CN107437267A - Vegetation region high spectrum image analogy method - Google Patents

Vegetation region high spectrum image analogy method Download PDF

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CN107437267A
CN107437267A CN201610361984.5A CN201610361984A CN107437267A CN 107437267 A CN107437267 A CN 107437267A CN 201610361984 A CN201610361984 A CN 201610361984A CN 107437267 A CN107437267 A CN 107437267A
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CN107437267B (en
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张文娟
莫云华
张兵
陈正超
高连如
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Institute of Remote Sensing and Digital Earth of CAS
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Abstract

The present invention relates to a kind of vegetation region high spectrum image analogy method, vegetation biochemical parameter calculating is carried out for multispectral data, obtain vegetation biochemical parameter image, and then typical vegetation radiative transfer model PROSAIL is utilized, vegetation biochemical parameter is input to model, realizes that high spectrum image is simulated, high-precision spectrum picture can be obtained, information content, low manufacture cost, efficiency high can be improved.

Description

Vegetation region high spectrum image analogy method
Technical field
The invention belongs to a kind of spectrum picture analogy method, and in particular to a kind of vegetation region high spectrum image analogy method.
Background technology
High spectrum image simulation is view data that high spectral resolution is calculated by model construction, existing method Be mainly based upon multispectral image data classified, abundance inverting, and object light modal data in combination, carry out spectrum charting or line Property mixing obtain high spectrum image, this method requires to obtain high-precision synchronous spectrum data, to ensure the precision of image simulation, And limited by algorithm, Subsection spectrum is mainly realized in multispectral data simulates hyperspectral image data, but it is untrue It is positive to improve information content.
The content of the invention
The present invention is directed to simulates high-spectral data process currently with the methods of classification, abundance inverting based on multispectral data Present in synchrodata be difficult to acquisition problem, devise a kind of high spectrum image analogy method for vegetation area, first Vegetation biochemical parameter calculating is carried out for multispectral image data, obtains vegetation biochemical parameter image, and then utilize typical vegetation Radiative transfer model PROSAIL, vegetation biochemical parameter figure is input to model, realizes that high spectrum image is simulated, can obtain high-precision The spectrum picture of degree, information content, low manufacture cost, efficiency high can be improved.
In order to achieve the above object, the present invention has following technical scheme:
A kind of vegetation region high spectrum image analogy method of the present invention, there is following steps:
For a M row, N row, L wave band multispectral image data Rmulti, for the high spectrum image of vegetation area Analogy method step is as follows:
(1), sample data generation step:
1) value:Blade construction parameter N:Span 0.5~4, step-length 0.5;Chlorophyll content Cab:Span 5~ 80, step-length 10, chlorophyll content Cab unit is μ g/cm2;Dry matter weight of leaf content Cm:Span 0.003~0.033, Step-length 0.003, dry matter weight of leaf content Cm unit is g/cm2;Carotenoid content Car:Span 0.5~16, step-length 1, carotenoid content Car unit are μ g/cm2;Leaf area index LAI:Span 1.5~6, step-length 0.5.2) to upper 5 parameter values for stating step 1) carry out 9860 groups of biochemical parameters that permutation and combination obtains, and set following fixed input parameter, Form 9860 groups of input datas:
The fixed input parameter:
Brown cellulose content is 0, water content 0.024cm, and hot spot-effect parameter is 0.01, and soil lightness parameter is 1, the sun Zenith angle is 30 °, and view zenith angle is 10 °, and relative bearing is 0 °;
3) above-mentioned 9860 groups of input datas are directed to, is calculated using PROSAIL models, tries to achieve corresponding canopy reflectance spectrum Data, form matrix;
4) the above-mentioned canopy reflectance spectrum data got are directed to, according to the spectral response functions of the multispectral data, are carried out Equivalent Calculation, corresponding multispectral reflectivity data is obtained, for i-th of multispectral data corresponding to kth group input data The reflectivity ρ of wave bandmulti(k, λ (i)) is:
Wherein fλ(i)(1, j) it is wave-length coverage corresponding to i-th of wave band, nw (i) number, f for corresponding toλ(i)(2, j) and the The corresponding spectral response functions of the wave-length coverage of i wave band, ρ (k, fλ(i)(1, j)) be kth group input data in i-th The corresponding canopy reflectance spectrum data of the wave-length coverage of wave band, matrix is obtained after carrying out Equivalent Calculation to all samples and wave band ρmulti(ns, L), ns correspond to sample group number 9860, and L corresponds to multispectral data wave band number;
(2) biochemical parameter, obtained for combinations thereof and the multispectral reflectivity data ρ correspondingly tried to achievemulti(ns, L), model construction is carried out, is the step of structure:
1) sample data is divided into a part as training data, another part is as test data, for above-mentioned steps (1) data of value, the number of training randomly selected are 7888, and test sample number is 1972;
2) training data is directed to, vector machine model is supported and kernel function is set, supporting vector machine model is using recurrence The epsilon-SVR models commonly used in modeling, penalty parameter c is its relevant parameter;Kernel function uses RBF kernel functions, and g is its pass Join parameter;
3) after supporting vector machine model and kernel function is set, for epsilon-SVR models and RBF kernel functions, its Relevant parameter is c and g, and training data is inputted into SVMs, and biochemistry can be obtained using the relevant parameter value of system default Parameter computation model;
(3) for blade construction parameter N, chlorophyll content Cab, dry matter weight of leaf content Cm, carotenoid content Car, Leaf area index LAI, relevant parameter c and g value corresponding to being calculated is set according to above-mentioned model and kernel function, and then, for Multispectral image data, based on epsilon-SVR models, gaussian radial basis function RBF kernel functions, and corresponding c and g values, utilize SVMs carries out Parameter Map calculating respectively, obtains blade construction parameter N, chlorophyll content Cab, dry matter weight of leaf content Cm, carotenoid content Car, leaf area index LAI Parameter Map;
(4) blade construction parameter N, chlorophyll content Cab, dry matter weight of leaf content Cm, carotenoid content are being obtained On the basis of Car, leaf area index LAI Parameter Maps, following fixed input parameter is set to each pixel on image:
Brown cellulose content is 0, water content 0.024cm, and hot spot-effect parameter is 0.01, and soil lightness parameter is 1, the sun Zenith angle is 30 °, and view zenith angle is 10 °, and relative bearing is 0 °;
And then with reference to the Parameter Map of above-mentioned 5 kinds of parameters being calculated, by PROSAIL models calculate by pixel Realize that high spectrum image is simulated, obtain vegetation area high spectrum image.
Wherein, the step (2) also includes:In order to obtain optimal biochemical parameter computation model, for the test number According to optimizing relevant parameter c and g value using grid-search algorithms.
Wherein, the relevant parameter c and g of the optimization value are set as follows:C, g span is disposed as 2-8-~28, Step-size in search is arranged to 2i, wherein i value is arranged to 1.
Due to taking above technical scheme, the advantage of the invention is that:
The present invention carries out vegetation biochemical parameter calculating for multispectral data, obtains vegetation biochemical parameter image, Jin Erli With typical vegetation radiative transfer model PROSAIL, vegetation biochemical parameter is input to model, realizes that high spectrum image is simulated, energy High-precision spectrum picture is obtained, information content, low manufacture cost, efficiency high can be improved.
Brief description of the drawings
Fig. 1 is the general flow chart of the present invention;
Fig. 2 is sample data generation module flow chart of the present invention;
Fig. 3 is model construction module flow chart of the present invention;
Fig. 4 is that biochemical parameter figure of the present invention builds block flow diagram;
Fig. 5 is high spectrum image analog module flow chart of the present invention.
Embodiment
Following examples are used to illustrate the present invention, but are not limited to the scope of the present invention.
Referring to Fig. 1-5:
A kind of vegetation region high spectrum image analogy method of the present invention,
The overall procedure of the present invention is divided into four parts:" sample data generation module ", " model construction module ", " biochemistry Parameter Map computing module ", " high-spectral data analog module ", referring to Fig. 1,
Data explanation:
1st, multispectral image RmultiIt is a three-dimensional matrice:M rows, N row, L wave band;
2nd, multispectral image centre wavelength array λ (L), wherein λ (i) represent the centre wavelength of i-th of wave band;
3rd, the common L of the spectral response functions of multispectral image, fλ(i)(2, nw (i)) be i-th wave band (1 (i≤L's) Spectral response functions, it is the array of one two row, first is classified as wavelength, and second is classified as spectral response value, and nw (i) rings for the spectrum Answer line number corresponding to function.
A kind of vegetation region high spectrum image analogy method step of the present invention is as follows:
First, sample data generation module, referring to Fig. 2,
Step 1:Carry out biochemical parameter value setting:Blade construction parameter N, chlorophyll content Cab, dry matter weight of leaf are contained Cm, carotenoid content Car, leaf area index LAI are measured, value is carried out according to scope and the fixed step size of table 1 below, it is right respectively Answer vectorial Nv, Cabv, Cmv, Carv, LAIv;
The parameter of table 1 and its value
Step 2:PROSAIL mode input data are set:Permutation and combination is carried out to vectorial Nv, Cabv, Cmv, Carv, LAIv 9860 groups of obtained biochemical parameters, and set other fixation input parameters as shown in the table, thus 9860 groups of input datas are formed, Matrix Para (ns, np) is designated as, wherein ns=9860, np correspond to the number of parameters of input data, are the every a line of 12, Para matrixes Represent one group of input data;
The input parameter that the model of table 2 is fixed
Step 3:Try to achieve canopy reflectance spectrum data:For above-mentioned 9860 groups of input data Para (ns, np), utilize PROSAIL models are calculated, and try to achieve corresponding canopy reflectance spectrum data, form matrix ρ (ns, nb), and wherein ns=9860 is right 9860 groups of input datas are answered, nb corresponds to the wavelength information of canopy reflectance spectrum data, and wavelength information is from 400nm to 2500nm, spectrum Canopy reflectance spectrum data corresponding to kth group input data are represented at intervals of 1nm, ρ (k, *);
Step 4:It is equivalent to carry out spectrum, obtains multiple-spectrum canopy reflectivity data:Reflected for the above-mentioned canopy got Rate data, according to the spectral response functions of the multispectral data, Equivalent Calculation is carried out, obtain corresponding multispectral reflectivity number According to.For the reflectivity ρ of i-th of wave band of multispectral data corresponding to kth group input datamulti(k, λ (i)) is:
Wherein ρ (k, fλ(i)(1, j)) it is that the wavelength of corresponding kth group input data is fλ(i)Canopy reflectance spectrum number when (1, j) According to.Matrix ρ is obtained after carrying out Equivalent Calculation to all samples and wave bandmulti(ns, L), ns correspond to sample group number 9860, and L is corresponding Multispectral data wave band number.
2nd, model construction module, referring to Fig. 3,
Step 1:Sample data prepares:Input data Para (ns, np) and corresponding multiple-spectrum canopy data ρmulti (ns, L) forms 9860 groups of sample datas, is classified as two parts, from 7888 sample datas randomly selected as training number According to remaining 1972 data are as test data;
Step 2:Supporting vector machine model and kernel function are set:Supporting vector machine model uses what is commonly used in regression modeling Epsilon-SVR models, penalty parameter c are its relevant parameters;Kernel function uses RBF kernel functions, and g is its relevant parameter;
Step 3:Relevant parameter optimizes and determined:For epsilon-SVR models and RBF kernel functions, relevant parameter be c and g;After SVMs type and kernel function type is set, training data is inputted into SVMs, utilizes system default Relevant parameter value i.e. can obtain biochemical parameter computation model.In order to obtain optimal computation model, for test data, use Grid-search algorithms are associated parameter optimization;Grid data service is a kind of parameter optimization method more commonly used at present, first Optimizing parameter c and g span and the step-length of search are determined respectively, then build regression model respectively using each group parameter Precision of prediction is obtained, finally selects optimal parameter combination;Relevant parameter c, g of optimization setting are as shown in table 3 below, wherein, C, g span is disposed as 2-8~28, step-size in search is arranged to 2i, wherein i value is arranged to 1, i.e. value is arranged to 2-8、 2-7、2-6、2i…26、27、28
Parameter setting when table 3 is based on grid data service parameter optimization
3rd, biochemical parameter figure structure module, referring to Fig. 4,
Step 1:Parameter N computation model is established:According to the model building method of module 2, blade construction parameter N is carried out Model construction, try to achieve corresponding c and g values.
Step 2:Parameter Cab computation model structure:According to the model building method of module 2, chlorophyll content Cab is entered Row model construction, try to achieve corresponding c and g values.
Step 3:Parameter Car computation model structure:According to the model building method of module 2, to carotenoid content Car carries out model construction, tries to achieve corresponding c and g values.
Step 4:Parameter Cm computation model structure:According to the model building method of module 2, to dry matter weight of leaf content Cm Model construction is carried out, tries to achieve corresponding c and g values.
Step 5:Parameter LAI computation model structure:According to the model building method of module 2, leaf area index LAI is entered Row model construction, try to achieve corresponding c and g values.
Step 6:Biochemical parameter, which is carried out, based on multispectral image data solves charting:Calculated by above-mentioned 5 biochemical parameters Relevant parameter-c corresponding to acquisition and-g is worth, based on epsilon-SVR models, gaussian radial basis function (RBF) kernel function, respectively to more Spectral image data RmultiParameter Map corresponding to progress calculates, and obtains blade construction parameter N, chlorophyll content Cab, blade dry Matter content Cm, carotenoid content Car, leaf area index LAI Parameter Maps, corresponding Parameter Map matrix:para_imgN、 para_imgCab、para_imgCm、para_imgCar、para_imgLAI, matrix size is M rows, N row.
4th, high spectrum image analog module, referring to Fig. 5,
Step 1:Input is set:Obtaining blade construction parameter N, chlorophyll content Cab, dry matter weight of leaf content Cm, class On the basis of carotene carotene content Car, leaf area index LAI Parameter Maps, other are set to fix input parameter to each pixel on image Shown in following 4:
The input parameter that the model of table 4 is fixed
Step 2:High spectrum image is simulated:With reference to 5 width Parameter Maps of inverting:para_imgN、para_imgCab、para_ imgCm、para_imgCar、para_imgLAI, by PROSAIL models calculate by pixel and realize that high spectrum image is simulated, obtain To vegetation area high spectrum image.It is a three-dimensional matrice hyper_img that EO-1 hyperion analog image matrix, which is,:Wherein M rows, N row, Wave band number is 400nm to 2500nm scopes, spectrum interval 1nm.
PROSAIL models:PROSAIL models are to combine the vegetation radiative transfer model formed with SAIL by PROSPECT, It carries out Reflectivity for Growing Season spectrum generation according to vegetation structure, biochemical parameter, can calculated mainly for broad-leaved Vegetation canopy To for 400nm to 2500nm scopes, spectrum interval is 1nm hyperspectral remote sensing.Wherein PROSPECT models be by The leaf reflectance model that Jacquemoud and Baret is proposed first in nineteen ninety, the model improve in nineteen ninety-five. PROSPECT models can simulate reflectivity and transmissivity of the blade in the range of visible ray to short infrared wave band, and they are seen Work is the function of blade construction parameter and biochemical parameter.SAIL models are an extensions of Suits models, can preferably be embodied The leaf area index LAI and Leaf angle inclination distribution LAD of horizontal homogeneous canopy are to bidirectional reflectance--distribution function BRDF variation tendencies Influence, by the extensive use of remote sensing academia.
Epsilon-SVR models and gaussian radial basis function (RBF) kernel function:Regression analysis is being carried out using SVMs During, it is necessary to it is supported the selection of vector machine model and the selection of kernel function.
For regression problem, supporting vector machine model has epsilon-SVR models, nu-SVR models etc., in regression modeling Currently used is epsilon-SVR models, and penalty parameter c is its relevant parameter;
When carrying out regression analysis using SVMs, kernel function causes the calculating brought from lower dimensional space to higher dimensional space Complexity substantially reduces so that SVMs completes the conversion from non-linear to linear;The linear core of common kernel function Function, Polynomial kernel function, gaussian radial basis function (RBF) kernel function, multilayer perceptron (Sigmoid) kernel function etc..Gauss is radially Base (RBF) kernel function is applied to the situation of linearly inseparable, and number of parameters is moderate, therefore uses the kernel function more, and g is its pass Join parameter.
Blade construction parameter N is to describe the parameter that blade is divided into how many layers.
Leaf area index (leaf area index) is called leaf-area coefficient, refers to plant leaf blade in land area of one unit The gross area accounts for the multiple of land area.
View zenith angle, observed azimuth in observation geometry can be obtained by remote sensor observation condition, generally be referred to by user It is fixed.
Solar zenith angle, solar azimuth are calculated according to test block longitude and latitude, image acquisition time and obtained.Due to sun height It is 90 ° to spend angle with solar zenith angle sum, therefore calculates sun altitude and be just readily available solar zenith angle, altitude of the sun The calculation formula at angle is as follows:
In formula,Sun altitude is represented, δ represents solar declination,Local latitude is represented, t represents solar hour angle.The sun Azimuthal calculation formula is as follows:
In formula, A represents solar azimuth,Sun altitude is represented, δ represents solar declination,Represent local latitude.
Relative bearing is the difference of solar azimuth and observed azimuth.
The parameters such as soil lightness parameter, hot spot-effect parameter, equivalent water thickness, brown pigment are according to test block concrete condition Set, and specified by user.
Step-length, it is that calculative numerical value is uniformly divided into several sections, the length in each section is just step-length, i.e. phase The interval of adjacent two values, such as:The value of some parameter setting is from 0-10, is step-length with 1, then the vector of formation is:0,1, 2,3,4,5,6,7,8,9,10。
Grid data service is a kind of parameter optimization method more commonly used at present, determines optimizing parameter c and g respectively first Span and the step-length of search, regression model is then built respectively using each group parameter and obtains precision of prediction, is finally selected Optimal parameter combination.
Above-described is only the preferred embodiment of the present invention, it is noted that for one of ordinary skill in the art For, without departing from the concept of the premise of the invention, various modifications and improvements can be made, these belong to the present invention Protection domain.

Claims (3)

1. a kind of vegetation region high spectrum image analogy method, it is characterised in that have following steps:
For a M row, N row, L wave band multispectral image data Rmulti, simulated for the high spectrum image of vegetation area Method and step is as follows:
(1), sample data generation step:
1) value:Blade construction parameter N:Span 0.5~4, step-length 0.5;Chlorophyll content Cab:Span 5~80, Step-length 10, chlorophyll content Cab unit is μ g/cm2;Dry matter weight of leaf content Cm:Span 0.003~0.033, step-length 0.003, dry matter weight of leaf content Cm unit is g/cm2;Carotenoid content Car:Span 0.5~16, step-length 1, class Carotene carotene content Car unit is μ g/cm2;Leaf area index LAI:Span 1.5~6, step-length 0.5;
2) to above-mentioned steps 1) 5 parameter values carry out the obtained 9860 groups of biochemical parameters of permutation and combination, and set following solid Determine input parameter, form 9860 groups of input datas:
The fixed input parameter:
Brown cellulose content is 0, water content 0.024cm, and hot spot-effect parameter is 0.01, and soil lightness parameter is 1, sun zenith Angle is 30 °, and view zenith angle is 10 °, and relative bearing is 0 °;
3) above-mentioned 9860 groups of input datas are directed to, is calculated using PROSAIL models, tries to achieve corresponding canopy reflectance spectrum number According to formation matrix;
4) the above-mentioned canopy reflectance spectrum data got are directed to, according to the spectral response functions of the multispectral data, are carried out equivalent Calculate, corresponding multispectral reflectivity data is obtained, for i-th of wave band of multispectral data corresponding to kth group input data Reflectivity ρmulti(k, λ (i)) is:
<mrow> <msub> <mi>&amp;rho;</mi> <mrow> <mi>m</mi> <mi>u</mi> <mi>l</mi> <mi>t</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>&amp;lambda;</mi> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mi>w</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </munderover> <mi>&amp;rho;</mi> <mo>(</mo> <mi>k</mi> <mo>,</mo> <msub> <mi>f</mi> <mrow> <mi>&amp;lambda;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>)</mo> <mo>*</mo> <msub> <mi>f</mi> <mrow> <mi>&amp;lambda;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mi>w</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </munderover> <msub> <mi>f</mi> <mrow> <mi>&amp;lambda;</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
Wherein fλ(i)(1, j) it is wave-length coverage corresponding to i-th of wave band, nw (i) number, f for corresponding toλ(i)(2, j) and i-th The corresponding spectral response functions of the wave-length coverage of wave band, ρ (k, fλ(i)(1, j)) be kth group input data in i-th of wave band The corresponding canopy reflectance spectrum data of wave-length coverage, obtain matrix ρ after carrying out Equivalent Calculation to all samples and wave bandmulti (ns, L), ns correspond to sample group number 9860, and L corresponds to multispectral data wave band number;
(2) biochemical parameter, obtained for combinations thereof and the multispectral reflectivity data ρ correspondingly tried to achievemulti(ns, L), enters Row model construction, it is the step of structure:
1) sample data is divided into a part as training data, another part to take for above-mentioned steps (1) as test data The data of value, the number of training randomly selected are 7888, and test sample number is 1972;
2) training data is directed to, vector machine model is supported and kernel function is set, supporting vector machine model uses regression modeling In commonly use epsilon-SVR models, penalty parameter c is its relevant parameter;Kernel function uses RBF kernel functions, and g is its association ginseng Number;
3) after supporting vector machine model and kernel function is set, for epsilon-SVR models and RBF kernel functions, it is associated Parameter is c and g, and training data is inputted into SVMs, and biochemical parameter can be obtained using the relevant parameter value of system default Computation model;
(3) for blade construction parameter N, chlorophyll content Cab, dry matter weight of leaf content Cm, carotenoid content Car, blade face Product index LAI, relevant parameter c and g value corresponding to being calculated is set according to above-mentioned model and kernel function, and then, for light more View data is composed, based on epsilon-SVR models, gaussian radial basis function RBF kernel functions, and corresponding c and g values, utilizes support Vector machine carries out Parameter Map calculating respectively, obtains blade construction parameter N, chlorophyll content Cab, dry matter weight of leaf content Cm, class Carotene carotene content Car, leaf area index LAI Parameter Map;
(4) blade construction parameter N, chlorophyll content Cab, dry matter weight of leaf content Cm, carotenoid content Car, leaf are being obtained On the basis of area index LAI Parameter Maps, following fixed input parameter is set to each pixel on image:
Brown cellulose content is 0, water content 0.024cm, and hot spot-effect parameter is 0.01, and soil lightness parameter is 1, sun zenith Angle is 30 °, and view zenith angle is 10 °, and relative bearing is 0 °;
And then with reference to the Parameter Map of above-mentioned 5 kinds of parameters being calculated, by PROSAIL models calculate by pixel and realize High spectrum image is simulated, and obtains vegetation area high spectrum image.
2. a kind of vegetation region high spectrum image analogy method as claimed in claim 1, it is characterised in that the step (2) is also wrapped Include:In order to obtain optimal biochemical parameter computation model, for the test data, pass is optimized using grid-search algorithms Join parameter c and g value.
A kind of 3. vegetation region high spectrum image analogy method as claimed in claim 1, it is characterised in that the association ginseng of the optimization Number c and g value sets as follows:C, g span is disposed as 2-8-~28, step-size in search is arranged to 2i, wherein i value sets It is set to 1.
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