CN104574346A - Optical remote sensing image decomposition algorithm - Google Patents
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Abstract
本发明属于遥感图像处理领域,具体涉及一种光学遥感图像分解算法。它包括:步骤一:数据读取;读取存储的原始图像数据,步骤二:对数变换;对F(x,y)取对数,即f(x,y)=lg(F(x,y)),步骤三:小波分解;进行离散小波变换,小波基为哈尔小波,步骤四:逆变换;用零取代{Hp,t},与低频子图Lt进行小波逆变换,得到图像f空间域的低频图像Li,步骤五:分形计算;步骤六:循环判断;如果Di≤Dd,执行步骤七,否则令i值加1,然后执行步骤三小波分解,步骤七:最佳尺度判断;步骤八:图像生成。本发明的效果是:克服了传统的图像分解算法中无准确判别最优分解尺度的问题。
The invention belongs to the field of remote sensing image processing, in particular to an optical remote sensing image decomposition algorithm. It includes: step 1: data reading; read the stored original image data, step 2: logarithmic transformation; take the logarithm of F(x, y), that is, f(x, y)=lg(F(x, y)), step 3: wavelet decomposition; perform discrete wavelet transform, the wavelet base is Haar wavelet, step 4: inverse transform; replace {H p,t } with zero, and perform wavelet inverse transform with the low-frequency subgraph L t to obtain For the low-frequency image L i in the space domain of image f, step 5: fractal calculation; step 6: loop judgment; if D i ≤ D d , execute step 7, otherwise add 1 to the value of i, and then execute step 3 wavelet decomposition, step 7: Optimal scale judgment; Step 8: Image generation. The effect of the invention is that it overcomes the problem that the optimal decomposition scale cannot be accurately judged in the traditional image decomposition algorithm.
Description
技术领域technical field
本发明属于遥感图像处理领域,具体涉及一种光学遥感图像分解算法。The invention belongs to the field of remote sensing image processing, in particular to an optical remote sensing image decomposition algorithm.
背景技术Background technique
目前,在遥感领域为了更准确的获得地表物质成分空间分布的特征,经常采用地形校正的方法来消除地形的影响。为此,利用小波多分辨分析方法来研究遥感图像上不同尺度目标的特征已成为一种公认的思想,实现的方法是利用小波函数将原始图像分解为不同尺度的子图,然后利用子图进行不同尺度特征的目标分类和识别。但是,如何确定分解的级别是一个难题。现行图像分解算法通常利用不同级别分解结果,经过与实际特征相对比的试验来确定。这种方法主要是经验性的,不仅费时,而且缺少理论依据,难以推广。At present, in the field of remote sensing, in order to obtain the characteristics of the spatial distribution of surface material components more accurately, the method of terrain correction is often used to eliminate the influence of terrain. For this reason, it has become a recognized idea to use wavelet multi-resolution analysis method to study the characteristics of targets of different scales on remote sensing images. Object classification and recognition with features at different scales. However, how to determine the level of decomposition is a difficult problem. The current image decomposition algorithm usually uses different levels of decomposition results, and is determined through experiments compared with actual features. This method is mainly empirical, not only time-consuming, but also lacks theoretical basis, so it is difficult to promote.
发明内容Contents of the invention
本发明的目的是针对现有技术缺陷,提供一种光学遥感图像分解算法。The purpose of the present invention is to provide an optical remote sensing image decomposition algorithm aiming at the defects of the prior art.
本发明是这样实现的:一种光学遥感图像分解算法,包括下述步骤:The present invention is achieved in that a kind of optical remote sensing image decomposition algorithm comprises the following steps:
步骤一:数据读取Step 1: Data reading
读取存储的原始图像数据,读取出的图像为灰度值,即本步骤得到的数据为三维数组,其中两维是图像的横纵坐标,第三维是坐标对应的灰度值,本步骤得到的结果用(x,y,F(x,y))表示,其中x,y分别为图像的横纵坐标,F(x,y)为点(x,y)的灰度值,Read the stored original image data, and the read image is the gray value, that is, the data obtained in this step is a three-dimensional array, in which two dimensions are the horizontal and vertical coordinates of the image, and the third dimension is the gray value corresponding to the coordinates. This step The obtained result is represented by (x, y, F(x, y)), where x, y are the horizontal and vertical coordinates of the image, and F(x, y) is the gray value of the point (x, y),
步骤二:对数变换Step 2: Logarithmic transformation
对F(x,y)取对数,即f(x,y)=lg(F(x,y)),Take the logarithm of F(x,y), that is, f(x,y)=lg(F(x,y)),
本步骤得到的结果用(x,y,f(x,y))表示,在后续表示中也用f表示f(x,y)构成的图像的集合,The result obtained in this step is represented by (x, y, f(x, y)), and in the subsequent representation, f is also used to represent the set of images formed by f(x, y).
步骤三:小波分解Step 3: Wavelet decomposition
对步骤二得到的灰度值用Mallat算法进行离散小波变换,小波基为哈尔小波,The gray value obtained in step 2 is subjected to discrete wavelet transform using the Mallat algorithm, and the wavelet base is the Haar wavelet.
本步骤对f进行分解,得到小波变换系数{Lt,Hp,t},Lt表示尺度t下图像f的低频子图像,Hp,t表示在尺度t下p方向的高频子图像,这里p=1,2,3,p=1表示水平方向,p=2表示垂直方向,p=3表示对角方向,In this step, f is decomposed to obtain wavelet transform coefficients {L t , H p,t }, L t represents the low-frequency sub-image of image f at scale t, and H p,t represents the high-frequency sub-image of image f at scale t in direction p , where p=1, 2, 3, p=1 represents the horizontal direction, p=2 represents the vertical direction, p=3 represents the diagonal direction,
步骤四:逆变换Step 4: Inverse Transform
用零取代{Hp,t},与低频子图Lt进行小波逆变换,得到图像f空间域的低频图像Li,在第一次计算时i=t,Li表示i尺度下的空间域的低频图像,在后续迭代计算中i的值根据后续步骤确定,在后续步骤中将Li图像作为待判断图像L0,Substitute {H p,t } with zero, perform wavelet inverse transformation with the low-frequency sub-image Lt, and obtain the low-frequency image L i in the spatial domain of the image f. In the first calculation, i=t, and L i represents the spatial domain at the scale i In the subsequent iterative calculation, the value of i is determined according to the subsequent steps. In the subsequent steps, the L i image is used as the image to be judged L 0 ,
步骤五:分形计算Step 5: Fractal calculation
用Matlab的Fraclab模块读入低频图像L0和DEM,并用盒计维数工具计算,在保证互相关系数等于1的前提下,取连续五点使得拟合最大误差与拟合点跨度比最小时的回归方程计算得到的盒计维数为所计算的盒计维数值,分别得到低频图像L0和DEM的盒计维数Di和Dd,Use the Fraclab module of Matlab to read in the low-frequency image L 0 and DEM, and use the box dimension tool to calculate. Under the premise of ensuring that the cross-correlation coefficient is equal to 1, take five consecutive points so that the maximum fitting error and the fitting point span ratio are the smallest The box count dimension calculated by the regression equation is the calculated box count dimension value, and the box count dimensions D i and D d of the low-frequency image L 0 and DEM are obtained respectively,
步骤六:循环判断Step 6: Loop Judgment
如果Di≤Dd,执行步骤七,否则令i值加1,然后执行步骤三小波分解,If D i ≤ D d , go to step 7, otherwise add 1 to the value of i, and then go to step 3 for wavelet decomposition,
步骤七:最佳尺度判断Step 7: Judgment of the best scale
判断Di-1-Dt的绝对值和Di-Dd的绝对值的大小,如果Abs(Di-Dd)≤Abs(Di-1-Dd),最佳分解尺度为i,否则最佳尺度为i-1,最佳尺度附值给Ibest,Judging the absolute value of D i-1 -D t and the absolute value of D i -D d , if Abs(D i -Dd)≤Abs(D i-1 -D d ), the best decomposition scale is i, Otherwise, the best scale is i-1, and the best scale is assigned a value to I best ,
所述的Abs表示绝对值,The Abs means the absolute value,
步骤八:图像生成Step Eight: Image Generation
用零取代{Hp,t},t=1,2,…,Ibest,p=1,2,3,与尺度Ibest下的低频子图进行小波逆变换,再进行逆对数变化得到空间域的低频图像——地形子图,Replace {H p,t } with zero, t=1,2,...,I best , p=1,2,3, perform wavelet inverse transformation with the low-frequency subgraph under the scale I best , and then perform inverse logarithmic transformation to get Low-frequency images in the spatial domain - terrain submaps,
用高频子图集合{Hp,t},t=1,2,…,Ibest,p=1,2,3与零进行小波逆变换,再进行逆对数变化得到空间域的高频图像——岩性子图,Use the high-frequency subgraph set {H p,t }, t=1,2,...,I best , p=1,2,3 and zero to perform wavelet inverse transformation, and then perform inverse logarithmic change to obtain the high frequency in the space domain image - lithology submap,
输出代表岩性的高频子图和代表地形的低频子图。Output a high-frequency submap representing lithology and a low-frequency submap representing topography.
如上所述的一种光学遥感图像分解算法,其中,所述的DEM是与图像f定义在同一空间域的地表高程图像,同样是三维数组,可以用(x,y,D(x,y))表示,其中x,y分别为图像的横纵坐标,D(x,y)为点(x,y)的高程值。An optical remote sensing image decomposition algorithm as described above, wherein the DEM is a surface elevation image defined in the same spatial domain as the image f, which is also a three-dimensional array, and can be used (x, y, D(x, y) ), where x and y are the horizontal and vertical coordinates of the image respectively, and D(x, y) is the elevation value of the point (x, y).
使用本发明的效果是:本发明首先利用取对数的运算,把遥感图像所包含的信息由乘性运算结果转换成加性运算结果;然后利用小波函数对图像进行分解。为了确定分解级别,通过计算DEM和低频子图的分形维数是否相等(在一定误差范围内)的方法,来判断最优的小波变换尺度,最终把图像分解为空间域的低频地形子图和空间域的高频的岩性子图,克服了传统的图像分解算法中无准确判别最优分解尺度的问题。因此,将分形维数计算和小波分解相结合的方法,克服了需要靠经验来判断小波分解尺度和地形校正效果不明显的缺点,可以大大提高图像分解的效果,对于遥感地物识别和遥感数据融合有重要的意义和实用价值。该分解算法的思想还可以推广到其他光学图象的分解应用之中。The effect of using the present invention is: firstly, the present invention converts the information contained in the remote sensing image from the result of multiplicative operation to the result of additive operation by taking logarithm; and then uses wavelet function to decompose the image. In order to determine the decomposition level, the optimal wavelet transform scale is judged by calculating whether the fractal dimensions of the DEM and the low-frequency submap are equal (within a certain error range), and finally the image is decomposed into the low-frequency topographic submap and the low-frequency topographic submap in the spatial domain. The high-frequency lithology submap in the space domain overcomes the problem of inaccurate determination of the optimal decomposition scale in the traditional image decomposition algorithm. Therefore, the method of combining fractal dimension calculation with wavelet decomposition overcomes the shortcomings of needing to rely on experience to judge the scale of wavelet decomposition and the effect of terrain correction is not obvious, and can greatly improve the effect of image decomposition. Fusion has important significance and practical value. The idea of the decomposition algorithm can also be extended to other optical image decomposition applications.
附图说明Description of drawings
图1是本发明方法的基本流程图;Fig. 1 is the basic flowchart of the inventive method;
图2是DS矿区TM图像小波分解结果。Fig. 2 is the wavelet decomposition result of TM image in DS mining area.
具体实施方式Detailed ways
一种光学遥感图像分解算法,包括下述步骤:An optical remote sensing image decomposition algorithm, comprising the following steps:
步骤一:数据读取Step 1: Data reading
读取存储的原始图像数据,读取出的图像为灰度值,即本步骤得到的数据为三维数组,其中两维是图像的横纵坐标,第三维是坐标对应的灰度值。本步骤得到的结果用(x,y,F(x,y))表示,其中x,y分别为图像的横纵坐标,F(x,y)为点(x,y)的灰度值。Read the stored original image data, and the read image is the gray value, that is, the data obtained in this step is a three-dimensional array, in which two dimensions are the horizontal and vertical coordinates of the image, and the third dimension is the gray value corresponding to the coordinates. The result obtained in this step is represented by (x, y, F(x, y)), where x, y are the horizontal and vertical coordinates of the image, and F(x, y) is the gray value of the point (x, y).
步骤二:对数变换Step 2: Logarithmic transformation
对F(x,y)取对数,即f(x,y)=lg(F(x,y))。Take the logarithm of F(x,y), that is, f(x,y)=lg(F(x,y)).
本步骤将影响遥感图像的两个因素——地物和地形,由乘性运算转换为加性运算。In this step, the two factors that affect the remote sensing image - surface objects and terrain, are converted from multiplicative operations to additive operations.
本步骤得到的结果用(x,y,f(x,y))表示,在后续表示中也用f表示f(x,y)构成的图像的集合。The result obtained in this step is represented by (x, y, f(x, y)), and in the subsequent representation, f is also used to represent the set of images formed by f(x, y).
步骤三:小波分解Step 3: Wavelet decomposition
对步骤二得到的灰度值用Mallat算法进行离散小波变换,小波基为哈尔小波。The gray value obtained in step 2 is subjected to discrete wavelet transformation using the Mallat algorithm, and the wavelet base is Haar wavelet.
本步骤对f进行分解,得到小波变换系数{Lt,Hp,t},Lt表示尺度t下图像f的低频子图像,Hp,t表示在尺度t下p方向的高频子图像。这里p=1,2,3,p=1表示水平方向,p=2表示垂直方向,p=3表示对角方向。计算结果如附图2所示。In this step, f is decomposed to obtain wavelet transform coefficients {L t , H p,t }, L t represents the low-frequency sub-image of image f at scale t, and H p,t represents the high-frequency sub-image of image f at scale t in direction p . Here p=1, 2, 3, p=1 represents the horizontal direction, p=2 represents the vertical direction, and p=3 represents the diagonal direction. The calculation results are shown in Figure 2.
步骤四:逆变换Step 4: Inverse Transform
用零取代{Hp,t},与低频子图Lt进行小波逆变换,得到图像f空间域的低频图像Li。在第一次计算时i=t,Li表示i尺度下的空间域的低频图像,在后续迭代计算中i的值根据后续步骤确定。本申请将Li图像作为待判断图像L0。Replace {H p,t } with zero, and perform wavelet inverse transformation with the low-frequency sub-image Lt to obtain the low-frequency image L i in the spatial domain of the image f. In the first calculation, i=t, L i represents the low-frequency image in the spatial domain at scale i, and the value of i is determined according to subsequent steps in subsequent iterative calculations. In this application, the L i image is taken as the image to be judged L 0 .
步骤五:分形计算Step 5: Fractal calculation
用Matlab的Fraclab模块读入低频图像L0和DEM,并用盒计维数工具计算,在保证互相关系数等于1的前提下,取连续五点使得拟合最大误差与拟合点跨度比最小时的回归方程计算得到的盒计维数为所计算的盒计维数值。分别得到低频图像L0和DEM的盒计维数Di和Dd。Use the Fraclab module of Matlab to read in the low-frequency image L 0 and DEM, and use the box dimension tool to calculate. Under the premise of ensuring that the cross-correlation coefficient is equal to 1, take five consecutive points so that the maximum fitting error and the fitting point span ratio are the smallest The box count dimension calculated by the regression equation is the calculated box count dimension value. The box count dimensions D i and D d of the low frequency image L 0 and DEM are obtained respectively.
所述的DEM是与图像f定义在同一空间域的地表高程图像,同样是三维数组,可以用(x,y,D(x,y))表示,其中x,y分别为图像的横纵坐标,D(x,y)为点(x,y)的高程值。The DEM is a surface elevation image defined in the same spatial domain as the image f, which is also a three-dimensional array and can be represented by (x, y, D(x, y)), where x and y are the horizontal and vertical coordinates of the image respectively , D(x, y) is the elevation value of the point (x, y).
步骤六:循环判断Step 6: Loop Judgment
如果Di≤Dd,执行步骤七,否则令i值加1,然后执行步骤三小波分解。If D i ≤ D d , execute step seven, otherwise add 1 to the value of i, and then execute step three for wavelet decomposition.
在某次计算中,分解到第5级时,L0的分形维数为2.16599,小于DEM的分形维数2.27822,所以停止于第5级。In a certain calculation, when decomposing to the fifth level, the fractal dimension of L 0 is 2.16599, which is smaller than the fractal dimension of DEM 2.27822, so it stops at the fifth level.
步骤七:最佳尺度判断Step 7: Judgment of the best scale
判断Di-1-Dt的绝对值和Di-Dd的绝对值的大小,如果Abs(Di-Dd)≤Abs(Di-1-Dd),最佳分解尺度为i,否则最佳尺度为i-1。最佳尺度附值给Ibest。Judging the absolute value of D i-1 -D t and the absolute value of D i -D d , if Abs(D i -Dd)≤Abs(D i-1 -D d ), the best decomposition scale is i, Otherwise the optimal scale is i-1. The best scale attaches value to I best .
所述的Abs表示绝对值。Said Abs means absolute value.
步骤八:图像生成Step Eight: Image Generation
用零取代{Hp,t},t=1,2,…,Ibest,p=1,2,3。与尺度Ibest下的低频子图进行小波逆变换,再进行逆对数变化得到空间域的低频图像——地形子图。Replace {H p,t } with zero, t=1,2,...,I best , p=1,2,3. Perform wavelet inverse transformation with the low-frequency submap under the scale I best , and then perform inverse logarithmic transformation to obtain the low-frequency image in the spatial domain—topographic submap.
用高频子图集合{Hp,t},t=1,2,…,Ibest,p=1,2,3与零进行小波逆变换,再进行逆对数变化得到空间域的高频图像——岩性子图。Use the high-frequency subgraph set {H p,t }, t=1,2,...,I best , p=1,2,3 and zero to perform wavelet inverse transformation, and then perform inverse logarithmic change to obtain the high frequency in the space domain Image - Lithology submap.
输出代表岩性的高频子图和代表地形的低频子图。Output a high-frequency submap representing lithology and a low-frequency submap representing topography.
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Cited By (3)
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