CN111897988A - A kind of hyperspectral remote sensing image classification method and system - Google Patents

A kind of hyperspectral remote sensing image classification method and system Download PDF

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CN111897988A
CN111897988A CN202010678850.2A CN202010678850A CN111897988A CN 111897988 A CN111897988 A CN 111897988A CN 202010678850 A CN202010678850 A CN 202010678850A CN 111897988 A CN111897988 A CN 111897988A
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何芳
贾维敏
张峰干
伍宗伟
沈晓卫
赵建伟
胡豪杰
金伟
何佑明
朱玉杰
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Rocket Force University of Engineering of PLA
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Abstract

本发明涉及一种高光谱遥感图像分类方法及系统。该方法包括获取高光谱遥感图像;根据所述高光谱遥感图像的像素点确定锚点;根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图;根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型;获取待分类的高光谱遥感图像;采用所述二部图的半监督学习模型对所述待分类的高光谱遥感图像进行分类。本发明所提供的一种高光谱遥感图像分类方法及系统,能够降低计算复杂度,提高分类精度。

Figure 202010678850

The invention relates to a hyperspectral remote sensing image classification method and system. The method includes acquiring a hyperspectral remote sensing image; determining an anchor point according to the pixel points of the hyperspectral remote sensing image; and constructing an adaptive two According to the self-adaptive bipartite graph, a semi-supervised learning method is used to construct a semi-supervised learning model of the bipartite graph; the hyperspectral remote sensing image to be classified is obtained; the semi-supervised learning model of the bipartite graph is used to The hyperspectral remote sensing images to be classified are classified. The method and system for classifying hyperspectral remote sensing images provided by the present invention can reduce computational complexity and improve classification accuracy.

Figure 202010678850

Description

一种高光谱遥感图像分类方法及系统A kind of hyperspectral remote sensing image classification method and system

技术领域technical field

本发明涉及高光谱遥感和机器学习领域,特别是涉及一种高光谱遥感图像分类方法及系统。The invention relates to the fields of hyperspectral remote sensing and machine learning, in particular to a hyperspectral remote sensing image classification method and system.

背景技术Background technique

高光谱遥感即高光谱分辨率遥感,作为一种窄波段成像方式,能发现宽波段中无法探测的物质,兴起于20世纪80年代,是一种重要的对地观测技术。高光谱遥感技术在给我们的实际生活提供帮助的同时,也引出了一系列的信息提取与模式识别的问题,主要体现在高维数据处理与分析上。随着成像光谱技术的发展,更高的光谱分辨率带来了更多的光谱波段数,更广的覆盖范围带来了更大的数据量。因此,高光谱技术在提供丰富的光谱信息的同时,也给高光谱数据处理提出了新的挑战。Hyperspectral remote sensing is hyperspectral resolution remote sensing. As a narrow-band imaging method, it can discover substances that cannot be detected in wide-band. It emerged in the 1980s and is an important earth observation technology. While hyperspectral remote sensing technology provides help to our real life, it also leads to a series of problems of information extraction and pattern recognition, which are mainly reflected in high-dimensional data processing and analysis. With the development of imaging spectroscopy technology, higher spectral resolution brings more spectral bands, and wider coverage brings a larger amount of data. Therefore, while providing rich spectral information, hyperspectral technology also poses new challenges for hyperspectral data processing.

分类是高光谱数据处理的重要领域。高光谱影像分类是利用地物的光谱信息和空间信息,根据一定的分类准则,如“物以类聚”,对图像中的每个像素点赋予一个类别标记。高光谱分类技术对提取专题信息、监测地物动态变化具有重要的作用,广泛应用于制作专题地图、工程勘探、交通规划管理、环境监测、土地利用和农作物估产等领域中。Classification is an important area of hyperspectral data processing. Hyperspectral image classification is to use the spectral information and spatial information of ground objects, according to certain classification criteria, such as "clustering of objects", to assign a category label to each pixel in the image. Hyperspectral classification technology plays an important role in extracting thematic information and monitoring the dynamic changes of ground objects. It is widely used in the production of thematic maps, engineering exploration, traffic planning and management, environmental monitoring, land use and crop yield estimation.

原始的遥感影像分类方法是人工目视解释法,该方法对工作人员的地学知识和研判经验具有较高的要求,并且分类结果受工作人员的经验和知识储备影响较大。人工目视效率较低,并且耗费较大的人力、物力。由于遥感数据量的急剧增长,人工目视方法已经无法满足需求。分类问题的本质是模式识别。随着计算机技术的不断发展,利用机器学习方法可以实现智能化数据分析,获取数据间的隐藏关系。基于机器学习产生的各种分类算法在一定程度上提高了高光谱影像的分类效果。The original remote sensing image classification method is the manual visual interpretation method, which has high requirements on the staff's geoscience knowledge and research and judgment experience, and the classification results are greatly affected by the staff's experience and knowledge reserve. Artificial vision is less efficient and consumes a lot of manpower and material resources. Due to the rapid increase in the amount of remote sensing data, the artificial visual method has been unable to meet the demand. The essence of the classification problem is pattern recognition. With the continuous development of computer technology, the use of machine learning methods can realize intelligent data analysis and obtain hidden relationships between data. Various classification algorithms based on machine learning have improved the classification effect of hyperspectral images to a certain extent.

机器学习是人工智能和模式识别领域的核心课题,根据是否利用类标信息,又可分为监督学习(Supervised Learning)、无监督学习(Unsupervised Learning)和半监督学习(Semi-supervised Learning,SSL)。监督学习借助于输入数据的类标信息,以概率函数、代数函数或人工神经网络为基函数模型,进行迭代计算。无监督学习不使用类标信息,主要应用于数据的聚类中。半监督学习使用少量的标记信息和大量的无标记信息构建学习模型。由于高光谱数据量较大,样本的标记需要耗费较大的人力、物力,因此半监督学习方法在高光谱影像处理中具有重要的应用。Machine learning is a core subject in the field of artificial intelligence and pattern recognition. According to whether the classification information is used, it can be divided into supervised learning (Supervised Learning), Unsupervised Learning (Unsupervised Learning) and Semi-supervised Learning (SSL) . Supervised learning uses the class label information of the input data to perform iterative calculation with probability function, algebraic function or artificial neural network as the basis function model. Unsupervised learning does not use class label information and is mainly used in data clustering. Semi-supervised learning uses a small amount of labeled information and a large amount of unlabeled information to build a learning model. Due to the large amount of hyperspectral data, the labeling of samples requires a lot of manpower and material resources, so semi-supervised learning methods have important applications in hyperspectral image processing.

基于图的半监督学习方法概念清晰,易于实现,近年来受到了广泛的关注。然而,传统的图方法在构图过程中及矩阵求逆过程中的计算复杂度较高,无法处理大规模高光谱影像。此外,传统图方法一般都是输入一个固定的图,图的质量好坏直接影响后续的分类效果。Graph-based semi-supervised learning methods have clear concepts and are easy to implement, and have received extensive attention in recent years. However, the traditional graph method has high computational complexity in the process of composition and matrix inversion, and cannot handle large-scale hyperspectral images. In addition, traditional graph methods generally input a fixed graph, and the quality of the graph directly affects the subsequent classification effect.

发明内容SUMMARY OF THE INVENTION

本发明的目的是提供一种高光谱遥感图像分类方法及系统,能够降低计算复杂度,提高分类精度。The purpose of the present invention is to provide a hyperspectral remote sensing image classification method and system, which can reduce the computational complexity and improve the classification accuracy.

为实现上述目的,本发明提供了如下方案:For achieving the above object, the present invention provides the following scheme:

一种高光谱遥感图像分类方法,包括:A hyperspectral remote sensing image classification method, comprising:

获取高光谱遥感图像;Obtain hyperspectral remote sensing images;

根据所述高光谱遥感图像的像素点确定锚点;所述锚点为随机选取的高光谱遥感图像的像素点;所述锚点的数量小于高光谱遥感图像中的像素点的数量;An anchor point is determined according to the pixel points of the hyperspectral remote sensing image; the anchor point is a randomly selected pixel point of the hyperspectral remote sensing image; the number of the anchor points is less than the number of pixels in the hyperspectral remote sensing image;

根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图;According to the pixel points of the hyperspectral remote sensing image and the anchor points, the adaptive proximity assignment principle is adopted to construct an adaptive bipartite graph;

根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型;所述二部图的半监督学习模型以自适应二部图为输入,以所述高光谱遥感图像的类别为输出;According to the adaptive bipartite graph, a semi-supervised learning method is used to construct a semi-supervised learning model of the bipartite graph; the semi-supervised learning model of the bipartite graph takes the adaptive bipartite graph as input, and uses the hyperspectral remote sensing The category of the image is output;

获取待分类的高光谱遥感图像;Obtain hyperspectral remote sensing images to be classified;

采用所述二部图的半监督学习模型对所述待分类的高光谱遥感图像进行分类。The hyperspectral remote sensing image to be classified is classified using the semi-supervised learning model of the bipartite graph.

可选的,所述根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图,具体包括:Optionally, according to the pixel points of the hyperspectral remote sensing image and the anchor points, the adaptive proximity assignment principle is used to construct an adaptive bipartite graph, which specifically includes:

根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建相似性矩阵;According to the pixel point of the hyperspectral remote sensing image and the anchor point, adopt the principle of adaptive proximity assignment to construct a similarity matrix;

根据所述相似性矩阵构建自适应二部图。An adaptive bipartite graph is constructed from the similarity matrix.

可选的,所述根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型,之前还包括:Optionally, according to the adaptive bipartite graph, a semi-supervised learning method is used to construct a semi-supervised learning model of the bipartite graph, which further includes:

采用半监督学习目标对所述自适应二部图进行优化。The adaptive bipartite graph is optimized using a semi-supervised learning objective.

可选的,所述根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型,具体包括:Optionally, according to the adaptive bipartite graph, a semi-supervised learning method is used to construct a semi-supervised learning model of the bipartite graph, specifically including:

利用公式

Figure BDA0002585137140000031
确定目标函数;Z为相似性矩阵,U为新的相似矩阵,
Figure BDA0002585137140000032
为像素点的软标签矩阵,
Figure BDA0002585137140000033
为锚点的软标签矩阵,
Figure BDA0002585137140000034
表示所有像素点的标签矩阵,B为对角矩阵,α为规则化参数,LS为拉普拉斯矩阵;Use the formula
Figure BDA0002585137140000031
Determine the objective function; Z is the similarity matrix, U is the new similarity matrix,
Figure BDA0002585137140000032
is the soft label matrix of pixels,
Figure BDA0002585137140000033
is the soft label matrix of anchor points,
Figure BDA0002585137140000034
Represents the label matrix of all pixels, B is the diagonal matrix, α is the regularization parameter, and L S is the Laplace matrix;

采用迭代优化方式对所述目标函数进行求解,得到像素点的标签;所述标签用于进行高光谱遥感图像的分类。The objective function is solved in an iterative optimization manner to obtain the labels of the pixel points; the labels are used to classify the hyperspectral remote sensing images.

一种高光谱遥感图像分类系统,包括:A hyperspectral remote sensing image classification system, comprising:

高光谱遥感图像获取模块,用于获取高光谱遥感图像;Hyperspectral remote sensing image acquisition module, used to acquire hyperspectral remote sensing images;

锚点确定模块,用于根据所述高光谱遥感图像的像素点确定锚点;所述锚点为随机选取的高光谱遥感图像的像素点;所述锚点的数量小于高光谱遥感图像中的像素点的数量;The anchor point determination module is used for determining anchor points according to the pixel points of the hyperspectral remote sensing image; the anchor points are randomly selected pixel points of the hyperspectral remote sensing image; the number of the anchor points is less than the number of the hyperspectral remote sensing images. the number of pixels;

自适应二部图构建模块,用于根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图;an adaptive bipartite graph building module, configured to construct an adaptive bipartite graph according to the pixel points and the anchor points of the hyperspectral remote sensing image, using the principle of adaptive proximity assignment;

二部图的半监督学习模型构建模块,用于根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型;所述二部图的半监督学习模型以自适应二部图为输入,以所述高光谱遥感图像的类别为输出;The semi-supervised learning model building module of bipartite graph is used for constructing a semi-supervised learning model of bipartite graph by adopting semi-supervised learning method according to the adaptive bipartite graph; the semi-supervised learning model of the bipartite graph is based on the self- Adapt the bipartite map as input, and use the category of the hyperspectral remote sensing image as output;

待分类的高光谱遥感图像获取模块,用于获取待分类的高光谱遥感图像;The hyperspectral remote sensing image acquisition module to be classified is used to acquire the hyperspectral remote sensing image to be classified;

分类模块,用于采用所述二部图的半监督学习模型对所述待分类的高光谱遥感图像进行分类。A classification module for classifying the hyperspectral remote sensing image to be classified by using the semi-supervised learning model of the bipartite graph.

可选的,所述自适应二部图构建模块具体包括:Optionally, the adaptive bipartite graph building module specifically includes:

相似性矩阵构建单元,用于根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建相似性矩阵;a similarity matrix construction unit, configured to construct a similarity matrix according to the pixel point of the hyperspectral remote sensing image and the anchor point, using an adaptive proximity assignment principle;

自适应二部图构建单元,用于根据所述相似性矩阵构建自适应二部图。An adaptive bipartite graph construction unit, configured to construct an adaptive bipartite graph according to the similarity matrix.

可选的,还包括:Optionally, also include:

优化模块,用于采用半监督学习目标对所述自适应二部图进行优化。An optimization module for optimizing the adaptive bipartite graph using a semi-supervised learning objective.

可选的,所述二部图的半监督学习模型构建模块具体包括:Optionally, the semi-supervised learning model building module of the bipartite graph specifically includes:

目标函数确定单元,用于利用公式

Figure BDA0002585137140000041
确定目标函数;Z为相似性矩阵,U为新的相似矩阵,
Figure BDA0002585137140000042
为像素点的软标签矩阵,
Figure BDA0002585137140000043
为锚点的软标签矩阵,
Figure BDA0002585137140000044
表示所有像素点的标签矩阵,B为对角矩阵,α为规则化参数,LS为拉普拉斯矩阵;Objective function determination unit for utilizing the formula
Figure BDA0002585137140000041
Determine the objective function; Z is the similarity matrix, U is the new similarity matrix,
Figure BDA0002585137140000042
is the soft label matrix of pixels,
Figure BDA0002585137140000043
is the soft label matrix of anchor points,
Figure BDA0002585137140000044
Represents the label matrix of all pixels, B is the diagonal matrix, α is the regularization parameter, and L S is the Laplace matrix;

像素点的标签确定单元,用于采用迭代优化方式对所述目标函数进行求解,得到像素点的标签;所述标签用于进行高光谱遥感图像的分类。The label determination unit of the pixel point is used to solve the objective function in an iterative optimization manner to obtain the label of the pixel point; the label is used to classify the hyperspectral remote sensing image.

根据本发明提供的具体实施例,本发明公开了以下技术效果:According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

本发明所提供的一种高光谱遥感图像分类方法及系统,通过将随机选取的部分高光谱遥感图像的像素点确定为锚点,构建锚点与像素点之间的自适应二部图,减少了构图的参数,降低了计算的复杂度;在根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型,对构建的自适应二部图不断的优化,提高了图的质量,进而提高了分类的精度。The method and system for classifying hyperspectral remote sensing images provided by the present invention, by determining randomly selected pixel points of some hyperspectral remote sensing images as anchor points, and constructing an adaptive bipartite graph between the anchor points and the pixel points, reducing The parameters of the composition are reduced, and the computational complexity is reduced; according to the adaptive bipartite graph, a semi-supervised learning method is used to construct a semi-supervised learning model of the bipartite graph, and the constructed adaptive bipartite graph is continuously optimized. The quality of the graph is improved, which in turn improves the accuracy of the classification.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案,下面将对实施例中所需要使用的附图作简单地介绍,显而易见地,下面描述中的附图仅仅是本发明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动性的前提下,还可以根据这些附图获得其他的附图。In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some of the present invention. In the embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative labor.

图1为本发明所提供的一种高光谱遥感图像分类方法流程示意图;1 is a schematic flowchart of a method for classifying hyperspectral remote sensing images provided by the present invention;

图2为本发明所提供的一种高光谱遥感图像分类系统结构示意图。FIG. 2 is a schematic structural diagram of a hyperspectral remote sensing image classification system provided by the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

本发明的目的是提供一种高光谱遥感图像分类方法及系统,能够降低计算复杂度,提高分类精度。The purpose of the present invention is to provide a hyperspectral remote sensing image classification method and system, which can reduce the computational complexity and improve the classification accuracy.

为使本发明的上述目的、特征和优点能够更加明显易懂,下面结合附图和具体实施方式对本发明作进一步详细的说明。In order to make the above objects, features and advantages of the present invention more clearly understood, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

图1为本发明所提供的一种高光谱遥感图像分类方法流程示意图,如图1所示,本发明所提供的一种高光谱遥感图像分类方法,包括:1 is a schematic flowchart of a method for classifying hyperspectral remote sensing images provided by the present invention. As shown in FIG. 1 , a method for classifying hyperspectral remote sensing images provided by the present invention includes:

S101,获取高光谱遥感图像。所述高光谱遥感图像的像素点用矩阵表示为

Figure BDA0002585137140000051
n表示像元的个数,d表示每个像元的波段数。S101, acquiring a hyperspectral remote sensing image. The pixels of the hyperspectral remote sensing image are represented by a matrix as
Figure BDA0002585137140000051
n represents the number of pixels, and d represents the number of bands per pixel.

S102,根据所述高光谱遥感图像的像素点确定锚点;所述锚点为随机选取的高光谱遥感图像的像素点;所述锚点的数量小于高光谱遥感图像中的像素点的数量。即从原始的n个像素点中选取m个锚点,锚点用矩阵表示为

Figure BDA0002585137140000052
S102: Determine anchor points according to pixels of the hyperspectral remote sensing image; the anchor points are randomly selected pixels of the hyperspectral remote sensing image; the number of anchor points is less than the number of pixels in the hyperspectral remote sensing image. That is, m anchor points are selected from the original n pixels, and the anchor points are represented by a matrix as
Figure BDA0002585137140000052

S103,根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图。自适应近邻分配原则为两点之间距离越近,属于同一类的概率越大。S103 , according to the pixel points of the hyperspectral remote sensing image and the anchor points, adopt the principle of adaptive proximity assignment to construct an adaptive bipartite graph. The principle of adaptive neighbor assignment is that the closer the distance between two points, the greater the probability of belonging to the same class.

S103具体包括:S103 specifically includes:

根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建相似性矩阵Z。According to the pixel points and the anchor points of the hyperspectral remote sensing image, the similarity matrix Z is constructed by adopting the principle of adaptive proximity assignment.

Z为:Z is:

Figure BDA0002585137140000061
Figure BDA0002585137140000061

其中,zij为相似矩阵Z中的第i行第j列元素,

Figure BDA0002585137140000062
为相似矩阵Z中的第i行,γ为规则化参数。令
Figure BDA0002585137140000063
Figure BDA0002585137140000064
是一个向量,它的第j个元素为eij,因此,(1)式写成如下向量形式:Among them, z ij is the i-th row and j-th column element in the similarity matrix Z,
Figure BDA0002585137140000062
is the ith row in the similarity matrix Z, and γ is the regularization parameter. make
Figure BDA0002585137140000063
Figure BDA0002585137140000064
is a vector whose j-th element is e ij , therefore, equation (1) is written in the following vector form:

Figure BDA0002585137140000065
Figure BDA0002585137140000065

公式(2)对应的拉格朗日函数为:The Lagrangian function corresponding to formula (2) is:

Figure BDA0002585137140000066
Figure BDA0002585137140000066

其中,η和βi≥0是拉格朗日乘子。where η and β i ≥ 0 are Lagrange multipliers.

zi的最优解应该满足公式(3)关于zi的导数等于0,即:The optimal solution of zi should satisfy the derivative of formula (3) with respect to zi equal to 0, namely:

Figure BDA0002585137140000067
Figure BDA0002585137140000067

对于zi中的第j个元素,有:For the jth element in zi , there are:

Figure BDA0002585137140000068
Figure BDA0002585137140000068

根据KKT条件,zijβij=0,由式(5)可得:According to the KKT condition, zi ij β ij = 0, which can be obtained from formula (5):

Figure BDA0002585137140000069
Figure BDA0002585137140000069

其中

Figure BDA00025851371400000610
因此,zij的解为:in
Figure BDA00025851371400000610
Therefore, the solution of z ij is:

Figure BDA00025851371400000611
Figure BDA00025851371400000611

根据所述相似性矩阵构建自适应二部图。An adaptive bipartite graph is constructed from the similarity matrix.

所述自适应二部图为:The adaptive bipartite graph is:

Figure BDA0002585137140000071
Figure BDA0002585137140000071

S104,根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型;所述二部图的半监督学习模型以自适应二部图为输入,以所述高光谱遥感图像的类别为输出;S104, according to the adaptive bipartite graph, adopt a semi-supervised learning method to construct a semi-supervised learning model of the bipartite graph; the semi-supervised learning model of the bipartite graph takes the adaptive bipartite graph as an input, and uses the high The category of the spectral remote sensing image is output;

在S104之前还包括:Also included before S104:

采用半监督学习目标对所述自适应二部图进行优化。The adaptive bipartite graph is optimized using a semi-supervised learning objective.

目标是学习一个新的相似矩阵

Figure BDA0002585137140000072
或者
Figure BDA0002585137140000073
如下:The goal is to learn a new similarity matrix
Figure BDA0002585137140000072
or
Figure BDA0002585137140000073
as follows:

Figure BDA0002585137140000074
Figure BDA0002585137140000074

使优化的相似矩阵S与给出的近邻矩阵W越接近越好,所以需要解决如下问题:The closer the optimized similarity matrix S is to the given nearest neighbor matrix W, the better, so the following problems need to be solved:

Figure BDA0002585137140000075
Figure BDA0002585137140000075

根据式(8)和式(9)中S和W的特殊结构,式(10)可以转换为:According to the special structure of S and W in formula (8) and formula (9), formula (10) can be converted into:

Figure BDA0002585137140000076
Figure BDA0002585137140000076

S104具体包括:S104 specifically includes:

利用公式

Figure BDA0002585137140000077
确定目标函数;Z为相似性矩阵,U为新的相似矩阵,
Figure BDA0002585137140000078
为像素点的软标签矩阵,
Figure BDA0002585137140000079
为锚点的软标签矩阵,
Figure BDA00025851371400000710
表示所有像素点的标签矩阵,B为对角矩阵,α为规则化参数,LS为拉普拉斯矩阵。Use the formula
Figure BDA0002585137140000077
Determine the objective function; Z is the similarity matrix, U is the new similarity matrix,
Figure BDA0002585137140000078
is the soft label matrix of pixels,
Figure BDA0002585137140000079
is the soft label matrix of anchor points,
Figure BDA00025851371400000710
Represents the label matrix of all pixels, B is the diagonal matrix, α is the regularization parameter, and L S is the Laplacian matrix.

采用迭代优化方式对所述目标函数进行求解,得到像素点的标签;所述标签用于进行高光谱遥感图像的分类。The objective function is solved in an iterative optimization manner to obtain the labels of the pixel points; the labels are used to classify the hyperspectral remote sensing images.

其中,目标函数具体的确定过程为:Among them, the specific determination process of the objective function is as follows:

考虑在基于图的半监督学习中,图的质量最优,提出如下模型:Considering the optimal quality of graphs in graph-based semi-supervised learning, the following model is proposed:

Figure BDA00025851371400000711
Figure BDA00025851371400000711

其中,

Figure BDA0002585137140000081
分别表示原始数据和锚点的软标签矩阵。
Figure BDA0002585137140000082
表示所有数据(原始数据和锚点)的标签矩阵。由于训练样本是从原始数据中选出的一部分数据点,因此,Y可以写为
Figure BDA0002585137140000083
其中
Figure BDA0002585137140000084
B是对角矩阵,对角线上的第i个元素是规则化参数βi。B也可以写为
Figure BDA0002585137140000085
Figure BDA0002585137140000086
α是规则化参数。in,
Figure BDA0002585137140000081
Soft label matrices representing raw data and anchors, respectively.
Figure BDA0002585137140000082
A matrix of labels representing all data (raw data and anchors). Since the training samples are a subset of data points selected from the original data, Y can be written as
Figure BDA0002585137140000083
in
Figure BDA0002585137140000084
B is a diagonal matrix, and the ith element on the diagonal is the regularization parameter β i . B can also be written as
Figure BDA0002585137140000085
Figure BDA0002585137140000086
α is the regularization parameter.

在图论中,LS=DS-S是拉普拉斯矩阵,

Figure BDA0002585137140000087
是度矩阵,第i个对角线上的元素为di=∑jsij。DS也可以写为
Figure BDA0002585137140000088
其中
Figure BDA0002585137140000089
是一个对角矩阵,对角线上的元素为U的行和,
Figure BDA00025851371400000810
也是对角矩阵,对角线上的元素为U的列和,
Figure BDA00025851371400000811
由于公式(12)中的约束条件为
Figure BDA00025851371400000812
可以得到Dr=In,其中
Figure BDA00025851371400000813
是单位矩阵。因此,
Figure BDA00025851371400000814
然后,LS可采用如下方式进行标准化:In graph theory, L S = D S -S is the Laplace matrix,
Figure BDA0002585137140000087
is a degree matrix, and the element on the ith diagonal is di =j s ij . D S can also be written as
Figure BDA0002585137140000088
in
Figure BDA0002585137140000089
is a diagonal matrix, the elements on the diagonal are the row sums of U,
Figure BDA00025851371400000810
is also a diagonal matrix, the elements on the diagonal are the column sums of U,
Figure BDA00025851371400000811
Since the constraints in Equation (12) are
Figure BDA00025851371400000812
It can be obtained that D r =In , where
Figure BDA00025851371400000813
is the identity matrix. therefore,
Figure BDA00025851371400000814
Then, L S can be normalized as follows:

Figure BDA00025851371400000815
Figure BDA00025851371400000815

其中,

Figure BDA00025851371400000816
是单位矩阵。in,
Figure BDA00025851371400000816
is the identity matrix.

因此,标准化拉普拉斯矩阵后对应的最终目标函数为:Therefore, the corresponding final objective function after normalizing the Laplacian matrix is:

Figure BDA00025851371400000817
Figure BDA00025851371400000817

采用迭代优化方式对公式(14)进行求解的过程为:The process of solving formula (14) by iterative optimization is as follows:

当F,G固定时,公式(14)等价于:When F, G are fixed, formula (14) is equivalent to:

Figure BDA00025851371400000818
Figure BDA00025851371400000818

根据标准化后拉普拉斯矩阵的基本性质,可以得到如下关系:According to the basic properties of the normalized Laplace matrix, the following relationship can be obtained:

Figure BDA00025851371400000819
Figure BDA00025851371400000819

其中,fi是F的第i行,di=∑jsij,gj是G的第i行,dj=∑isjiwhere f i is the ith row of F, d i =∑ j s ij , g j is the ith row of G, d j =∑ i s ji .

根据公式(9)中S的特殊结构,公式(16)等价于:According to the special structure of S in Equation (9), Equation (16) is equivalent to:

Figure BDA0002585137140000091
Figure BDA0002585137140000091

因此,公式(15)也可以写为:Therefore, equation (15) can also be written as:

Figure BDA0002585137140000092
Figure BDA0002585137140000092

由于公式(18)中对不同的i都是独立的,因此可以对每一个i对应的目标函数进行求解。令

Figure BDA0002585137140000093
vi、ui、zi表示向量,他们中的第j个元素分别为vij、uij和zij。因此,对于每一个i,公式(18)可以写成如下的向量形式:Since formula (18) is independent for different i, the objective function corresponding to each i can be solved. make
Figure BDA0002585137140000093
v i , ui , and zi represent vectors, and the jth elements in them are v ij , u ij and z ij , respectively. Therefore, for each i, equation (18) can be written in vector form as follows:

Figure BDA0002585137140000094
Figure BDA0002585137140000094

公式(19)与公式(2)有相同的形式,可采用相同的方法进行求解。Formula (19) has the same form as formula (2), and can be solved by the same method.

当U固定时,公式(14)等价于:When U is fixed, formula (14) is equivalent to:

Figure BDA0002585137140000095
Figure BDA0002585137140000095

Figure BDA0002585137140000096
公式(20)可以确定为:make
Figure BDA0002585137140000096
Formula (20) can be determined as:

Figure BDA0002585137140000097
Figure BDA0002585137140000097

通过对J(Q)进行求导,可以得到如下公式:By derivation of J(Q), the following formula can be obtained:

Figure BDA0002585137140000098
Figure BDA0002585137140000098

因此,最终解为:Therefore, the final solution is:

Figure BDA0002585137140000099
Figure BDA0002585137140000099

Bα可以写为

Figure BDA00025851371400000910
其中
Figure BDA00025851371400000911
式(23)等价于:B α can be written as
Figure BDA00025851371400000910
in
Figure BDA00025851371400000911
Equation (23) is equivalent to:

Figure BDA0002585137140000101
Figure BDA0002585137140000101

令L11=In+Bαn

Figure BDA0002585137140000102
L22=Bαm+Im,采用如下分块矩阵求逆公式求解公式(24)中的第一项:Let L 11 =In + B αn ,
Figure BDA0002585137140000102
L 22 =B αm +I m , use the following block matrix inversion formula to solve the first term in formula (24):

Figure BDA0002585137140000103
Figure BDA0002585137140000103

其中,

Figure BDA0002585137140000104
由于
Figure BDA0002585137140000105
Figure BDA0002585137140000106
的计算复杂度为O(n3),对于大规模高光谱数据,计算量太大,因此,采用如下Woodbury矩阵(A-UCV)-1=A-1+A-1U(C-1-VA-1U)-1VA-1求解大规模矩阵C1求逆问题,将计算复杂度降低到O(nm2)。in,
Figure BDA0002585137140000104
because
Figure BDA0002585137140000105
beg
Figure BDA0002585137140000106
The computational complexity is O(n 3 ), which is too large for large-scale hyperspectral data. Therefore, the following Woodbury matrix (A-UCV) -1 =A -1 +A -1 U(C -1 - VA -1 U) -1 VA -1 solves the large-scale matrix C 1 inversion problem, reducing the computational complexity to O(nm 2 ).

Figure BDA0002585137140000107
Figure BDA0002585137140000107

基于如上推导,我们可以得到最终的软标签矩阵为:Based on the above derivation, we can get the final soft label matrix as:

Figure BDA0002585137140000108
Figure BDA0002585137140000108

根据软标签矩阵F,得到数据点xi的标签为:According to the soft label matrix F, the label of the data point x i is obtained as:

Figure BDA0002585137140000109
Figure BDA0002585137140000109

整个模型的计算复杂度为O(ndmt+nm2),而传统的基于图的半监督学习模型的计算复杂度为O(n2d+n3)。其中,n、m、d和t分别为样本数量,锚点数,维度和迭代次数。因此,对于处理大规模高光谱数据,能够快速准确的进行分类。The computational complexity of the entire model is O(ndmt+nm 2 ), while the computational complexity of traditional graph-based semi-supervised learning models is O(n 2 d+n 3 ). Among them, n, m, d and t are the number of samples, the number of anchor points, the dimension and the number of iterations, respectively. Therefore, for processing large-scale hyperspectral data, classification can be performed quickly and accurately.

S105,获取待分类的高光谱遥感图像。S105, obtaining a hyperspectral remote sensing image to be classified.

S106,采用所述二部图的半监督学习模型对所述待分类的高光谱遥感图像进行分类。S106, using the semi-supervised learning model of the bipartite graph to classify the hyperspectral remote sensing image to be classified.

图2为本发明所提供的一种高光谱遥感图像分类系统结构示意图,如图2所示,本发明所提供的一种高光谱遥感图像分类系统,包括:高光谱遥感图像获取模块201、锚点确定模块202、自适应二部图构建模块203、二部图的半监督学习模型构建模块204、待分类的高光谱遥感图像获取模块205和分类模块206。FIG. 2 is a schematic structural diagram of a hyperspectral remote sensing image classification system provided by the present invention. As shown in FIG. 2, a hyperspectral remote sensing image classification system provided by the present invention includes: a hyperspectral remote sensing image acquisition module 201, an anchor A point determination module 202 , an adaptive bipartite graph building module 203 , a semi-supervised learning model building module for bipartite graphs 204 , a hyperspectral remote sensing image acquisition module 205 to be classified, and a classification module 206 .

高光谱遥感图像获取模块201用于获取高光谱遥感图像。The hyperspectral remote sensing image acquisition module 201 is used to acquire hyperspectral remote sensing images.

锚点确定模块202用于根据所述高光谱遥感图像的像素点确定锚点;所述锚点为随机选取的高光谱遥感图像的像素点;所述锚点的数量小于高光谱遥感图像中的像素点的数量。The anchor point determination module 202 is configured to determine an anchor point according to the pixel points of the hyperspectral remote sensing image; the anchor point is a randomly selected pixel point of the hyperspectral remote sensing image; the number of the anchor points is less than that in the hyperspectral remote sensing image. the number of pixels.

自适应二部图构建模块203用于根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图。The adaptive bipartite graph construction module 203 is configured to construct an adaptive bipartite graph according to the pixel points and the anchor points of the hyperspectral remote sensing image, using the principle of adaptive proximity assignment.

二部图的半监督学习模型构建模块204用于根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型;所述二部图的半监督学习模型以自适应二部图为输入,以所述高光谱遥感图像的类别为输出。The semi-supervised learning model building module 204 of the bipartite graph is used for constructing a semi-supervised learning model of the bipartite graph according to the self-adaptive bipartite graph using a semi-supervised learning method; the semi-supervised learning model of the bipartite graph is based on the self- The adaptive bipartite map is used as input, and the category of the hyperspectral remote sensing image is used as output.

待分类的高光谱遥感图像获取模块205用于获取待分类的高光谱遥感图像。The hyperspectral remote sensing image acquisition module 205 to be classified is configured to acquire the hyperspectral remote sensing image to be classified.

分类模块206用于采用所述二部图的半监督学习模型对所述待分类的高光谱遥感图像进行分类。The classification module 206 is used for classifying the hyperspectral remote sensing image to be classified by using the semi-supervised learning model of the bipartite graph.

所述自适应二部图构建模块203具体包括:相似性矩阵构建单元和自适应二部图构建单元。The adaptive bipartite graph building module 203 specifically includes: a similarity matrix building unit and an adaptive bipartite graph building unit.

相似性矩阵构建单元用于根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建相似性矩阵.The similarity matrix construction unit is used to construct a similarity matrix according to the pixel points of the hyperspectral remote sensing image and the anchor points, using the principle of adaptive proximity assignment.

自适应二部图构建单元用于根据所述相似性矩阵构建自适应二部图。The adaptive bipartite graph construction unit is configured to construct an adaptive bipartite graph according to the similarity matrix.

本发明所提供的一种高光谱遥感图像分类系统,还包括:优化模块。The hyperspectral remote sensing image classification system provided by the present invention further comprises: an optimization module.

优化模块用于采用半监督学习目标对所述自适应二部图进行优化。An optimization module is used to optimize the adaptive bipartite graph using a semi-supervised learning objective.

所述二部图的半监督学习模型构建模块204具体包括:目标函数确定单元和像素点的标签确定单元。The semi-supervised learning model building module 204 of the bipartite graph specifically includes: an objective function determination unit and a pixel label determination unit.

目标函数确定单元用于利用公式

Figure BDA0002585137140000111
确定目标函数;Z为相似性矩阵,U为新的相似矩阵,
Figure BDA0002585137140000121
为像素点的软标签矩阵,
Figure BDA0002585137140000122
为锚点的软标签矩阵,
Figure BDA0002585137140000123
表示所有像素点的标签矩阵,B为对角矩阵,α为规则化参数,LS为拉普拉斯矩阵。The objective function determination unit is used to utilize the formula
Figure BDA0002585137140000111
Determine the objective function; Z is the similarity matrix, U is the new similarity matrix,
Figure BDA0002585137140000121
is the soft label matrix of pixels,
Figure BDA0002585137140000122
is the soft label matrix of anchor points,
Figure BDA0002585137140000123
Represents the label matrix of all pixels, B is the diagonal matrix, α is the regularization parameter, and L S is the Laplacian matrix.

像素点的标签确定单元用于采用迭代优化方式对所述目标函数进行求解,得到像素点的标签;所述标签用于进行高光谱遥感图像的分类。The label determination unit of the pixel point is used to solve the objective function in an iterative optimization manner to obtain the label of the pixel point; the label is used to classify the hyperspectral remote sensing image.

本说明书中各个实施例采用递进的方式描述,每个实施例重点说明的都是与其他实施例的不同之处,各个实施例之间相同相似部分互相参见即可。对于实施例公开的系统而言,由于其与实施例公开的方法相对应,所以描述的比较简单,相关之处参见方法部分说明即可。The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same and similar parts between the various embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant part can be referred to the description of the method.

本文中应用了具体个例对本发明的原理及实施方式进行了阐述,以上实施例的说明只是用于帮助理解本发明的方法及其核心思想;同时,对于本领域的一般技术人员,依据本发明的思想,在具体实施方式及应用范围上均会有改变之处。综上所述,本说明书内容不应理解为对本发明的限制。In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only used to help understand the methods and core ideas of the present invention; meanwhile, for those skilled in the art, according to the present invention There will be changes in the specific implementation and application scope. In conclusion, the contents of this specification should not be construed as limiting the present invention.

Claims (8)

1.一种高光谱遥感图像分类方法,其特征在于,包括:1. a hyperspectral remote sensing image classification method, is characterized in that, comprises: 获取高光谱遥感图像;Obtain hyperspectral remote sensing images; 根据所述高光谱遥感图像的像素点确定锚点;所述锚点为随机选取的高光谱遥感图像的像素点;所述锚点的数量小于高光谱遥感图像中的像素点的数量;An anchor point is determined according to the pixel points of the hyperspectral remote sensing image; the anchor point is a randomly selected pixel point of the hyperspectral remote sensing image; the number of the anchor points is less than the number of pixels in the hyperspectral remote sensing image; 根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图;According to the pixel points of the hyperspectral remote sensing image and the anchor points, the adaptive proximity assignment principle is adopted to construct an adaptive bipartite graph; 根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型;所述二部图的半监督学习模型以自适应二部图为输入,以所述高光谱遥感图像的类别为输出;According to the adaptive bipartite graph, a semi-supervised learning method is used to construct a semi-supervised learning model of the bipartite graph; the semi-supervised learning model of the bipartite graph takes the adaptive bipartite graph as input, and uses the hyperspectral remote sensing The category of the image is output; 获取待分类的高光谱遥感图像;Obtain hyperspectral remote sensing images to be classified; 采用所述二部图的半监督学习模型对所述待分类的高光谱遥感图像进行分类。The hyperspectral remote sensing image to be classified is classified using the semi-supervised learning model of the bipartite graph. 2.根据权利要求1所述的一种高光谱遥感图像分类方法,其特征在于,所述根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图,具体包括:2. A kind of hyperspectral remote sensing image classification method according to claim 1, it is characterized in that, described according to the pixel point of described hyperspectral remote sensing image and described anchor point, adopt adaptive proximity assignment principle, construct adaptive Two pictures, including: 根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建相似性矩阵;According to the pixel point of the hyperspectral remote sensing image and the anchor point, adopt the principle of adaptive proximity assignment to construct a similarity matrix; 根据所述相似性矩阵构建自适应二部图。An adaptive bipartite graph is constructed from the similarity matrix. 3.根据权利要求1所述的一种高光谱遥感图像分类方法,其特征在于,所述根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型,之前还包括:3. A kind of hyperspectral remote sensing image classification method according to claim 1, is characterized in that, described according to described adaptive bipartite graph, adopts semi-supervised learning method, constructs the semi-supervised learning model of bipartite graph, before. Also includes: 采用半监督学习目标对所述自适应二部图进行优化。The adaptive bipartite graph is optimized using a semi-supervised learning objective. 4.根据权利要求1所述的一种高光谱遥感图像分类方法,其特征在于,所述根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型,具体包括:4. a kind of hyperspectral remote sensing image classification method according to claim 1, is characterized in that, described according to described adaptive bipartite graph, adopts semi-supervised learning method, constructs the semi-supervised learning model of bipartite graph, specifically include: 利用公式
Figure FDA0002585137130000021
确定目标函数;Z为相似性矩阵,U为新的相似矩阵,
Figure FDA0002585137130000022
为像素点的软标签矩阵,
Figure FDA0002585137130000023
为锚点的软标签矩阵,
Figure FDA0002585137130000024
表示所有像素点的标签矩阵,B为对角矩阵,α为规则化参数,LS为拉普拉斯矩阵;
Use the formula
Figure FDA0002585137130000021
Determine the objective function; Z is the similarity matrix, U is the new similarity matrix,
Figure FDA0002585137130000022
is the soft label matrix of pixels,
Figure FDA0002585137130000023
is the soft label matrix of anchor points,
Figure FDA0002585137130000024
Represents the label matrix of all pixels, B is the diagonal matrix, α is the regularization parameter, and L S is the Laplace matrix;
采用迭代优化方式对所述目标函数进行求解,得到像素点的标签;所述标签用于进行高光谱遥感图像的分类。The objective function is solved in an iterative optimization manner to obtain the labels of the pixel points; the labels are used to classify the hyperspectral remote sensing images.
5.一种高光谱遥感图像分类系统,其特征在于,包括:5. A hyperspectral remote sensing image classification system, characterized in that, comprising: 高光谱遥感图像获取模块,用于获取高光谱遥感图像;Hyperspectral remote sensing image acquisition module, used to acquire hyperspectral remote sensing images; 锚点确定模块,用于根据所述高光谱遥感图像的像素点确定锚点;所述锚点为随机选取的高光谱遥感图像的像素点;所述锚点的数量小于高光谱遥感图像中的像素点的数量;The anchor point determination module is used for determining anchor points according to the pixel points of the hyperspectral remote sensing image; the anchor points are randomly selected pixel points of the hyperspectral remote sensing image; the number of the anchor points is less than the number of the hyperspectral remote sensing images. the number of pixels; 自适应二部图构建模块,用于根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建自适应二部图;an adaptive bipartite graph building module, configured to construct an adaptive bipartite graph according to the pixel points and the anchor points of the hyperspectral remote sensing image, using the principle of adaptive proximity assignment; 二部图的半监督学习模型构建模块,用于根据所述自适应二部图,采用半监督学习方法,构建二部图的半监督学习模型;所述二部图的半监督学习模型以自适应二部图为输入,以所述高光谱遥感图像的类别为输出;The semi-supervised learning model building module of bipartite graph is used for constructing a semi-supervised learning model of bipartite graph by adopting semi-supervised learning method according to the adaptive bipartite graph; the semi-supervised learning model of the bipartite graph is based on the self- Adapt the bipartite map as input, and use the category of the hyperspectral remote sensing image as output; 待分类的高光谱遥感图像获取模块,用于获取待分类的高光谱遥感图像;The hyperspectral remote sensing image acquisition module to be classified is used to acquire the hyperspectral remote sensing image to be classified; 分类模块,用于采用所述二部图的半监督学习模型对所述待分类的高光谱遥感图像进行分类。A classification module for classifying the hyperspectral remote sensing image to be classified by using the semi-supervised learning model of the bipartite graph. 6.根据权利要求5所述的一种高光谱遥感图像分类系统,其特征在于,所述自适应二部图构建模块具体包括:6. A kind of hyperspectral remote sensing image classification system according to claim 5, is characterized in that, described adaptive bipartite graph building module specifically comprises: 相似性矩阵构建单元,用于根据所述高光谱遥感图像的像素点和所述锚点,采用自适应邻近分配原则,构建相似性矩阵;a similarity matrix construction unit, configured to construct a similarity matrix according to the pixel point of the hyperspectral remote sensing image and the anchor point, using an adaptive proximity assignment principle; 自适应二部图构建单元,用于根据所述相似性矩阵构建自适应二部图。An adaptive bipartite graph construction unit, configured to construct an adaptive bipartite graph according to the similarity matrix. 7.根据权利要求5所述的一种高光谱遥感图像分类系统,其特征在于,还包括:7. A kind of hyperspectral remote sensing image classification system according to claim 5, is characterized in that, also comprises: 优化模块,用于采用半监督学习目标对所述自适应二部图进行优化。An optimization module for optimizing the adaptive bipartite graph using a semi-supervised learning objective. 8.根据权利要求5所述的一种高光谱遥感图像分类系统,其特征在于,所述二部图的半监督学习模型构建模块具体包括:8. a kind of hyperspectral remote sensing image classification system according to claim 5, is characterized in that, the semi-supervised learning model building module of described bipartite graph specifically comprises: 目标函数确定单元,用于利用公式
Figure FDA0002585137130000031
确定目标函数;Z为相似性矩阵,U为新的相似矩阵,
Figure FDA0002585137130000032
为像素点的软标签矩阵,
Figure FDA0002585137130000033
为锚点的软标签矩阵,
Figure FDA0002585137130000034
表示所有像素点的标签矩阵,B为对角矩阵,α为规则化参数,LS为拉普拉斯矩阵;
Objective function determination unit for utilizing the formula
Figure FDA0002585137130000031
Determine the objective function; Z is the similarity matrix, U is the new similarity matrix,
Figure FDA0002585137130000032
is the soft label matrix of pixels,
Figure FDA0002585137130000033
is the soft label matrix of anchor points,
Figure FDA0002585137130000034
Represents the label matrix of all pixels, B is the diagonal matrix, α is the regularization parameter, and L S is the Laplace matrix;
像素点的标签确定单元,用于采用迭代优化方式对所述目标函数进行求解,得到像素点的标签;所述标签用于进行高光谱遥感图像的分类。The label determination unit of the pixel point is used to solve the objective function in an iterative optimization manner to obtain the label of the pixel point; the label is used to classify the hyperspectral remote sensing image.
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