CN101329724A - Optimized human face recognition method and apparatus - Google Patents

Abstract

The invention discloses an optimized face recognition method and a device thereof, which improve the rate of facial image recognition. The technical proposal is that: the method and the device combine principal component analysis and linear discriminant analysis to solve the recognition problem; namely, the principal component analysis is carried out first before the conduction of the linear discriminant analysis so as to obtain relatively low dimensional space, then the space is utilized to carry out the linear discriminant analysis, and therefore, an intra-class dispersion matrix can not be caused and the process of the linear discrimination is effective. The invention firstly adopts the principal component analysis to obtain the best feature description, based on which, optimum identifying features are obtained by adopting the linear discriminant analysis, thereby greatly reducing the space dimension of facial features; finally, a minimum distance method is adopted to carry out classification and identification and therefore the rate of recognizing human faces is evidently increased. The method and the device of the invention are applied to face recognition.

Description

A kind of face identification method of optimization and device

Technical field

The present invention relates to a kind of optimization of face recognition algorithms, relate in particular to face identification method and device in conjunction with principal component analysis (PCA) in the recognition of face (PCA) and linear discriminant analysis (LDA).

Background technology

Along with the development and the development of technology of society, the lifting at full speed of the soft hardware performance of computing machine especially in recent years, each side is urgent day by day to the requirement of rapidly and efficiently auto authentication.Biological identification technology has been obtained great attention and development at scientific research field.Because biological characteristic is people's a inherent attribute, has very strong self stability and individual difference, be the most desirable foundation of authentication therefore.Wherein, utilizing face characteristic to carry out authentication is again the most direct means, with fingerprint, iris, other human body living creature characteristic recognition systems such as palmmprint are compared, face identification system is friendly more, convenient, be easy to be accepted by the user, wide application is arranged, for example may be used on the public security monitoring of deploying to ensure effective monitoring and control of illegal activities, the prison monitoring, judicial authentication, civil aviaton's safety check, entry and exit of the port control, customs's authentication, bank's authentication, smart identity cards, intelligent entrance guard, intelligent video monitoring, the intelligence access and exit control, the checking of driver's driving license, all kinds of bank cards, fiscard, credit card, deposit card holder's authentication, many aspects such as social insurance authentication, can also be applied to aspects such as medical treatment and video conference, show its great vitality.Recognition of face (Face Recognition) is to utilize the Computer Analysis facial image, and the extract effective identifying information is used for distinguishing a special kind of skill of identity.After promptly the known person face being carried out standardization, by someway with database in people's face sample compare, seek the relevant information of corresponding people's face and this people's face in the storehouse.

Face recognition technology comprises the detection of people's face, the pre-service of people's face, feature extraction and recognition of face.How effective feature extraction is important the dealing with problems of recognition of face with identification.

These two kinds of methods of principal component analysis (PCA) (PCA) and linear discriminant analysis (LDA) are arranged in traditional face recognition technology.

The thought source of principal component analysis (PCA) (PCA) is in Karhunen-Loeve transformation, and purpose is to seek the bases of the unit orthogonal vector of one group of optimum as the subspace, rebuilds former sample with their linear combination then, and to make under this meaning that is reconstituted in the square error minimum be optimum; The image-region that is about to whole people's face is regarded a kind of random vector as, the high dimension vector that will characterize people's face by Karhunen-Loeve transformation is mapped in the subspace of being opened by the several features vector, utilizes the linear combination of these eigenface to describe, expresses and approach facial image.

The parameter that relates generally in principal component analysis (PCA) is as follows: the different people of the known c of having class, every class people has N respectively _i(i=1,2 ..., c) width of cloth facial image, then always total $N=\underset{i=1}{\overset{c}{\mathrm{\Σ}}}{N}_i$ Width of cloth training image promptly has N known sample of c class, and every class has N _i(i=1,2 ..., c) width of cloth facial image, i.e. N ₁Individual sample belongs to X ₁Class, N ₂Individual sample belongs to X ₂Class, N _iIndividual sample belongs to X _iClass, X _iIt is i class sample set.If every width of cloth facial image is w * h pixel, at first it is expanded into the column vector that n=w * h ties up by row or column, then N sample can simply be expressed as: x _i(i=1,2 ..., N).

The average face of training sample set is defined as: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i$ (formula 1)

Vector x after the training sample centralization _i: x _i=x _i-m (formula 2)

The covariance matrix C of training sample: $C_{m\×N}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left({\stackrel{\‾}{x}}_i\right){\left({\stackrel{\‾}{x}}_i\right)}^T$ (formula 3)

The concrete step of principal component analysis (PCA) is:

(1) each width of cloth image stretching is become delegation's (or row) vector, constitute the facial image matrix, try to achieve the average face and the centralization of image then, obtain the covariance matrix of sample at last, promptly formula 3.

(2) calculate eigenwert and the proper vector of covariance matrix C, press nonzero eigenvalue λ _iOrder from big to small is with characteristic of correspondence vector u _iArrange, preceding k the eigenvectors matrix of being formed is eigenface space (projection matrix) U, and each of U is classified proper vector a: U=[u as ₁, u ₂..., u _k].

(3) with the training image x after each width of cloth centralization _iProject to projector space, obtain its respective projection coefficient, form the projection coefficient matrix W _i=U ^TX, x=[x ₁, x ₂..., x _N], this moment, the facial image of n dimension just became the k dimension after projection originally, had reached the effect of dimensionality reduction.

(4) y will be obtained after each width of cloth test sample book centralization _j=y _j-m also projects to projector space, obtains the projection coefficient matrix W ₂=U ^TY, y=[y ₁, y ₂..., y _M], M is the test sample book number, differentiates with minimum Eustachian distance at last.

From the effect of principal component analysis (PCA), principal component analysis (PCA) is based on the lowest mean square criterion, makes the energy minimum of image impairment, the error minimum between reconstructed image and the original image, and it has best expression ability, but does not have best distinguishing ability.Principal component analytical method is that statistics is optimum, square error minimum before and after its feasible compression, and the data component (being pivot) that keeps variance maximum in the former sample, this makes the lower dimensional space after the conversion that good expression ability be arranged, but the training of principal component analysis (PCA) is non-supervision, promptly can't utilize the classification information of training sample, does not consider in the class and the problem between class, but, there is not best distinguishing ability the utilization of putting together of whole samples.

Linear discriminant analysis is that the separability with sample is preferably target, attempts to seek dispersion minimum in the class that one group of linear transformation makes every class, and makes dispersion maximum between class, has best distinguishing ability.Be after sample projects to this linear change space, the sample of same item is gathered as far as possible, inhomogeneous sample as far as possible separately.

The parameter that linear discriminant analysis relates generally to is as follows:

I class sample average is: $m_i=\frac{1}{N_i}\underset{x\∈X_i}{\mathrm{\Σ}}x$ (formula 4)

The within class scatter matrix S of sample _w: $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Σ}}}(x_{\mathrm{ij}}-m_i){(x_{\mathrm{ij}}-m_i)}^T$ (formula 5)

Dispersion matrix S between the class of sample _b: $S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\Σ}}}{N}_i(m_i-m){(m_i-m)}^T$ (formula 6)

Linear discriminant analysis is sought an optimum linearity conversion W exactly and is made dispersion minimum in the class, and dispersion maximum between class promptly satisfies: $W=\underset{w}{\arg \max }\frac{\left|W^T{S}_{b}W\right|}{\left|W^T{S}_{w}W\right|};$ W can be by separating generalized eigenvalue problem S _bW=S _wW Λ tries to achieve.As within class scatter matrix S _wWhen nonsingular, the column vector of optimum linearity conversion W is S _w ^-1S _bProper vector, this group vector be also referred to as optimum discriminant vector collection.

It is normally unusual that yet the problem that can run into when practical application is exactly the sample within class scatter matrix, this be because the sample number of training sample often less than sample number of pixels that each sample comprised, for example in the ORL face database, the pixel of its facial image is 112 * 92, be converted into vector representation later on just up to 10304 dimensions, and the sample number of training is usually much smaller than this number, so, recognition of face under normal circumstances always runs into one " small sample ", cause within class scatter matrix unusual, linear discriminant analysis just can not directly be used like this.

Summary of the invention

The object of the present invention is to provide a kind of face identification method of optimization, improved the discrimination of facial image.

Another object of the present invention is to provide a kind of face identification device of optimization, improved the discrimination of facial image.

Technical scheme of the present invention is: the present invention has disclosed a kind of face identification method of optimization, and principal component analysis (PCA) and linear discriminant analysis are combined, and this method comprises:

(1) with the training sample set x of facial image _i, i=1,2 ... N, after the centralization, according to formula $C_{m\×N}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left({\stackrel{\‾}{x}}_i\right){\left({\stackrel{\‾}{x}}_i\right)}^T$ Calculate covariance matrix C, wherein N is the sum of training sample, x _iBe the vector after the training sample centralization, m is the average face of training sample set;

(2) m the eigenvalue of maximum characteristic of correspondence vector of calculating covariance matrix C, this m proper vector formed the principal component analysis (PCA) projection matrix: $W_{\mathrm{pca}}=[{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_1^{\mathrm{pca}},...,{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_2^{\mathrm{pca}},...,W_m^{\mathrm{pca}}],$ M≤N-c wherein, c are the different people's that concentrates of this training sample number;

(3) utilize this principal component analysis (PCA) projection matrix, the facial image space is converted into the eigenface space of dimensionality reduction, the best that obtains facial image is described feature: $y_i={(y_1^i,y_2^i,...,y_m^i)}^T=W_{\mathrm{pca}}^T(x_i-m),$ i＝1，2，...N；

(4) calculate by y ₁.., y _i... y _NScatter matrix S in the class that constitutes _wAnd scatter matrix S between class _b

(5) compute matrix S _w ^-1S _bK eigenvalue of maximum characteristic of correspondence vector W ₁ ^Lda..., W _i ^Lad... W _k ^Lda, wherein k is a matrix S _w ^-1S _bThe number of eigenvalue of maximum, constitute the linear discriminant analysis projection matrix by this k eigenvalue of maximum characteristic of correspondence vector $W_{\mathrm{lda}}=[{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_1^{\mathrm{lda}},...,{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_2^{\mathrm{lda}},...,W_k^{\mathrm{lda}}];$

(6) utilize the linear discriminant analysis projection matrix that this further dimensionality reduction in eigenface space is differentiated the space to k dimension the best, obtain the optimal classification feature of facial image: $z_i=(z_1^i,z_2^i,...,z_k^i)=W_{\mathrm{lda}}^T{y}_i,$ I=1 wherein, 2 ... N;

(7) calculate transition matrix W=W _PcaW _Lda, with as last projecting direction;

(8) test sample book and training sample are projected to transition matrix W respectively, obtain projection coefficient separately;

(9) differentiate according to minimum Eustachian distance.

The face identification method of above-mentioned optimization, wherein, in step (1), the centralization of training sample further comprises:

The average face of calculation training sample set: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i;$

Vector x after the calculation training center of a sampleization _i: x _i=x _i-m.

The face identification method of above-mentioned optimization, wherein, step (4) further comprises:

Calculating i class sample average is: $m_i=\frac{1}{N_i}\underset{y\&Element;Y_i}{\mathrm{\&Sigma;}}y;$

Calculating is by y ₁.., y _i... y _NScatter matrix S in the sample class that constitutes _w: $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(y_{\mathrm{ij}}-m_i){(y_{\mathrm{ij}}-m_i)}^T;$

Scatter matrix S between the class of calculating sample _b: $S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_i(m_i-m){(m_i-m)}^T.$

The present invention has also disclosed a kind of face identification device of optimization, and principal component analysis (PCA) and linear discriminant analysis are combined, and this device comprises:

The covariance matrix computing module is with the training sample set x of facial image _i, i=1,2 ... N, after the centralization, according to formula $C_{m\&times;N}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left({\stackrel{\&OverBar;}{x}}_i\right){\left({\stackrel{\&OverBar;}{x}}_i\right)}^T$ Calculate covariance matrix C, wherein N is the sum of training sample, x _iBe the vector after the training sample centralization, m is the average face of training sample set;

Principal component analysis (PCA) projection matrix computing module, m the eigenvalue of maximum characteristic of correspondence vector of calculating covariance matrix C, this m proper vector formed the principal component analysis (PCA) projection matrix: $W_{\mathrm{pca}}=[{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_1^{\mathrm{pca}},...,{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_2^{\mathrm{pca}},...,W_m^{\mathrm{pca}}],$ M≤N-c wherein, c are the different people's that concentrates of this training sample number;

The eigenface space obtains module, and the principal component analysis (PCA) projection matrix that utilizes this principal component analysis (PCA) projection matrix computing module to obtain is converted into the eigenface space of dimensionality reduction with the facial image space, and the best that obtains facial image is described feature: $y_i={(y_1^i,y_2^i,...,y_m^i)}^T=W_{\mathrm{pca}}^T(x_i-m),$ i＝1，2，...N；

The scatter matrix computing module calculates by y ₁..., y _i... y _NScatter matrix S in the class that constitutes _wAnd scatter matrix S between class _b

Linear discriminant analysis projection matrix computing module, compute matrix S _w ^-1S _bK eigenvalue of maximum characteristic of correspondence vector W ₁ ^Lda..., W _i ^Lda... W _k ^Lda, wherein k is a matrix S _w ^-1S _bThe number of eigenvalue of maximum, constitute the linear discriminant analysis projection matrix by this k eigenvalue of maximum characteristic of correspondence vector $W_{\mathrm{lda}}=[{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_1^{\mathrm{lda}},...,{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_2^{\mathrm{lda}},...,W_k^{\mathrm{lda}}];$

The best space of differentiating obtains module, utilizes the linear discriminant analysis projection matrix that this further dimensionality reduction in eigenface space is differentiated the space to k dimension the best, obtains the optimal classification feature of facial image: $z_i=(z_1^i,z_2^i,...,z_k^i)=W_{\mathrm{lda}}^T{y}_i,$ I=1 wherein, 2 ... N;

The transform matrix calculations module is calculated transition matrix W=W _PcaW _Lda, with as last projecting direction;

The projection coefficient computing module projects to transition matrix W respectively with test sample book and training sample, obtains projection coefficient separately;

Discrimination module is differentiated according to minimum Eustachian distance.

The face identification device of above-mentioned optimization, wherein, this covariance matrix computing module also comprises:

Training sample centralization unit further comprises:

The average face computing unit, the average face of calculation training sample set: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i;$

The centralization vector calculation unit, the vector x after the calculation training center of a sampleization _i: x _i=x _i-m.The face identification device of above-mentioned optimization, wherein, the scatter matrix computing module further comprises:

The sample average computing unit, calculate i class sample average and be: $m_i=\frac{1}{N_i}\underset{y\&Element;Y_i}{\mathrm{\&Sigma;}}y;$

Scatter matrix computing unit in the class calculates by y ₁.., y _i... y _NScatter matrix S in the sample class that constitutes _w: $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(y_{\mathrm{ij}}-m_i){(y_{\mathrm{ij}}-m_i)}^T;$

Scatter matrix computing unit between class, scatter matrix S between the class of calculating sample _b: $S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_i(m_i-m){(m_i-m)}^T.$

The present invention contrasts prior art following beneficial effect: because linear discriminant analysis is owing to the within class scatter matrix singular problem causes, utilization of the present invention combines principal component analysis (PCA) and linear discriminant analysis and addresses this problem, promptly before carrying out linear discriminant analysis, carry out principal component analysis (PCA) earlier, obtain the space of relative low-dimensional, the then enterprising line linearity discriminatory analysis in this space again, unusual and the linear discriminant process is effective with regard to not causing within class scatter matrix like this.Traditional linear discriminant analysis makes dispersion maximum between the class of the sample after the projection and dispersion minimum in the class, that is to say that the sample of sample same item on new space gathers together after the projection, and inhomogeneous sample then separates, and has good separation property.And traditional principal component analysis (PCA) is the data component that keeps variance maximum in the former sample, so the former sample of expression that principal component analysis (PCA) can be best has best expression ability, but does not have distinguishing ability.The present invention at first adopts principal component analysis (PCA) to obtain the best feature of describing, and then adopt linear discriminant analysis to obtain best diagnostic characteristics on this basis, thereby greatly reduce the dimension in face characteristic space, adopt minimum distance method to carry out Classification and Identification at last, significantly improved the discrimination of facial image.

Description of drawings

Fig. 1 is the process flow diagram of preferred embodiment of the face identification method of optimization of the present invention.

Fig. 2 is the block diagram of preferred embodiment of the face identification device of optimization of the present invention.

Fig. 3 is the block diagram of the preferred embodiment of scatter matrix computing module of the present invention.

Embodiment

The invention will be further described below in conjunction with drawings and Examples.

Main thought of the present invention is that principal component analysis (PCA) and linear discriminant analysis are combined, and Fig. 1 shows the flow process of preferred embodiment of the face identification method of optimization of the present invention, sees also Fig. 1, is the detailed description to each step in the method below.

Step S100: calculation training sample set x _i, i=1,2 ... the average face m of N: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i.$ Wherein N is the sample size that training sample is concentrated.

Step S101: the vector x after the calculation training center of a sampleization _i: x _i=x _i-m.

Step S102: calculate covariance matrix: $C_{m\&times;N}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left({\stackrel{\&OverBar;}{x}}_i\right){\left({\stackrel{\&OverBar;}{x}}_i\right)}^T.$

Step S103: calculate m the eigenvalue of maximum characteristic of correspondence vector of covariance matrix C, form principal component analysis (PCA) (PCA) projection matrix by this m proper vector: $W_{\mathrm{pca}}=[{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_1^{\mathrm{pca}},...,{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_2^{\mathrm{pca}},...,W_m^{\mathrm{pca}}],$ Wherein m≤N-c forms this training sample set by different people's facial image, and c is the classification number of facial image.

Step S104: utilize this principal component analysis (PCA) projection matrix, the facial image space is converted into the eigenface space of dimensionality reduction, the best that obtains each width of cloth facial image is described feature: $y_i={(y_1^i,y_2^i,...,y_m^i)}^T=W_{\mathrm{pca}}^T(x_i-m),$ i＝1，2，..N。

Step S105: calculate by y ₁.., y _i... y _NScatter matrix S in the class that constitutes _wAnd scatter matrix S between class _b

Scatter matrix S in the compute classes _wAnd scatter matrix S between class _bDetailed process be:

The first step: calculating i class sample average is: $m_i=\frac{1}{N_i}\underset{y\&Element;Y_i}{\mathrm{\&Sigma;}}y;$

Second step: calculate by y ₁.., y _i... y _NScatter matrix S in the sample class that constitutes _w: $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(y_{\mathrm{ij}}-m_i){(y_{\mathrm{ij}}-m_i)}^T;$

The 3rd step: scatter matrix S between the class of calculating sample _b: $S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_i(m_i-m){(m_i-m)}^T.$

Step S106: compute matrix S _w ^-1S _bK eigenvalue of maximum characteristic of correspondence vector W ₁ ^Lda..., W _i ^Lda... W _k ^Lda, wherein k is a matrix S _w ^-1S _bThe number of eigenvalue of maximum, constitute the linear discriminant analysis projection matrix by this k eigenvalue of maximum characteristic of correspondence vector $W_{\mathrm{lda}}=[{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_1^{\mathrm{lda}},...,{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_2^{\mathrm{lda}},...,W_k^{\mathrm{lda}}].$

Step S107: utilize the linear discriminant analysis projection matrix that this further dimensionality reduction in eigenface space is differentiated the space to k dimension the best, obtain the optimal classification feature of facial image: $z_i=(z_1^i,z_2^i,...,z_k^i)=W_{\mathrm{lda}}^T{y}_i,$ I=1 wherein, 2 ... N.

Step S108: calculate transition matrix W=W _PcaW _Lda, with as last projecting direction.

Step S109: test sample book and training sample are projected to transition matrix W respectively, obtain projection coefficient separately.

Step S110: differentiate according to minimum Eustachian distance.

Training sample in the present embodiment and test sample book can derive from the ORL storehouse, and this ORL storehouse is the facial image database that is used to test face recognition algorithms that Cambridge University's Bell Laboratory was made in 1994.This database comprises everyone 10 width of cloth images that 40 people take at different time, the image of totally 400 256 gray levels, and size is 112 * 92.Facial image in the ORL database is the front elevation picture, and tilt variation and rotation change are about 20%, and dimensional variation is about 10%.The background light of facial image has certain variation in addition, the expression of people's face also different (comprising and open eyes and close one's eyes, smile and do not laugh at that the image when wearing glasses and not wearing glasses is arranged).

Corresponding to above-mentioned method embodiment, the present invention also provides a kind of face identification device of optimization, and this same device also is to combine principal component analysis (PCA) and linear discriminant analysis, and Fig. 2 shows the preferred embodiment of face identification device.See also Fig. 2, the embodiment of device comprises that covariance matrix computing module 10, principal component analysis (PCA) projection matrix computing module 11, eigenface space obtain module 12, scatter matrix computing module 13, linear discriminant analysis projection matrix computing module 14, best space acquisition module 15, transform matrix calculations module 16, projection coefficient computing module 17, the discrimination module 18 differentiated.

Covariance matrix computing module 10 is with the training sample set x of facial image _i, i=1,2 ... N after the centralization, calculates covariance matrix: $C_{m\&times;N}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left({\stackrel{\&OverBar;}{x}}_i\right){\left({\stackrel{\&OverBar;}{x}}_i\right)}^T,$ Wherein N is the sum of training sample, x _iBe the vector after the training sample centralization.Also comprise training sample centralization unit 100 in the covariance matrix computing module 10, in training sample centralization unit 100, further comprise average face computing unit 1000 and centralization vector calculation unit 1001.The average face of average face computing unit 1000 calculation training sample sets: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i.$ Vector x after the centralization vector calculation unit 1001 calculation training center of a sampleization _i: x _i=x _i-m.

Principal component analysis (PCA) projection matrix computing module 11 calculates m the eigenvalue of maximum characteristic of correspondence vector of covariance matrix C, and this m proper vector formed the principal component analysis (PCA) projection matrix: $W_{\mathrm{pca}}=[{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_1^{\mathrm{pca}},...,{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_2^{\mathrm{pca}},...,W_m^{\mathrm{pca}}],$ M≤N-c wherein, c are the different people's that concentrates of this training sample number.The eigenface space obtains the principal component analysis (PCA) projection matrix that module 12 utilizes this principal component analysis (PCA) projection matrix computing module to obtain, and the facial image space is converted into the eigenface space of dimensionality reduction, obtains projection coordinate's vector of each width of cloth facial image: $y_i={(y_1^i,y_2^i,...,y_m^i)}^T=W_{\mathrm{pca}}^T(x_i-m),$ i＝1，2，...N。

Scatter matrix computing module 13 calculates by y ₁.., y _i... y _NScatter matrix S in the class that constitutes _wAnd scatter matrix S between class _bScatter matrix computing unit 132 between scatter matrix computing unit 131, class in as shown in Figure 3 be divided into sample average computing unit 130 of scatter matrix computing module 13, the class.Wherein sample average computing unit 130 calculating i class sample averages are: $m_i=\frac{1}{N_i}\underset{y\&Element;Y_i}{\mathrm{\&Sigma;}}y.$ Scatter matrix computing unit 131 calculates by y in the class ₁.., y _i... y _NScatter matrix S in the sample class that constitutes _w: $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(y_{\mathrm{ij}}-m_i){(y_{\mathrm{ij}}-m_i)}^T.$ Scatter matrix S between the class of scatter matrix computing unit 132 calculating samples between class _b: $S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_i(m_i-m){(m_i-m)}^T.$

Linear discriminant analysis projection matrix computing module 14 compute matrix S _w ^-1S _bK eigenvalue of maximum characteristic of correspondence vector W ₁ ^Lda..., W _i ^Lda... W _k ^Lda, wherein k is a matrix S _w ^-1S _bThe number of eigenvalue of maximum; Constitute the linear discriminant analysis projection matrix by this k eigenvalue of maximum characteristic of correspondence vector $W_{\mathrm{lda}}=[{\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_1^{\mathrm{lda}},...,{\mathrm{<figure-callout\; id="2"\; label="W"\; filenames="A20081004110500141.png"\; state="\{\{state\}\}">W</figure-callout>}}_2^{\mathrm{lda}},...,W_k^{\mathrm{lda}}].$ The best space acquisition module 15 of differentiating utilizes the linear discriminant analysis projection matrix that this further dimensionality reduction in eigenface space is differentiated the space to k dimension the best, obtains $z_i=(z_1^i,z_2^i,...,z_k^i)=W_{\mathrm{lda}}^T{y}_i,$ I=1 wherein, 2 ... N.Transform matrix calculations module 16 is calculated transition matrix W=W _PcaW _Lda, with as last projecting direction.Projection coefficient computing module 17 projects to transition matrix W respectively with test sample book and training sample, obtains projection coefficient separately.Differentiate according to minimum Eustachian distance by discrimination module 18 at last.

Principal component analysis (PCA) is a kind of simple, practical algorithm based on coefficient in transform domain, it is optimum from the angle of compression energy, it not only makes the square error minimum before and after the dimensionality reduction, and the lower dimensional space after the conversion has good people's face to represent ability, but do not have good people's face distinguishing ability.Linear discriminant analysis is the separability from sample, and purpose is exactly will find a space that sample is projected to best separability is arranged on this space afterwards, but usually can run into " small sample " problem in actual applications.The present invention combines principal component analysis (PCA) and linear discriminant analysis exactly, when solving small sample problem, has also improved the discrimination of people's face, is a kind of extraordinary face identification method.

The foregoing description provides to those of ordinary skills and realizes or use of the present invention; those of ordinary skills can be under the situation that does not break away from invention thought of the present invention; the foregoing description is made various modifications or variation; thereby protection scope of the present invention do not limit by the foregoing description, and should be the maximum magnitude that meets the inventive features that claims mention.

Claims (6)

1, a kind of face identification method of optimization combines principal component analysis (PCA) and linear discriminant analysis, and this method comprises:

(1) with the training sample set x of facial image _i, i=1,2 ..N is after the centralization, according to formula $C_{m\&times;N}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left({\stackrel{\&OverBar;}{x}}_i\right){\left({\stackrel{\&OverBar;}{x}}_i\right)}^T$ Calculate covariance matrix C, wherein N is the sum of training sample, x _iBe the vector after the training sample centralization, m is the average face of training sample set;

(2) m the eigenvalue of maximum characteristic of correspondence vector of calculating covariance matrix C, this m proper vector formed the principal component analysis (PCA) projection matrix: $W_{\mathrm{pca}}=[W_1^{\mathrm{pca}},...,W_2^{\mathrm{pca}},...,W_m^{\mathrm{pca}}],$ M≤N-c wherein, c are the different people's that concentrates of this training sample number;

(3) utilize this principal component analysis (PCA) projection matrix, the facial image space is converted into the eigenface space of dimensionality reduction, the best that obtains facial image is described feature: $y_i={(y_1^i,y_2^i,...,y_m^i)}^T=W_{\mathrm{pca}}^T(x_i-m),$ i＝1，2，..N；

(4) calculate by y ₁.., y _i... y _NScatter matrix S in the class that constitutes _wAnd scatter matrix S between class _b

(5) compute matrix S _w ^-1S _bK eigenvalue of maximum characteristic of correspondence vector W ₁ ^Lda..., W _i ^Lda... W _k ^Lda, wherein k is a matrix S _w ^-1S _bThe number of eigenvalue of maximum, constitute the linear discriminant analysis projection matrix by this k eigenvalue of maximum characteristic of correspondence vector $W_{\mathrm{lda}}=[W_1^{\mathrm{lda}},...,W_2^{\mathrm{lda}},...,W_k^{\mathrm{lda}}];$

(6) utilize the linear discriminant analysis projection matrix that this further dimensionality reduction in eigenface space is differentiated the space to k dimension the best, obtain the optimal classification feature of facial image: $z_i=(z_1^i,z_2^i,...,z_k^i)=W_{\mathrm{lda}}^T{y}_i,$ I=1 wherein, 2 ... N;

(7) calculate transition matrix W=W _PcaW _Lda, with as last projecting direction;

(8) test sample book and training sample are projected to transition matrix W respectively, obtain projection coefficient separately;

(9) differentiate according to minimum Eustachian distance.

2, the face identification method of optimization according to claim 1 is characterized in that, in step (1), the centralization of training sample further comprises:

The average face of calculation training sample set: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i;$

Vector x after the calculation training center of a sampleization _i: x _i=x _i-m.

3, the face identification method of optimization according to claim 1 is characterized in that, step (4) further comprises:

Calculating i class sample average is: $m_i=\frac{1}{N_i}\underset{y\&Element;Y_i}{\mathrm{\&Sigma;}}y;$

Calculating is by y ₁.., y _i... y _NScatter matrix in the sample class that constitutes $S_w:S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(y_{\mathrm{ij}}-m_i){(y_{\mathrm{ij}}-m_i)}^T;$

Scatter matrix between the class of calculating sample $S_b:S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_i(m_i-m){(m_i-m)}^T.$

4, a kind of face identification device of optimization combines principal component analysis (PCA) and linear discriminant analysis, and this device comprises:

The covariance matrix computing module is with the training sample set x of facial image _i, i=1,2 ... N, after the centralization, according to formula $C_{m\&times;N}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left({\stackrel{\&OverBar;}{x}}_i\right){\left({\stackrel{\&OverBar;}{x}}_i\right)}^T$ Calculate covariance matrix C, wherein N is the sum of training sample, x _iBe the vector after the training sample centralization, m is the average face of training sample set;

Principal component analysis (PCA) projection matrix computing module, m the eigenvalue of maximum characteristic of correspondence vector of calculating covariance matrix C, this m proper vector formed the principal component analysis (PCA) projection matrix: $W_{\mathrm{pca}}=[W_1^{\mathrm{pca}},...,W_2^{\mathrm{pca}},...,W_m^{\mathrm{pca}}],$ M≤N-c wherein, c are the different people's that concentrates of this training sample number;

The eigenface space obtains module, and the principal component analysis (PCA) projection matrix that utilizes this principal component analysis (PCA) projection matrix computing module to obtain is converted into the eigenface space of dimensionality reduction with the facial image space, and the best that obtains facial image is described feature: $y_i={(y_1^i,y_2^i,...,y_m^i)}^T=W_{\mathrm{pca}}^T(x_i-m),$ i＝1，2，...N；

The scatter matrix computing module calculates by y ₁.., y _i, ... and y _NScatter matrix S in the class that constitutes _wAnd scatter matrix S between class _b

Linear discriminant analysis projection matrix computing module, compute matrix S _w ^-1S _bK eigenvalue of maximum characteristic of correspondence vector W ₁ ^Lda..., W _i ^Lda... W _k ^Lda, wherein k is a matrix S _w ^-1S _bThe number of eigenvalue of maximum, constitute the linear discriminant analysis projection matrix by this k eigenvalue of maximum characteristic of correspondence vector $W_{\mathrm{lda}}=[W_1^{\mathrm{lda}},...,W_2^{\mathrm{lda}},...,W_k^{\mathrm{lda}}];$

The best space of differentiating obtains module, utilizes the linear discriminant analysis projection matrix that this further dimensionality reduction in eigenface space is differentiated the space to k dimension the best, obtains the optimal classification feature of facial image: $z_i=(z_1^i,z_2^i,...,z_k^i)=W_{\mathrm{lda}}^T{y}_i,$ I=1 wherein, 2 ... N;

The transform matrix calculations module is calculated transition matrix W=W _PcaW _Lds, with as last projecting direction;

The projection coefficient computing module projects to transition matrix W respectively with test sample book and training sample, obtains projection coefficient separately;

Discrimination module is differentiated according to minimum Eustachian distance.

5, the face identification device of optimization according to claim 4 is characterized in that, this covariance matrix computing module also comprises:

Training sample centralization unit further comprises:

The average face computing unit, the average face of calculation training sample set: $m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i;$

The centralization vector calculation unit, the vector x after the calculation training center of a sampleization _i: x _i=x _i-m.

6, the face identification device of optimization according to claim 4 is characterized in that, the scatter matrix computing module further comprises:

The sample average computing unit, calculate i class sample average and be: $m_i=\frac{1}{N_i}\underset{y\&Element;Y_i}{\mathrm{\&Sigma;}}y;$

Scatter matrix computing unit in the class calculates by y ₁.., y _i... y _NScatter matrix S in the sample class that constitutes _w: $S_w=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(y_{\mathrm{ij}}-m_i){(y_{\mathrm{ij}}-m_i)}^T;$

Scatter matrix computing unit between class, scatter matrix S between the class of calculating sample _b: $S_b=\frac{1}{N}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_i(m_i-m){(m_i-m)}^T.$

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