CN109615008A - Hyperspectral image classification method and system based on stack width learning - Google Patents
Hyperspectral image classification method and system based on stack width learning Download PDFInfo
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Abstract
The invention provides a hyperspectral image classification method and system based on stack width learning, which comprises the steps of firstly preprocessing input images, including normalization, wavelet decomposition and difference; secondly, selecting a small number of samples as training samples, and learning the empty spectrum features of the hyperspectral image by using a stack width learning model; and then, training by using the training sample to obtain a width learning classifier, and finally, inputting the characteristics of the test sample into the trained width learning classifier to obtain a class label. By utilizing the stack width learning model, more abstract space spectrum characteristics can be obtained, so that the method can obtain a very accurate classification result. Due to the characteristic of width learning, the method has smaller sample complexity, and can obtain better classification results only by a small number of training samples, so that the method is more beneficial to practical application.
Description
Technical field
The invention belongs to remote sensing to influence processing and analysis technical field, devise a kind of hyperspectral image classification method and be
System, can be used for resource management, scene interpretation, precision agriculture, urban planning and prevents and reduces natural disasters.
Background technique
Frontier science and technology of the high-spectrum remote-sensing as remote sensing fields have a wide range of applications in military affairs with civil field.Bloom
The abundant spectral information of spectrogram picture also brings series of features extraction and mould while providing more information to terrain classification
The new problem of formula identification.A series of problems, such as researchers are high, training sample is few for data dimension in classification hyperspectral imagery
It has made intensive studies.However up to the present, the above problem does not obtain effective solution also.
Firstly, many Dimensionality Reduction methods are by sequential use in high spectrum image in order to handle the high problem of data dimension
Classification.These methods can also obtain the feature of reflection spectrum low dimensional manifold structure while reducing data dimension.For example, office
Portion's linearly embedding (Locally Linear Embedding, LLE) and part Fisher discriminant analysis (Local Fisher ' s
DiscriminantAnalysis, LFDA) etc. manifold learnings be applied to classification hyperspectral imagery, be effectively promoted point
The performance of class system.However early stage classification hyperspectral imagery, researchers and have ignored merely with the spectral signature of image
Important space and contextual information.
In recent years, the empty spectrum signature extraction algorithm towards classification hyperspectral imagery gradually rises, and becomes main stream approach.Base
Think that a possibility that pixel in regional area belongs to same category is larger in the classification method of empty spectrum signature.Firstly, Ma Er
Numerous classical technologies such as section's husband's random field (Markov Random Field), Gabor wavelet and mathematical morphology are used to obtain
Take the spatial information of image.For example, Quesada-Barriuso et al. creates expanded configuration section from wavelet character
(ExtendedMorphological Profile, EMP) obtains a kind of new empty spectrum signature；Li et al. people proposes based on circulation
Maximum a posteriori marginal probability (the Maximizer of the Posterior Marginal by Loopy of belief propagation
Belief Propagation, MPM-LBP) method obtains empty spectrum signature, and this method obtains side in terms of spectrum and space two
Edge probability distribution；Zhong et al. devises the tensor sky spectrum signature extracting method with identification.Kang et al., which is devised, to be based on
The empty spectrum signature of holding edge filter (Edge-preservingFiltering, EPF) extracts frame；Soltani-Farani etc.
People devises spatial perception dictionary learning (SpatialAware Dictionary Learning, SADL) method, and this method is melted
Spectrum and contextual information are closed；Recently, Li et al. people, which also proposed, carries out the frame that empty spectrum signature learns in conjunction with various features, this
One frame can effectively handle border issue.These methods obtain preferable as a result, to classification hyperspectral imagery system is promoted
The performance of system is of great significance, and shows the importance that sky spectrum signature correctly classifies to realization.
However, the above method is generally only the empty spectrum signature for obtaining single layer (or shallow-layer), it is higher level without obtaining
Empty spectrum signature.Existing research shows that learning as the feature abstraction ability of the increase deep learning model of depth gradually increases
The character representation ability arrived is also stronger.Therefore researchers begin trying deep learning method being introduced into classification hyperspectral imagery
In.Chen et al. is using principal component analysis (Principle Component Analysis, PCA) and stacks automatic coding machine
(Stacked Autoencoders) learns empty spectrum signature.Hu et al. is merely with depth convolutional neural networks (Deep
Convolutional Neural Networks, DCNN) study spectral signature.Yue et al. learns bloom using PCA and DCNN
The empty spectrum signature of spectrogram picture.It is not difficult to find that existing correlative study is mostly merely with the depth for having processing gray scale or color image
Spend learning structure, and designing new deep learning structure according to the characteristic of high spectrum image, and sample complex compared with
Height can not handle the small sample problem in practical application well.How to establish effective and to different high spectrum images
Data have the feature learning method of certain universality, still need to be studied.Currently based on the high-spectrum of deep learning
As sort research mainly faces following problems:
(1) sample complex is higher.How to enable categorizing system can be from less training sample as the mankind
Effective feature is arrived in middle study, is a problem in the urgent need to address.It is non-thread that the solution of this problem depends on discovery higher-dimension
The intrinsic structure of property data.
(2) spatial information is under-utilized.Spatial information is not dissolved into depth structure by existing method well, mostly
It is that spatial information is utilized in pretreatment stage.How " collection of illustrative plates " characteristic of high spectrum image to be utilized to construct new depth
Practising model value must further investigate.
In view of the above-mentioned problems, present invention design constructs new empty spectrum signature learning method under deep learning frame, it is perfect
The method and model of classification have very important significance to the actual needs for meeting economy and society development.
Summary of the invention
It is an object of the invention to be directed to the deficiency of above-mentioned prior art, propose a kind of based on the bloom for stacking width study
Image classification method is composed, is difficult to learn effective characteristic of division to solve the problems, such as the prior art in classification hyperspectral imagery, and
The problems such as sample complex is high proposes the performance of classification hyperspectral imagery.
Realize the object of the invention technical solution are as follows: firstly, pre-processing to input picture, including normalize, is small
Wave Decomposition and difference；Secondly, choosing a small amount of sample as training sample, learn EO-1 hyperion using width learning model is stacked
The empty spectrum signature of image；Then, width Study strategies and methods are obtained using training sample training, finally, by the feature of test sample
It is input in trained width Study strategies and methods and obtains class label.Specific step is as follows:
Step 1, high spectrum image to be processed is normalized；
Step 2, wavelet decomposition is carried out to each pixel, retains the low-frequency component decomposed for the first time and for the second time；
Step 3, Difference Calculation is carried out to each pixel, obtains the new expression of pixel；
Step 4, the low-frequency component of each pixel (being obtained by step 2) and difference (being obtained by step 3) are connected into one
New vector is as pretreated output；
Step 5, high spectrum image of the input by step 1-4 processing, selects from the high spectrum image after pretreatment
Mark the pixel of class label as training sample in advance, remaining pixel is as test sample；
Step 6, the hierarchical model with L layers is alternately constructed by what width study and Gabor filtered, utilizes training
The class label and spatial information of sample are trained the model, obtain the hierarchical model and training sample for feature learning
This empty spectrum signature；
Step 7, test sample is input in trained hierarchical model, extracts the empty spectrum signature of test sample；
Step 8, empty spectrum signature and class label the training width Study strategies and methods of training sample are utilized；
Step 9, the empty spectrum signature of obtained test sample is input in width Study strategies and methods, obtains test sample
Class label completes classification.
Further, the specific implementation of step 6 is as follows,
The number of plies for 6a) determining hierarchical model is L, enables l={ 1,2 ... L }；
6b) using low frequency part concatenated in training sample and differential data as the input of the hierarchical model first layer；
6c) using the training sample training width learning model of label, standardization processing is carried out to the output of model, is obtained
Probability output；
6d) utilize step 6c) each of obtained width learning model processing training sample pixel is trained, and carry out
Standardization processing obtains new data cube；
Multi-scale filtering, the definition of Gabor filter 6e) are carried out using Gabor filter in the output of step 6d)
Are as follows:
Wherein
x0=xcos θ+ysin θ and y0=-xsin θ+ycos θ, (2)
γ is length-width ratio, and θ is direction, and δ is effective width, and λ is wavelength；
6f) filtered data and original normalized data are spliced, and form new data cube；
6g) data cube for obtaining 6f) executes step 6c as input, circulation) -6f), successively obtain total L layers of filter
Wave number evidence；
Hierarchical model 6h) is obtained, and exports the empty spectrum signature of training sample.
Further, formula high spectrum image being normalized in step 1 is as follows, its spectral value range is made to exist
Within [0,1],
Wherein, Mx=max (I (:)), Mn=min (I (:)) is respectively the maximum value and minimum of pixel value on input picture
Value, andIt is the pixel I that coordinate is (i, j)ijInA bands of a spectrum,For coordinate on normalized high spectrum image
For the pixel of (i, j)InA bands of a spectrum.
The present invention also provides a kind of based on the classification hyperspectral imagery system for stacking width study, which is characterized in that including
Following module:
Normalized module, for high spectrum image to be processed to be normalized；
Wavelet decomposition module retains the low frequency decomposed for the first time with second for carrying out wavelet decomposition to each pixel
Ingredient；
Difference Calculation module obtains the new expression of pixel for carrying out Difference Calculation to each pixel；
Pre-process output module, for by the low-frequency component (being obtained by wavelet decomposition module) and difference of each pixel (by
Difference Calculation obtains) a new vector is connected into as pretreated output；
Training sample chooses module, for inputting the high spectrum image Jing Guo above-mentioned resume module, after pretreatment
It selects to have marked the pixel of class label as training sample in advance in high spectrum image, remaining pixel is as test sample；
Hierarchical model constructs module, alternately constructs the layer with L layers for what is filtered by width study and Gabor
Secondary model is trained the model using the class label and spatial information of training sample, obtains the layer for feature learning
The empty spectrum signature of secondary model and training sample；
Test sample sky spectrum signature extraction module is extracted for test sample to be input in trained hierarchical model
The empty spectrum signature of test sample；
Width Study strategies and methods training module, for the empty spectrum signature and class label training width using training sample
Practise classifier；
Categorization module is surveyed for the empty spectrum signature of obtained test sample to be input in width Study strategies and methods
The class label of sample sheet completes classification.
Further, the specific implementation of hierarchical model building module is as follows,
The number of plies for 6a) determining hierarchical model is L, enables l={ 1,2 ... L }；
6b) using low frequency part concatenated in training sample and differential data as the input of the hierarchical model first layer；
6c) using the training sample training width learning model of label, standardization processing is carried out to the output of model, is obtained
Probability output；
6d) utilize step 6c) train each pixel in obtained width learning model processing training sample, professional etiquette of going forward side by side
Generalized processing, obtains new data cube；
Multi-scale filtering, the definition of Gabor filter 6e) are carried out using Gabor filter in the output of step 6d)
Are as follows:
x0=xcos θ+ysin θ and y0=-xsin θ+ycos θ, (2)
Wherein x and y respectively represents the transverse and longitudinal coordinate of filter coefficient, and γ is length-width ratio, and θ is direction, and δ is effective width, λ
It is wavelength；
6f) filtered data and original normalization data are spliced, and form new data cube；
6g) data cube for obtaining 6f) executes step 6c as input, circulation) -6f), successively obtain total L layers of filter
Wave number evidence；
Hierarchical model 6h) is obtained, and exports the empty spectrum signature of training sample.
Further, formula high spectrum image being normalized in normalized module is as follows, normalization
Make its spectral value range within [0,1] after processing,
Wherein, Mx=max (I (:)), Mn=min (I (:)) is respectively the maximum value and minimum of pixel value on input picture
Value, andIt is the pixel I that coordinate is (i, j)ijInA bands of a spectrum,To be sat on normalized high spectrum image
It is designated as the pixel of (i, j)InA bands of a spectrum.
Compared with prior art, the present invention its remarkable advantage are as follows: first, relative to the existing bloom based on spectral information
Spectrum signature extraction algorithm, the present invention is learnt using width and Gabor filtering sufficiently combines the empty spectrum spy that high-spectral data includes
Sign.Second, using hierarchical model of the invention, more abstract empty spectrum signature can be obtained, therefore method of the invention can be with
Obtain point-device classification results.Third, the present invention has lesser sample complex, only due to the characteristic of width study
A small amount of training sample is needed to can be obtained by relatively good classification results, therefore it is more conducive to practical application.
Detailed description of the invention
Fig. 1 is of the invention based on the hyperspectral image classification method flow diagram for stacking width study.
Fig. 2 is that present invention experiment uses image and its true atural object classification chart.
Fig. 3 is the classification results full figure that all kinds of methods obtain.
Specific embodiment
Referring to the drawings, technical solutions and effects of the present invention is described in further detail.
Referring to Fig.1, steps are as follows for realization of the invention:
1) a panel height spectrum picture is inputted, and image is normalized, makes its range within [0,1].
Enable Itr={ I1,I2,…,INThe training set that is made of N number of pixel, wherein Ii∈Rd(i=1,2 ..., N) it is
I training sample, and they belong to C class；Image is normalized, is standardized as data value by following steps
[0,1]:
Wherein, Mx=max (I (:)), Mn=min (I (:)) is respectively the maximum value and minimum of pixel value on input picture
Value, andIt is the pixel I that coordinate is (i, j)ijInA bands of a spectrum,For coordinate on normalized high spectrum image
For the pixel of (i, j)InA bands of a spectrum.
2) each pixel after standardization processing is decomposed using DB5 small echo, retains first time and second point
The low frequency part a of solution1And a2；
3) difference d is calculated to each pixel after standardization processing；
4) for any one pixel splice step 2) -3) output obtain new expression；
5) select the pixel of p% as training sample from the output data cube of the step 4), it is remaining as test
Sample can carry out handmarking, therefore the class label of training sample is wherein the training samples number chosen is seldom in advance
Know, p takes 2 in the present embodiment；
6) training hierarchical model；
Training hierarchical model is mainly the model that width study and Gabor filtering alternately obtain learning empty spectrum signature.
The present invention can use the label information of training sample using width study, and specific training process is as follows:
The number of plies for 6a) determining hierarchical model is L, enables l={ 1,2 ... L }；
6b) using low frequency part concatenated in training sample and differential data as the input of the hierarchical model first layer；
6c) using training sample training width learning model [1] of label, standardization processing is carried out to the output of model,
Obtain probability output；
6d) utilize step 6c) each of obtained width learning model processing training sample pixel is trained, and carry out
Standardize to [0,1], obtains new data cube；
Multi-scale filtering 6e) is carried out to the output of step 6d) using Gabor filter, Gabor filter is defined as:
x0=xcos θ+ysin θ and y0=-xsin θ+ycos θ, (2)
Wherein x and y respectively represents the transverse and longitudinal coordinate of filter coefficient, and γ is length-width ratio, and θ is direction, and δ is effective width, λ
It is wavelength, these parameters can manually be set according to data characteristic；
6f) filtered data and original normalization data ((training sample after being normalized i.e. in step 1)) row splicing,
Form new data cube；
6g) data cube for obtaining 6f) executes step as input (i.e. the input of the hierarchical model second layer), circulation
6c) -6f), successively obtain total L layers of filtering data；
Hierarchical model 6h) is obtained, and exports the empty spectrum signature of training sample；
[1] C.L.Philip Chen, Zhulin Liu, Broad Learning System:An Effective and
Efficient Incremental Learning System Without the Need for Deep Architecture,
IEEE Transactions on Neural Networks and Learning Systems, vol.29, no.`1, pp.10-
24,2018
7) the empty spectrum signature of training sample and class label training width Study strategies and methods are utilized；
8) the label pixel of residue 98% in high spectrum image is chosen as test sample, and the empty spectrum for extracting test sample is special
Sign；
9) feature of obtained test sample is input in width Study strategies and methods, obtains the class label of the sample, it is complete
Constituent class.
The present invention also provides a kind of based on the classification hyperspectral imagery system for stacking width study, which is characterized in that including
Following module:
Normalized module, for high spectrum image to be processed to be normalized；
Wavelet decomposition module retains the low frequency decomposed for the first time with second for carrying out wavelet decomposition to each pixel
Ingredient；
Difference Calculation module obtains the new expression of pixel for carrying out Difference Calculation to each pixel；
Pre-process output module, for by the low-frequency component (being obtained by wavelet decomposition module) and difference of each pixel (by
Difference Calculation obtains) a new vector is connected into as pretreated output；
Training sample chooses module, for inputting the high spectrum image Jing Guo above-mentioned resume module, after pretreatment
It selects to have marked the pixel of class label as training sample in advance in high spectrum image, remaining pixel is as test sample；
Hierarchical model constructs module, alternately constructs the layer with L layers for what is filtered by width study and Gabor
Secondary model is trained the model using the class label and spatial information of training sample, obtains the layer for feature learning
The empty spectrum signature of secondary model and training sample；
Test sample sky spectrum signature extraction module is extracted for test sample to be input in trained hierarchical model
The empty spectrum signature of test sample；
Width Study strategies and methods training module, for the empty spectrum signature and class label training width using training sample
Practise classifier；
Categorization module is surveyed for the empty spectrum signature of obtained test sample to be input in width Study strategies and methods
The class label of sample sheet completes classification.
The specific implementation of each module and each step are corresponding, and the present invention not writes.
Effect of the invention can be further illustrated with following emulation experiment:
(1) simulated conditions
The hardware condition of emulation of the invention are as follows: windows 7, Intel i7-4790 3.60GHz, 12GB memory；It is soft
Part platform are as follows: MatlabR2014a；
The image credit that emulation is selected is the high spectrum image of Indian Pines, shares 16 class atural objects in the image, such as
Shown in Fig. 2 (a), Fig. 2 (b) is the corresponding class logo image of Fig. 2 (a).The marker samples number of every one kind is as shown in table 1.
The inhomogeneous marker samples number of table 1
Emulation mode uses the method for the present invention and existing KELM, EPF, MPM-LBP and SADL method respectively.
(2) emulation content and result
The classification results of 2 distinct methods of table
Classification emulation is carried out to Fig. 2 (a) with the present invention and existing five kinds of methods, as a result such as table 2 and Fig. 3, in which:
OA is overall accuracy (Overall Accuracy)；
Fig. 3 (a) is the classification results figure with KELM method；
Fig. 3 (b) is the classification results figure with EPF method；
Fig. 3 (c) is the classification results figure with MPM-LBP method；
Fig. 3 (d) is the classification results figure with SADL method；
Fig. 3 (e) is the classification results figure with the method for the present invention.
Bright from the classification results chart of table 2 and Fig. 3, nicety of grading of the invention is substantially better than existing method, and view of classifying
Feel that effect is more preferable, remains the marginal information of image.Compared with the technology of the prior art, the present invention is solving high spectrum image point
Accuracy benefits are obvious when empty spectrum signature problem concerning study in class problem, and sample complex is low.
Specific embodiment described herein is only an example for the spirit of the invention.The neck of technology belonging to the present invention
The technical staff in domain can do the similar mode of different modify or supplement or adopts to described specific embodiment and substitute, but
Without departing from the spirit of the invention or going beyond the scope defined by the appended claims.
Claims (6)
1. a kind of based on the hyperspectral image classification method for stacking width study, which comprises the steps of:
Step 1, high spectrum image to be processed is normalized；
Step 2, wavelet decomposition is carried out to each pixel, retains the low-frequency component decomposed for the first time and for the second time；
Step 3, Difference Calculation is carried out to each pixel, obtains the new expression of pixel；
Step 4, by the low-frequency component of each pixel (being obtained by step 2) and difference (being obtained by step 3) be connected into one it is new
Vector is as pretreated output；
Step 5, high spectrum image of the input by step 1-4 processing selects preparatory from the high spectrum image after pretreatment
Mark the pixel of class label as training sample, remaining pixel is as test sample；
Step 6, the hierarchical model with L layers is alternately constructed by what width study and Gabor filtered, utilizes training sample
Class label and spatial information the model is trained, obtain the hierarchical model and training sample for feature learning
Empty spectrum signature；
Step 7, test sample is input in trained hierarchical model, extracts the empty spectrum signature of test sample；
Step 8, empty spectrum signature and class label the training width Study strategies and methods of training sample are utilized；
Step 9, the empty spectrum signature of obtained test sample is input in width Study strategies and methods, obtains the category of test sample
Label complete classification.
2. as described in claim 1 a kind of based on the hyperspectral image classification method for stacking width study, it is characterised in that: step
Rapid 6 specific implementation is as follows,
The number of plies for 6a) determining hierarchical model is L, enables l={ 1,2 ... L }；
6b) using low frequency part concatenated in training sample and differential data as the input of the hierarchical model first layer；
6c) using the training sample training width learning model of label, standardization processing is carried out to the output of model, obtains probability
Output；
6d) utilize step 6c) train each pixel in obtained width learning model processing training sample, professional etiquette of going forward side by side generalized
Processing, obtains new data cube；
Multi-scale filtering 6e) is carried out using Gabor filter in the output of step 6d), Gabor filter is defined as:
x0=xcos θ+ysin θ and y0=-xsin θ+ycos θ, (2)
Wherein x and y respectively represents the transverse and longitudinal coordinate of filter coefficient, and γ is length-width ratio, and θ is direction, and δ is effective width, and λ is wave
It is long；
6f) filtered data and original normalization data are spliced, and form new data cube；
6g) data cube for obtaining 6f) executes step 6c as input, circulation) -6f), successively obtain total L layers of filtering number
According to；
Hierarchical model 6h) is obtained, and exports the empty spectrum signature of training sample.
3. as described in claim 1 a kind of based on the hyperspectral image classification method for stacking width study, it is characterised in that: step
The formula that high spectrum image is normalized in rapid 1 is as follows, make after normalized its spectral value range [0,1] it
It is interior,
Wherein, Mx=max (I (:)), Mn=min (I (:)) is respectively the maximum value and minimum value of pixel value on input picture, and
AndIt is the pixel I that coordinate is (i, j)ijInA bands of a spectrum,For coordinate on normalized high spectrum image be (i,
J) pixelInA bands of a spectrum.
4. a kind of based on the classification hyperspectral imagery system for stacking width study, which is characterized in that including following module:
Normalized module, for high spectrum image to be processed to be normalized；
Wavelet decomposition module retains the low-frequency component decomposed for the first time with second for carrying out wavelet decomposition to each pixel；
Difference Calculation module obtains the new expression of pixel for carrying out Difference Calculation to each pixel；
Pre-process output module, for by the low-frequency component (being obtained by wavelet decomposition module) and difference of each pixel (by difference
It is calculated) a new vector is connected into as pretreated output；
Training sample chooses module, for inputting the high spectrum image Jing Guo above-mentioned resume module, from the bloom after pretreatment
It selects to have marked the pixel of class label as training sample in advance in spectrogram picture, remaining pixel is as test sample；
Hierarchical model constructs module, alternately constructs the level mould with L layers for what is filtered by width study and Gabor
Type is trained the model using the class label and spatial information of training sample, obtains the level mould for feature learning
The empty spectrum signature of type and training sample；
Test sample sky spectrum signature extraction module extracts test for test sample to be input in trained hierarchical model
The empty spectrum signature of sample；
Width Study strategies and methods training module, for the empty spectrum signature and class label training width study point using training sample
Class device；
Categorization module obtains test specimens for the empty spectrum signature of obtained test sample to be input in width Study strategies and methods
This class label completes classification.
5. as claimed in claim 4 a kind of based on the hyperspectral image classification method for stacking width study, it is characterised in that: layer
The specific implementation of secondary model construction module is as follows,
The number of plies for 6a) determining hierarchical model is L, enables l={ 1,2 ... L }；
6b) using low frequency part concatenated in training sample and differential data as the input of the hierarchical model first layer；
6c) using the training sample training width learning model of label, standardization processing is carried out to the output of model, obtains probability
Output；
6d) utilize step 6c) train each pixel in obtained width learning model processing training sample, professional etiquette of going forward side by side generalized
Processing, obtains new data cube；
Multi-scale filtering 6e) is carried out using Gabor filter in the output of step 6d), Gabor filter is defined as:
x0=xcos θ+ysin θ and y0=-xsin θ+ycos θ, (2)
Wherein x and y respectively represents the transverse and longitudinal coordinate of filter coefficient, and γ is length-width ratio, and θ is direction, and δ is effective width, and λ is wave
It is long；
6f) filtered data and original normalization data are spliced, and form new data cube；
6g) data cube for obtaining 6f) executes step 6c as input, circulation) -6f), successively obtain total L layers of filtering number
According to；
Hierarchical model 6h) is obtained, and exports the empty spectrum signature of training sample.
6. as claimed in claim 4 a kind of based on the hyperspectral image classification method for stacking width study, it is characterised in that: return
The formula that high spectrum image is normalized in one change processing module is as follows, its spectral value range is made after normalized
Within [0,1],
Wherein, Mx=max (I (:)), Mn=min (I (:)) is respectively the maximum value and minimum value of pixel value on input picture, and
AndIt is the pixel I that coordinate is (i, j)ijInA bands of a spectrum,For coordinate on normalized high spectrum image be (i,
J) pixelInA bands of a spectrum.
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| Publication number | Priority date | Publication date | Assignee | Title |
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