | | |} \frac{< < {x x}_{m m + + 11},, {x x}_{m m} > >}{| | | | {x x}_{m m + + 11} | | | | | | | | {x x}_{m m} | | | |} ((11 + + \frac{< < {r r}_{+ + 11},, {x x}_{+ + 11} > >}{< < {r r}_{m m},, {x x}_{m m} > >}))]]$

其中m∈[1，n-1]为光谱向量下标，初始值为1，r₊₁和x₊₁是波段数由m变为m+1时两个光谱向量相对应增加的分量，当m＝n-1时，公式变为公式传统SAM公式。Where m∈[1,n-1] is the subscript of the spectral vector, the initial value is 1, r ₊₁ and x ₊₁ are the components of the two spectral vectors correspondingly increased when the number of bands changes from m to m+1, when When m=n-1, the formula becomes the traditional SAM formula.

3.针对步骤2的分波段公式进行变换，将其写成

和x₊₁的函数式，将x₊₁作为自变量x，得出和x₊₁的函数关系式f(x)：3. Transform the sub-band formula in step 2, and write it as

and x ₊₁ functional formula, using x ₊₁ as the independent variable x, we get The functional relationship f(x) with x ₊₁ :

${θ θ}_{{r r}_{m m + + 11},, {x x}_{m m + + 11}} = = f f ((x x))$

该函数反应了每新增一个波段，相应的光谱角和所增加波段数据之间的函数关系，将函数改写成方程格式，得出：

This function reflects the functional relationship between each new band, the corresponding spectral angle and the added band data, and the function is rewritten into an equation format to obtain:

4.对步骤3的方程进行求解。该方程一般有两个解，本发明采用二分法求解该方程的数值近似解，得出两个解：x₀、x₁，规定x₀＜x₁。这两个解是可能造成相同光谱角

数值的光谱波段分量，其中有一个等于光谱向量x_n的第m+1个分量x₊₁，另一个解代入步骤2中公式可以得到相同的m+1维光谱角

4. Solve the equation in step 3. The equation generally has two solutions. The present invention adopts the dichotomy method to solve the numerical approximate solution of the equation, and obtains two solutions: x ₀ and x ₁ , and x ₀ < x ₁ is stipulated. Both solutions are possible resulting in the same spectral angle

Numerical spectral band components, one of which is equal to the m+1th component x ₊₁ of the spectral vector x _n , another solution can be substituted into the formula in step 2 to obtain the same m+1-dimensional spectral angle

5.根据步骤4得出的方程解，结合步骤3的函数式，进行负相关波段的判定。求出步骤3中函数f(x)在x₀、x₁两点处的导数f′(x₀)和f′(x₁)。在两个解x₀、x₁中做出负相关的判定如下，负相关记为x_-，同时得出针对负相关的修正量α：5. According to the equation solution obtained in step 4, combined with the functional formula in step 3, determine the negative correlation band. Find the derivatives f'(x ₀ ) and f'(x ₁ ) of the function f(x) at two points x ₀ and x ₁ in step 3. The determination of the negative correlation in the two solutions x ₀ and x ₁ is as follows, the negative correlation is recorded as x _- , and the correction amount α for the negative correlation is obtained at the same time:

$\{\begin{matrix} {x x}_{- -} = = {x x}_{00},, & α α = = | | \frac{{f f}^{' '} (({x x}_{00}))}{{f f}^{' '} (({x x}_{11}))} | | < < 11 \\ {x x}_{- -} = = {x x}_{11},, & α α = = | | \frac{{f f}^{' '} (({x x}_{00}))}{{f f}^{' '} (({x x}_{11}))} | | > > 11 \end{matrix}$

步骤3在m维光谱角已确定的前提下，给出了m+1维光谱角和光谱向量x_n新增分量x₊₁之间的函数关系f(x)。其导数的绝对值表明光谱角度值相对于幅值x₊₁变化的敏感度，极限为零，这说明在产生大导数绝对值的x处，

对光谱相似度的表征性能随之变差。因此，针对产生相同光谱角的x₀和x₁，以其导数的比值作为负相关的判定条件和修正量，是合理的。In step 3, on the premise that the m-dimensional spectral angle has been determined, the m+1-dimensional spectral angle is given and the functional relationship f(x) between the newly added component x ₊₁ of the spectral vector x _n . The absolute value of its derivative indicates the sensitivity of the spectral angle value to the change of the magnitude x _{+ 1} , and the limit is zero, which means that at x which produces a large absolute value of the derivative,

The performance of characterization of spectral similarity becomes worse accordingly. Therefore, for x ₀ and x ₁ that produce the same spectral angle, it is reasonable to use the ratio of their derivatives as the judgment condition and correction amount for negative correlation.

6.针对原始光谱角

结合步骤5的判定结果和修正量，进行负相关修正，如果光谱向量x_n真实的x₊₁被判定为负相关，得出相应光谱角修正值

6. For the original spectral angle

Combining the determination result and correction amount of step 5, carry out negative correlation correction, if the real x ₊₁ of the spectral vector x _n is judged to be negative correlation, obtain the corresponding spectral angle correction value

针对原始光谱角将上述判定及修正过程用于光谱向量的所有波段，即完成本发明提出的MNC-SAM算法，最终输出全波段修正的光谱角

For the original spectral angle Apply the above judgment and correction process to all bands of the spectral vector, that is, to complete the MNC-SAM algorithm proposed by the present invention, and finally output the corrected spectral angle of the full band

Claims

1. one kind is used for the spectrum angle map plotting method that high-spectrum remote sensing pursues wave band correction negative correlation, it is characterized in that step is following:

Step 1: for a panel height spectral remote sensing image I=f (x, y, n), (x, y) ∈ Z ²Be spatial resolution, n is the spectral band number.To waiting to judge the spectrum vector x in the image _nWith known reference spectra vector r _n,, draw two primary light spectral corners between the spectrum vector according to the definition of SAM algorithm

θ_{r_{n}, x_{n}} = \cos^{- 1} \frac{< r_{n}, x_{n} >}{| | r_{n} | | | | x_{n} | |}

Step 2: the formula of deployment step 1 draws the subrane form of primary light spectral corner

θ_{r_{m + 1}, x_{m + 1}} = \cos^{- 1} [\cos θ_{r_{m}, x_{m}} \frac{< r_{m + 1}, r_{m} >}{| | r_{m + 1} | | | | r_{m} | |} \frac{< x_{m + 1}, x_{m} >}{| | x_{m + 1} | | | | x_{m} | |} (1 + \frac{< r_{+ 1}, x_{+ 1} >}{< r_{m}, x_{m} >})]

Wherein m ∈ [1, n-1] is a spectrum vector subscript, and initial value is 1, the spectral band number that representative increases progressively one by one, r _{+ 1}And x _{+ 1}It is the component of wave band number corresponding increases of two spectrum vectors when becoming m+1 by m;

Step 3: with the x in step 2 formula _{+ 1}As independent variable x, generate with x _{+ 1}Function for independent variable draws And x _{+ 1}Between functional relation:

θ_{r_{m + 1}, x_{m + 1}} = f (x)

= \cos^{- 1} [\cos θ_{r_{m}, x_{m}} \frac{< r_{m + 1}, r_{m} >}{| | r_{m + 1} | | | | r_{m} | |} \frac{< x_{m + 1}, x_{m} >}{\sqrt{{| | x_{m} | |}^{2} + x^{2}} | | x_{m} | |} (1 + \frac{< r_{+ 1}, x >}{< r_{m}, x_{m} >})]

Make equation form

f (x) - θ_{r_{m + 1}, x_{m + 1}} = 0;

Step 4: the equation of step 3 found the solution draw approximate solution x ₀, x ₁, regulation x ₀＜x ₁, x ₀And x ₁For causing the same light spectral corner

The spectral band component of numerical value;

Step 5: the approximate solution that draws according to step 4, to x _{+ 1}Carry out negative correlation and judge, be designated as x _-, draw correction amount alpha simultaneously:

\{\begin{matrix} x_{-} = x_{0}, & α = | \frac{f^{'} (x_{0})}{f^{'} (x_{1})} | < 1 \\ x_{-} = x_{1}, & α = | \frac{f^{'} (x_{0})}{f^{'} (x_{1})} | > 1 \end{matrix};

Step 6: according to the result of determination and the correction of step 5; Subrane form

to the primary light spectral corner is carried out the negative correlation correction, gets

\{\begin{matrix} θ_{r_{m + 1}, x_{m + 1}}^{MNC - SAM} = \frac{1}{α} θ_{r_{m + 1}, x_{m + 1}}, & x_{+ 1} = x_{-} = x_{0} \\ θ_{r_{m + 1}, x_{m + 1}}^{MNC - SAM} = α θ_{r_{m + 1}, x_{m + 1}}, & x_{+ 1} = x_{-} = x_{1} \end{matrix}

Step 7: if m=n-1; Primary light spectral corner

correction finishes; Obtain final all band correction spectrum angle

otherwise; M=m+1 begins repetition from step 2.