CN108280470A - Discrete wavelet domain copula model image sorting techniques - Google Patents
Discrete wavelet domain copula model image sorting techniques Download PDFInfo
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- CN108280470A CN108280470A CN201810042253.3A CN201810042253A CN108280470A CN 108280470 A CN108280470 A CN 108280470A CN 201810042253 A CN201810042253 A CN 201810042253A CN 108280470 A CN108280470 A CN 108280470A
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Abstract
The present invention proposes to establish the method for copula models respectively on a kind of high-frequency sub-band in discrete wavelet and low frequency sub-band to indicate image, and applied to the classification of image.In the image characteristics extraction stage, image is subjected to three layer scattering wavelet decompositions first, establish Gauss copula models in 3 high-frequency sub-bands of each decomposition layer and 1 low frequency sub-band, three layers of totally 12 Gauss copula models, the similarity between Gauss copula models is calculated with Jeffrey distances.In the image classification stage, the weighting Jeffrey distances of 12 Gauss copula models of all subbands in discrete wavelet domain are calculated to realize image classification.Existing discrete wavelet domain Gauss copula models are compared to, classification accuracy can be improved 2 to 5 percentage points by the present invention.
Description
Technical field
The present invention relates to image classification fields, more particularly, to the image classification for establishing copula models in discrete wavelet domain
Method.
Background technology
Image classification is the important research content in computer vision, and key task is how to extract characteristics of image and profit
Image is identified with feature.Picture breakdown can be multiple dimensioned by discrete wavelet (Discrete Wavelet Transform, DWT)
Subband, to which we can extract the feature of image on different scale.DWT decompose after subband include several high-frequency sub-bands and
Low frequency sub-band, wherein high-frequency sub-band have highlighted the information such as the edge contour of image, and low frequency sub-band then remains the general picture letter of image
Breath.Image classification method of the tradition based on DWT mainly indicates to scheme using the high-frequency sub-band energy feature of DWT or statistical model
Picture.In recent years some documents focus on the performance that DWT has been improved since establishing multidimensional statistics model on the domains DWT.Copula models are exactly
It is a kind of the tool of multidimensional statistics model to be modeled on the domains DWT, and had been reported that the method that copula is established on the domains DWT,
And obtain good effect.
Gauss copula is common copula, its advantage is that comprehensive performance is preferable, convenience of calculation.Gauss copula
Density function (PDF) indicate it is as follows：
Wherein ξ=[ξ1,…,ξd], ξi=Φ-1(ui), Φ-1() is normal distribution inverse function, and R is the parameter of Gauss copula
As correlation matrix, R determines the correlation properties between stochastic variable.In cumulative distribution (CDF) the sequence u of edge distributioniIt is given
In the case of, R can be calculated with maximal possibility estimation, is indicated as follows：
Wherein N is column vector ξiLength, ξ=[ξ1,…,ξd].It can be seen that copula different edge point from formula above
Cloth uiIt is connected as a multidimensional density function.
Invention content
Existing literature reports the high-frequency sub-band in DWT and establishes copula models, and has ignored and built on its low frequency sub-band
Vertical copula models.It has been investigated that the copula models couplings on high and low frequency are got up that DWT can be further increased small
Wave graphical representation ability.Thus the present invention proposes to establish Gauss respectively in a kind of high-frequency sub-band and low frequency sub-band on the domains DWT
The image representing method of copula models, and applied to the classification of image.In image classification, with symmetrical KLD
(Kullback-Leibler Divergence) measures the similarity between two Gauss copula models, and symmetrical KLD claims
For Jeffrey distances.
Major programme of the present invention is foundation (intra-subband) dependency structure in low frequency and high-frequency sub-band, and
Multivariate probability model is established on dependency structure with Gauss copula.The present invention establishes a Gauss on each subband
Copula models, thus image classification is attributed to, Gauss copula models on all subbands are compared.Design scheme is retouched
State for：(1) one sub-picture is decomposed into 3 layers, every layer of high-frequency sub-band and 1 low frequency for there are 3 directions with DWT small echos first
Band, totally 12 subbands (low frequency sub-band on each decomposition layer retains).(2) a Gauss copula is established on each subband
Model.Subband is organized as to the observation matrix (each row correspond to a variable) of a multivariable, these observation matrixes embody
Dependence between several variables.Each column data of the extensive Gaussian Profile of single argument (GGD) fitting observation matrix is used first,
Determine the edge distribution of Gauss copula models.Then these univariate model (sides are separately connected with Gauss copula functions
Edge distributed model) it is a Gauss copula model.(3) these Gauss copula models are used for image classification.Gauss
Similarity between copula models embodies the similarity between image.The present invention indicates two with Jeffrey distances (JD)
A Gauss copula models (are expressed as h1And h2) similarity degree, i.e.,：
JD(h1,h2)=0.5* (KLD (h1,h2)+KLD(h2,h1))
Wherein
Wherein KLD (g1,g2) it is KLD distances between two Gauss copula functions；KLD(fi 1,fi 2) it is Gauss copula moulds
KLD distances between i-th of edge distribution of type.KLD(g1,g2) and KLD (fi 1,fi 2) be respectively：
Wherein γ=0.577216.It is an advantage of the invention that not only carrying the height for capturing different scale hypograph with copula models
Frequency information, while the low-frequency information (i.e. the profile information of image) of different scale hypograph is also captured, small echo is improved to image
Expression ability.
Description of the drawings
Fig. 1 is DWT decomposition diagrams of the present invention.
Fig. 2 is the scheme schematic diagram that the present invention establishes Gauss copula models on subband.
Specific implementation mode
The specific implementation step of the present invention is as follows：
Step 1, with discrete wavelet (DWT) by image IqCarry out three layers of decomposition.Every layer is decomposed, is had respectively horizontal, vertical
With 3 high-frequency sub-bands of diagonal side and 1 low frequency sub-band, it is expressed as： One is shared
12 subbands, as shown in Figure 1.
Step 2, a Gauss copula model is established on each subband.The essence for establishing Gauss copula models is meter
Calculate the parameter Θ of Gauss copula models.One shares 12 Gauss copula models, uses hk(x, Θ) is indicated, k=1 ..., 12,
Θ is parameter sets, the parameter alpha and β of its parameter R and its edge distribution GGD comprising Gauss copula functions, i.e. Θ=R, α,
β}.The foundation of each Gauss copula models needs following steps (see Fig. 2)：
Step 2.1, observation matrix (the N=sub-band coefficients of N × 9 are extracted on DWT subbands with 3 × 3 sliding windows
Number -2).Each position (totally 9 positions) in 3 × 3 windows corresponds to a variable (totally 9 variables).When window is in DWT
When taking sliding (from left to right from top to bottom, a mobile pixel position every time), it will appear different subband systems on 9 positions
Number.Corresponding all coefficients are connected in series the observed value for being this to dependent variable on one of position.
Step 2.2, it is fitted each column data of observation matrix respectively with the extensive Gaussian Profile of single argument (GGD), obtains 9
GGD edge distributions, use fi(xi) indicate, i=1 ..., 9.The probability density letter of GGD is calculated when fitting using maximum likelihood method
The parameter of number (PDF).The probability density function PDF of GGD is as follows：
Wherein, α and β is form parameter and scale parameter respectively.Due to local neighborhood coefficient of 9 column datas from DWT subbands, he
Have similar probability distribution, as long as thus calculate first row GGD estimates of parametersWith, in this way can be in terms of reducing
Calculate expense.
Step 2.3, it is estimated according to step 2.1WithCalculate the cumulative distribution function of corresponding sample point GGD
(CDF) value, i.e.,：
Step 2.4, Gauss copula input datas ξ is calculatedi。ξiIt is the input data of Gauss copula for column vector.Root
It is calculated according to 2.3It enablesObtain ξi=Φ-1(ui).Finally obtain ξ=[ξ1,…,
ξ9]。
Step 2.5, the corresponding Gauss copula correlation matrixes R of amplitude subband is calculated.According to the obtained ξ of step 2.4=
[ξ1,…,ξ9], the parameter R of Gauss copula functions is calculated with maximum likelihood method, that is, calculates following expression：
The correlation matrix R that a size is 9 × 9 can be obtained in this way.Edge distribution parameter and the parameter of copula functions in this way is complete
Portion, which calculates, to be completed to be expressed asGauss copula models are established.
Step 3, image classification.Input picture is Iq, classification is unknown.Its corresponding 12 Gausses copula model isThe image for having M known class in database, is expressed as Ij, corresponding to be characterized asTo image IqWhen being classified, need to calculate IqWith the image I in databasejIt is similar between feature
Degree, and choose and similarly spend the classification of highest image for IqClassification.It is calculated with the Jeffrey distances of following weighting
Similarity between two images：
Wherein wk, k=1 ..., 12 be the weight of 12 subbands respectively.Weight wkValue be equal to the corresponding Gauss of k-th of subband
The correct recognition rata of copula models in the database.Expression is meant that the recognition capability of some subband the strong, assigns bigger
Weight wk。It is the Jeffrey distances of the corresponding Gauss copula models of k-th of subband, is expressed as：
WhereinIt is corresponding two Gausses copula functions on k-th of subband；Similarly f1 k,Indicate k-th of son
Take the edge distribution of corresponding two Gausses copula models.It is meant that：Due to 9 in DWT subbands
A neighborhood variable is in approximately uniform distribution, thus these variables correspond to the Jeffrey of the edge distribution of Gauss copula models
Apart from value having the same.
Claims (3)
1. a kind of discrete wavelet domain copula model image sorting techniques, it is characterised in that this method has the following steps：
Step 1, with discrete wavelet (DWT) by image IqCarry out three layers of decomposition.Every layer is decomposed, is had respectively horizontal, vertical and diagonal
3 high-frequency sub-bands in side and 1 low frequency sub-band, are expressed as：Li, i=1,2,3.One shares 12 sons
Band, as shown in Figure 1.
Step 2, a Gauss copula model is established on each subband.The essence for establishing Gauss copula models is to calculate height
The parameter Θ of this copula model.One shares 12 Gauss copula models, uses hk(x, Θ) indicates that k=1 ..., 12, Θ are
Parameter sets, it includes the parameter alpha and β of the parameter R and its edge distribution GGD of Gauss copula functions, i.e. Θ={ R, α, β }.
The foundation of each Gauss copula models needs following steps.
Step 2.1, observation matrix (the N=sub-band coefficients of N × 9 are extracted on DWT subbands with 3 × 3 sliding windows
Number -2).Each position (totally 9 positions) in 3 × 3 windows corresponds to a variable (totally 9 variables).When window is in DWT subbands
When upper sliding (from left to right from top to bottom, a mobile pixel position every time), it will appear different sub-band coefficients on 9 positions.
Corresponding all coefficients are connected in series the observed value for being this to dependent variable on one of position.
Step 2.2, it is fitted each column data of observation matrix respectively with the extensive Gaussian Profile of single argument (GGD), obtains 9 GGD
Edge distribution uses fi(xi) indicate, i=1 ..., 9.The probability density function of GGD is calculated when fitting using maximum likelihood method
(PDF) parameter.The probability density function PDF of GGD is as follows：
Wherein, α and β is form parameter and scale parameter respectively.Due to local neighborhood coefficient of 9 column datas from DWT subbands, he
Have similar probability distribution, as long as thus calculate first row GGD estimates of parametersWith, in this way can be in terms of reducing
Calculate expense.
Step 2.3, it is estimated according to step 2.1WithCalculate the cumulative distribution function (CDF) of corresponding sample point GGD
Value, i.e.,：
Step 2.4, Gauss copula input datas ξ is calculatedi。ξiIt is the input data of Gauss copula for column vector.According to 2.3
It calculatesIt enablesObtain ξi=Φ-1(ui).Finally obtain ξ=[ξ1,…,ξ9]。
Step 2.5, the corresponding Gauss copula correlation matrixes R of amplitude subband is calculated.According to the obtained ξ of step 2.4=
[ξ1,…,ξ9], the parameter R of Gauss copula functions is calculated with maximum likelihood method, that is, calculates following expression：
The correlation matrix R that a size is 9 × 9 can be obtained in this way.Edge distribution parameter and the parameter of copula functions in this way is complete
Portion, which calculates, to be completed to be expressed asGauss copula models are established.
Step 3, image classification.Input picture is Iq, classification is unknown.Its corresponding 12 Gausses copula model isK=
1,…,12；The image for having M known class in database, is expressed as Ij, corresponding to be characterized asJ=1 ..., M.To image
IqWhen being classified, need to calculate IqWith the image I in databasejSimilarity degree between feature, and choose similar degree most
The classification of high image is IqClassification.The similarity between two images is calculated with the Jeffrey distances of following weighting：
Wherein wk, k=1 ..., 12 be the weight of 12 subbands respectively.Weight wkValue be equal to the corresponding Gauss of k-th of subband
The correct recognition rata of copula models in the database.Expression is meant that the recognition capability of some subband the strong, assigns bigger
Weight wk。It is the Jeffrey distances of the corresponding Gauss copula models of k-th of subband, is expressed as：
WhereinIt is corresponding two Gausses copula functions on k-th of subband；Similarly f1 k,Indicate k-th of son
Take the edge distribution of corresponding two Gausses copula models.It is meant that：Due to 9 in DWT subbands
A neighborhood variable is in approximately uniform distribution, thus these variables correspond to the Jeffrey of the edge distribution of Gauss copula models
Apart from value having the same.
2. a kind of discrete wavelet domain copula model image sorting techniques according to claim 1, it is characterised in that：To figure
As carrying out three layer scattering wavelet transformations, and establish Gauss copula respectively in the high-frequency sub-band of each decomposition layer and low frequency sub-band
Model, one shares 12 Gauss copula models.
3. described in a kind of discrete wavelet domain copula model images sorting technique according to claim 1 and claim 2
The 12 Gauss copula models established, it is characterised in that：By the weighting Jeffrey distances between 12 Gauss copula models
For image classification, i.e.,：
Wherein wk, k=12 is the weight of all 12 subbands of the DWT comprising low frequency sub-band.Weight wkValue be equal to k-th of subband
The correct recognition rata of corresponding Gauss copula models in the database.
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