CN106650811B - A kind of EO-1 hyperion mixed pixel classification method cooperateing with enhancing based on neighbour - Google Patents
A kind of EO-1 hyperion mixed pixel classification method cooperateing with enhancing based on neighbour Download PDFInfo
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Abstract
The present invention provides a kind of EO-1 hyperion mixed pixel classification method that enhancing is cooperateed with based on neighbour, comprising: the spectrum signature matrix of multiple target atural object is calculated using marked sample atural object;Multi-class classifier of the design based on spectral signature classifies atural object;Spatial structure characteristic is merged in classification results, and extracts neighbour's pixel;Category label is carried out to unmarked EO-1 hyperion atural object using the collaboration of neighbour's pixel;Unlabelled atural object is gradually carried out by classification annotation using alternative manner respectively;The space characteristics of Target scalar are further merged in the way of neighborhood extending, complete final classification label.Using multi-class classifier, species Jin Hang not classify the present invention simultaneously over the ground, solve the problems, such as that conventional sorting methods can not classify to background atural object;And in the way of neighbour's collaboration enhancing, gradually unlabelled ground object target is marked, has effectively merged the spectral signature and space characteristics of atural object, classifying quality is preferable.
Description
Technical field
Classification hyperspectral imagery technical field of the present invention more particularly to a kind of EO-1 hyperion mixing that enhancing is cooperateed with based on neighbour
Pixel classification method.
Background technique
For classification hyperspectral imagery as an important application in Hyperspectral imagery processing, final target is to image
In each pixel carry out classification ownership.High spectrum resolution remote sensing technique makes it in atural object category classification using more spectral bands
Aspect has big advantage, but the accuracy of object spectrum information is but also interference, background parts have in hyperspectral classification
Certain influence;On the other hand, since high-spectral data has the characteristics that high dimensional data amount is big and training sample is small, when making classification
It is also easy to produce Hughes phenomenon.
The classification method that the empty spectrum signature of high spectrum image combines in recent years is taken seriously, based on the m- space characteristics of spectrum
Hyperspectral image classification method has become current research hotspot, and such methods pass through combining space information feature and Spectral Properties
Sign, improves the precision of classification hyperspectral imagery.Major applications are one-to-one using the progress of the methods of support vector machines at present, or
The one-to-many classification of person;Such methods one the biggest problems are that can not classify to the background parts of high spectrum image,
It therefore is usually all to cause such method to lack accuracy by the way of removing background in classification of assessment method;In addition,
Such method is classified using pure member, is led to the limitation of classification method, is lacked versatility.
Summary of the invention
The present invention provides a kind of EO-1 hyperion mixed pixel classification method that enhancing is cooperateed with based on neighbour, solves above-mentioned technology and asks
Topic.
A kind of EO-1 hyperion mixed pixel classification method that enhancing is cooperateed with based on neighbour of the present invention, comprising:
The spectral signature matrix of multiple target atural object is calculated according to marked sample atural object;
The Target scalar is divided using the multi-class classifier based on the spectral signature matrix and constraint matrix
Class;
Neighbour's pixel is extracted again after the Abundances that the classifier obtains are merged spatial structure characteristic;
Category label is carried out according to Target scalar of neighbour's pixel collaboration to unmarked EO-1 hyperion, using alternative manner
Gradually unlabelled atural object is classified respectively;
Spatial structure characteristic is merged in classification results, and extracts neighbour's pixel, comprising:
Using formula
Convolutional calculation is carried out to classification results and obtains TG(k), wherein the σ is the standard deviation of gaussian filtering, and r is high
The filtering radius of this filtering, K are atural object class-mark, and the T (k) is the classification results of every kind of atural object classification;
To TG(k) the abundance Value Data in is ranked up, a pixel composition atural object classification of the maximum 2*n (k) of extraction of values
Neighbour gathers { MCset(k) }, wherein n (k) is the pixel number that kth class atural object increases mark newly every time.
Further, the spectral signature matrix that multiple target atural object is calculated according to marked sample atural object, comprising:
According to formula
Calculate the spectral signature vector of Target scalar, wherein dkFor the spectral signature vector of kth class Target scalar, dk=
{dk1,dk2,...dkL, L is wave band number, { CsetIt (k) } is marked kth class sample atural object set, NkFor { Cset(k) } in
Pixel number, HkIt (j) is { Cset(k) } spectral signature of j-th of pixel in;
The spectral signature matrix D of Target scalar end member, D=[d are calculated according to the spectral signature vector1,d2,...dp],
Wherein, p is atural object type number to be sorted, d1For the spectral signature of first kind atural object.
Further, described to use the multi-class classifier based on the spectral signature matrix and constraint matrix by the mesh
Mark atural object is classified, comprising:
According to the class number p of the Target scalar, the constraint matrix of classifier is set as C=[c1…cp], wherein cj
For the constrained vector of j-th of Target scalar, 1≤j≤p, for constraining jth class Target scalar;
It defines to p Target scalars while classifying using the spectral signature matrix and the constraint matrix
Multi-class classifier T, the classifier are as follows:
T=r (RL×L -1D(DTRL×L -1D)-1Cp×p) (3)
Wherein, R is the sample autocorrelation matrix of high spectrum image, the R are as follows:
Wherein, r=[r1r2...rn] it is hyperspectral image data, n is the pixel number of high spectrum image, and D is Spectral Properties
Levy matrix, L-band number.
Further, described that classification mark is carried out according to Target scalar of neighbour's pixel collaboration to unmarked EO-1 hyperion
Note, comprising:
Similitude is between defining the class of various Target scalars
dis(Hk(j))=| | M (k)-MHk(j)||2 (5)
Wherein, M (k) is the sample clustering center for having marked the kth class Target scalar of classification, MHkIt (j) is { MCset(k)}
In j-th of pixel spectral signature;
Similitude between the class of atural object is calculated in neighbour's set in sample and marked set according to similarity criterion between class;
A pixel of the n (k) of similitude maximum value between the class is labeled.
Further, after the use alternative manner is gradually classified unlabelled atural object respectively, further includes:
Expanded using neighbor operator, morphology and local expansion is carried out to classification results, for enhancing the space of data atural object
It is regional.
A kind of hyperspectral image classification method that enhancing is cooperateed with based on neighbour of the present invention, by gradually right with the pixel of label
Unlabelled pixel is marked, by using partially Target scalar spectral signature is calculated in the sample atural object of label, benefit
Preliminary classification is carried out with the multi-class classifier of design as a result, classification results are then merged spatial structure characteristic, and using closely
Unlabelled atural object is gradually carried out classification annotation by the mode of neighbour's collaboration enhancing respectively, to reach the classification of EO-1 hyperion mixed pixel
Purpose.Cooperate with the EO-1 hyperion mixed pixel classification method of enhancing multi-class based on spectral signature by defining one based on neighbour
Classifier can classify to all target categories, and background atural object can not be carried out by having effectively eliminated conventional sorting methods
The problem of classification, in method by neighbour cooperate with enhancing in the way of, and be done step-by-step by fusion space characteristics to unlabelled
Ground object target is marked, and classifying quality is preferable.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is this hair
Bright some embodiments for those of ordinary skill in the art without any creative labor, can be with
It obtains other drawings based on these drawings.
Fig. 1 is that the present invention is based on the EO-1 hyperion mixed pixel classification method flow charts that neighbour cooperates with enhancing;
Fig. 2 is that the present invention is based on the EO-1 hyperion mixed pixel classification method overall schematics that neighbour cooperates with enhancing;
Fig. 3 a and Fig. 3 b extract schematic diagram for the spatial structure characteristic of atural object to be sorted in the present invention;
Fig. 4 marks schematic diagram for the pixel based on neighbour's enhancing of target to be sorted in the present invention;
Fig. 5 is the neighborhood extending schematic diagram of target to be sorted in the present invention;
Fig. 6 a and Fig. 6 b are Purdue data classification result figure in the present invention;
Fig. 7 a and Fig. 7 b are Salinas data classification result figure in the present invention;
Fig. 8 a and Fig. 8 b are Pavia data classification result figure in the present invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
Fig. 1 is that the present invention is based on the EO-1 hyperion mixed pixel classification method flow chart that neighbour cooperates with enhancing, the present embodiment sides
Method, comprising:
Step 101, the spectrum signature matrix that multiple target atural object is calculated according to marked sample atural object;
Specifically, the present embodiment hyperspectral image data r=(r1,r2,...rn)T, wherein n is high spectrum image
Pixel number, ri(1 <=i <=n) indicates i-th of pixel of high spectrum image, ri=(ri1,ri2,...riL), L indicates bloom
The wave band number of spectrogram picture.
Known k is 1 < of atural object class-mark=k <=p, NumkFor whole numbers of samples of k class atural object, selected using random fashion
It takes a sample data of EO-1 hyperion n (k) to carry out pixel label, and forms marked set { Cset(k)}.The number of iterations is set as U=
Numk/ n (k) enables primary iteration number u=1.
According to marked set { Cset(k) }, NkFor { Cset(k) } the marked pixel number of kth class atural object in, according to public affairs
Formula (1) calculates the spectral vector d of ground object target to be sortedk:
Wherein, dkFor the spectral vector of Target scalar, { CsetIt (k) } is marked sample atural object set, NkFor { Cset(k)}
The marked pixel number of middle kth class atural object, HkIt (j) is { Cset(k) } the spectrum signature of the label pixel in.
Step 102, using the multi-class classifier based on the spectrum signature character matrix and constraint matrix by the mesh
Mark atural object is classified;
Specifically, the spectral signature of EO-1 hyperion is its most important information, and the present embodiment classifier is effective by design
Using multi-class spectral signature classifier identify earth's surface object.Specifically, according to the class number p of classification, generate to
The spectrum signature matrix D of class object end member1=[d1,d2,..dk...dp];Based on spectrum statistical nature D, pass through setting
Constraint matrix constrains all Target scalars, and a variety of atural objects are classified simultaneously using FIR filter.The p atural object same time-division of design
The multi-class classifier T of classkIt is as follows:
T=r (RL×L -1D(DTRL×L -1D)-1Cp×p) (2)
Wherein,Wherein Cp×p=[c1,c2,..cp] it is with 1 for cornerwise diagonal matrix,
Its column vector ciFor constraining i-th of ground object target;R is the spectrum autocorrelation matrix of high spectrum image, is defined as:Wherein r=[r1r2...rn], on the one hand multi-class classifier utilizes inverse matrix R-1High spectrum image
Sample spectrum carry out it is oppressive, have the function that weaken background, on the other hand can be realized simultaneously multiplely by constraint matrix D
The other classification of species;
Step 103 extracts neighbour's pixel after the Abundances that the classifier obtains are merged spatial structure characteristic again;
Specifically, by high-spectral data by obtaining the classification results of every kind of atural object classification after multi-class classifier T
T(k).The classification results of classifier T based on spectral information, which have, largely crosses classification noise, needs to merge in classification results empty
Between feature enhancing classification atural object spatial information, thus eliminate merely with spectral signature classify bring noise problem.Specifically
Way is to carry out convolutional calculation to classification results using gaussian filtering, is eliminated to the classification " particle " of crossing of classification results,
Formula are as follows:
Wherein σ is the standard deviation of gaussian filtering, and r is the filtering radius of gaussian filtering.
Step 104 carries out category label according to Target scalar of neighbour's pixel collaboration to unmarked EO-1 hyperion, uses
Alternative manner gradually classifies unlabelled atural object respectively.
Specifically, the present embodiment utilizes the neighbour of class atural object every in classification results to improve labeling effciency and precision
Pixel collaboration carries out ground substance markers.Extract the specific practice of neighbour's pixel are as follows: to TG(k) abundance Value Data is ranked up, and is mentioned
Take TG(k) neighbour of a pixel composition atural object classification of the maximum 2*n (k) of intermediate value gathers { MCset(k)}。
It carries out n (k) a pixel to unlabelled ground object target in the way of neighbour's collaboration to mark, specific practice are as follows: first
Similitude is as follows between first defining the class of every kind of atural object:
dis(Hk(j))=| | M (k)-MHk(j)||2 (5)
Wherein, M (k) is the sample clustering center for having marked the kth class Target scalar of classification, MHkIt (j) is { MCset(k)}
In j-th of pixel spectral signature;
{ MC is calculated using formula (4)set(k) } sample and { C inset(k) } similitude between the class of ground object target in, by dis
It is worth the smallest n (k) sample and carries out corresponding classification mark, and puts it into marked set { Cset(k) } in.
When unlabelled pixel being marked using marked sample, according to spectral signature and spatial structure characteristic phase
The mode of fusion selects neighbour's sample in classification results, then by neighbour's sample select classification similitude maximum i.e. away from
It is marked from the smallest pixel.In such a way that this neighbour cooperates with enhancing, the label precision of unmarked sample is improved, is had
Help the classification of high spectrum image.
U=u+1 is enabled, if u < U, goes to step 104, continues to carry out EO-1 hyperion mixed pixel label using iterative manner,
To gradually enhance the number of marked sample.
It is exemplified below the present invention is based on the EO-1 hyperion mixed pixel classification method that neighbour cooperates with enhancing, sample data is come
Derived from true high spectrum image: the high-spectral data of the test block Indian Pine, hereinafter referred to as Purdue data.The data
It is the farmland image obtained by AVIRIS sensor in the state of Indiana northwestward, image size is 145 × 145, spatial discrimination
20 meters of rate, original wave band number is 220, including 16 class atural object classifications;Its pseudocolour picture and true terrestrial object information such as Fig. 3 institute
Show.
It is arranged the number of iterations 10 times first, the initial value of u is 1.It is randomly selected from the truly measured data of experimental data
10% marked sample, and form marked set k { Cset(k) }, 1≤k≤16, table 1 to table 3 for every kind species
Not marked number.
Table 1
The spectrum signature calculation of sample atural object is carried out according to formula (1), and by the classification light for three width images being calculated
Spectrum signature matrix D=[d1,d2,...d16];
Constraint matrix C:C is set16×16, column vector ciFor constraining i-th of atural object classification of purdue;
Using constrained vector Matrix C come simultaneously constrain D, can simultaneously by 16 class ground object targets in purdue data simultaneously into
Row classification;
According to DkWith constraint matrix C, according to formula (2), the multi-class classifier T of definitionk(i) (1≤i≤16) calculate
The classification results of ground object target.
σ=1.5, r=11 are set, the spatial structure characteristic T of Purdue data classification result figure is extracted according to formula (3)
(iG) (1≤i≤16).The spatial extraction schematic diagram of 2nd class of Purdue data is as shown in figure 3, wherein Fig. 3 a is corn-
Second class first time classification results of notil classification, Fig. 3 b are the result figure after gaussian filtering, and shade therein indicates
The height of pixel Abundances.It can be seen that having effectively eliminated " particle " in classification results after space characteristics filtering
The space characteristics of noise, corn-notil atural object are incorporated and spectral classification result suffers.
To T (iG) (1≤i≤16) be ranked up, and selects every a neighbour's pixel of one kind 2*n (k), establish neighbour's set
MCset。
Below with the classification 1 of Purdue data, alfalfa data instance is illustrated.The pixel label of neighbour's enhancing is such as
Shown in Fig. 4 a, Fig. 4 b and Fig. 4 c.The size of example image is part (90:111,60:81) of original image.Wherein Fig. 4 a is marked
Alfalfa class atural object pixel, the label pixel collection specifically generated at random is combined into Cset, and specific coordinate is (96,73)
(98,68)(100,73)(100,74)(101,73);Neighbour's pixel of the Abundances sequence after spatial structure characteristic is merged
As shown in Fig. 4 b figure.Neighbour's pixel collection is combined into Mcset, specific coordinate value is (101,73), (100,73), (101,74), (100,
74), (101,72), (100,72), (102,73), (99,73), (102,74), (99,72);
Using formula (4) calculate neighbour's set Mcset and Cset in marked alfalfa atural object class between similitude,
Specific value is as shown in table 2.
Table 2
Then the data of table 2 are ranked up, 5 pixels (pixel number is 1,2,3,5,6) are selected to be marked, and by its
Marked set is put into update Cset.New label alfalfa data are as illustrated in fig. 4 c.
The above operation is all made of to three width images, can by EO-1 hyperion atural object classification neighbour cooperate with enhancing by way of by
Step expands marked pixel number.
U=u+1 is enabled, if u < 10, updates all class ground object target matrix Ds according to formula (1);Turn next to step E after
It is continuous to execute;When reaching u=11, iteration stopping, neighbour cooperates with enhancing label to complete, and the pixel in Cset set is as every
The classification results of class atural object.
Local expansion finally is carried out using classification results of the operator that Size of Neighborhood is 2*2 to Purdue image, enhances number
According to the area of space of atural object, the schematic diagram of extension is as shown in Figure 5.Wherein Fig. 5 left figure is the atural object after cooperateing with by neighbour
The result figure after neighbor operator that classification results are 2*2 by size is shown in Fig. 5 right figure, it can be seen that is expanded by neighborhood
After exhibition, the space characteristics of atural object, which have been characterized, to be come out, and represents the form and size of atural object.One group of Purdue data is final
For classification results as shown in fig. 6, Fig. 6 a is ground truth image, Fig. 6 b is one group of classification results of the invention.
Other two groups of true high-spectral datas, hereinafter referred to as Salinas data and Pavia number are also used in experiment
According to.Wherein: one group is by the high-spectrum in the mountain valley Salinas obtained using AVIRIS sensor in California, USA southern areas
Picture, hereinafter referred to as Salinas data.The size of the image is 512 × 217, and spatial resolution is 3.7 meters, contains 224 waves
Section includes 16 class atural objects, pseudocolour picture and true terrestrial object information as shown in figure 3, the number of initial Cset is as shown in table 3 altogether.
Another group is the city district image Pavia obtained using ROSIS-03 sensor in Pavia university overhead
University, hereinafter referred to as pavia data, the data image size are 610 × 340, and spatial resolution is 1.3 meters, are contained
103 wave bands, altogether including 9 class atural objects, pseudocolour picture and true terrestrial object information as shown in figure 3, the number such as table 4 of initial Cset
It is shown.
Table 3
Table 4
Atural object class-mark k | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Pixel number n (k) | 663 | 1865 | 210 | 306 | 135 | 503 | 133 | 368 | 95 |
The grountruth image of this two groups of group truthful datas is as shown in Fig. 7 a and Fig. 8 a, and one group of final classification result is as schemed
Shown in 7b and Fig. 8 b.By above based on neighbour cooperate with enhancing the obtained three groups of true classification results of classification method with
The result of Groundtruth image labeling can significantly find out that the classification method that this invention proposes is devised with Spectral Properties
Multi-class classifier based on sign can once classify to all atural object classifications, and effective solution tradition is with SVM
Based on classifier the problem of can not classifying to image background.
Quantify following with nicety of grading and kappa coefficient and classification side that this invention of objective appraisal is proposed
Method, classification rate OA are defined as follows:
Wherein p is atural object classification number, SiFor the i-th class in classification results, ground truth is also the pixel of the i-th class atural object
Number, NiFor the number of samples of the i-th class atural object in Ground truth result.
The nicety of grading of every kind of ground object target classification, calculation formula are as follows:
The calculation formula of Kappa coefficient are as follows:
Wherein:
N1iPresentation class result be divided into for the i-th class atural object be other atural objects pixel number;N2iIt indicates other atural objects
Mistake is divided into the pixel number of the i-th class atural object.
Table 5,6,7 is the nicety of grading of three panel height spectrum pictures and the specific value of kappa coefficient.It can be seen that the present invention
Classification method pretty good nicety of grading is all achieved for every kind of atural object classification, while kappa coefficient is also relatively high, shows this
The result of classification method and true classification results consistency are higher.
Table 5
Table 6
Table 7
Present invention utilizes the multi-categorizer testing results of spectrum statistical nature design, and unlabelled sample is carried out neighbour
From collaboration enhancing mark, it is gradually completing mixed pixel classification.In order to improve nicety of grading in method, using feature between composing and sky
Between the integrated mode of feature carry out EO-1 hyperion mixed pixel category feature judgement.Multi-class hyperspectral classification device is designed first,
After part sample is marked, by multi-class hyperspectral classification device, preliminary classification is detected as a result, then will test result
It is compared with marked atural object, selection is labeled apart from the collaboration of the smallest sample, gradually enhances marked sample
Number, then the signature of the spectrum by updating Target scalar, complete the classification of high spectrum image in the way of iteration.
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations;To the greatest extent
Pipe present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement;And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (5)
1. a kind of EO-1 hyperion mixed pixel classification method for cooperateing with enhancing based on neighbour characterized by comprising
The spectral signature matrix of multiple target atural object is calculated according to marked sample atural object;
The Target scalar is classified using the multi-class classifier based on the spectral signature matrix and constraint matrix;
Neighbour's pixel is extracted again after the Abundances that the classifier obtains are merged spatial structure characteristic;
Category label is carried out according to Target scalar of neighbour's pixel collaboration to unmarked EO-1 hyperion, gradually using alternative manner
Unlabelled atural object is classified respectively;
Spatial structure characteristic is merged in classification results, and extracts neighbour's pixel, comprising:
Using formula
Convolutional calculation is carried out to classification results and obtains TG(k), wherein the σ is the standard deviation of gaussian filtering, and r is gaussian filtering
Filtering radius, k be atural object class-mark, the T (k) is the classification results of every kind of atural object classification;
To TG(k) the abundance Value Data in is ranked up, neighbour's collection of a pixel composition atural object classification of the maximum 2*n (k) of extraction of values
Close { MCset(k) }, wherein n (k) is the pixel number that kth class atural object increases mark newly every time.
2. the method according to claim 1, wherein it is described according to marked sample atural object with calculating multiple target
The spectral signature matrix of object, comprising:
According to formula
Calculate the spectral signature vector of Target scalar, wherein dkFor the spectral signature vector of kth class Target scalar, dk={ dk1,
dk2,...dkL, L is wave band number, { CsetIt (k) } is marked kth class sample atural object set, NkFor { Cset(k) } picture in
First number, HkIt (j) is { Cset(k) } spectral signature of j-th of pixel in;
The spectral signature matrix D of Target scalar end member, D=[d are calculated according to the spectral signature vector1,d2,...dp], wherein
P is atural object type number to be sorted, d1For the spectral signature of first kind atural object.
3. the method according to claim 1, wherein described using based on the spectral signature matrix and constraint square
The multi-class classifier of battle array classifies the Target scalar, comprising:
According to the class number p of the Target scalar, set the constraint matrix of classifier asWherein, cjFor jth
The constrained vector of a Target scalar, 1≤j≤p, for constraining jth class Target scalar;
It is defined using the spectral signature matrix and the constraint matrix to multiclass p a Target scalars while classified
Other classifier T, the classifier are as follows:
T=r (RL×L -1D(DTRL×L -1D)-1Cp×p) (3)
Wherein, R is the sample autocorrelation matrix of high spectrum image, the R are as follows:
Wherein, r=[r1r2...rn] it is hyperspectral image data, n is the pixel number of high spectrum image, and D is spectral signature square
Battle array, L-band number.
4. the method according to claim 1, wherein described cooperate with according to neighbour's pixel to unmarked bloom
The Target scalar of spectrum carries out category label, comprising:
Similitude is between defining the class of various Target scalars
dis(Hk(j))=| | M (k)-MHk(j)||2 (5)
Wherein, M (k) is the sample clustering center for having marked the kth class Target scalar of classification, MHkIt (j) is { MCset(k) } jth in
The spectral signature of a pixel;
Similitude between the class of atural object is calculated in neighbour's set in sample and marked set according to similarity criterion between class;
A pixel of the n (k) of similitude maximum value between the class is labeled.
5. the method according to claim 1, wherein described gradually divided unlabelled atural object using alternative manner
After not classified, further includes:
Expanded using neighbor operator, morphology and local expansion is carried out to classification results, for enhancing the area of space of data atural object
Property.
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