CN102982322A - Face recognition method based on PCA (principal component analysis) image reconstruction and LDA (linear discriminant analysis) - Google Patents

Abstract

The invention discloses a face recognition method based on PCA image reconstruction and LDA and belongs to the technical field of computer image processing and pattern recognition. The face recognition method is based on a principal component analysis algorithm; an intra-class covariance matrix serves as a generation matrix for acquiring face feature subspaces of individuals; then an image to be recognized maps the feature subspaces to extract features; the image is reconstructed according to feature values; a residual image is subjected to the linear discriminant analysis; and finally, face recognition is realized by a minimum distance classification recognition algorithm. Compared with the prior feature subspace method, the face recognition method can better extract the face features of different people, and the face recognition rate is increased effectively. In addition, when a face database is required to be expanded, only the newly added faces are required for feature face training; not all the face feature subspaces are retrained; and the face recognition method also has good extendibility.

Description

Face identification method based on PCA Image Reconstruction and LDA

Technical field

The present invention relates to a kind of face identification method based on PCA Image Reconstruction and LDA, belong to Computer Image Processing and mode identification technology.

Background technology

Face recognition technology is to utilize the Computer Analysis facial image, therefrom extract effective identifying information, distinguish a special kind of skill of personal identification, facial image for input, at first judge and wherein whether have people's face, if there is people's face, then further provide position, size and each main face organ's of everyone face positional information, and according to these information, further extract the identity characteristic that comprises in everyone face, and itself and oneself known that the people's face in the face database compares, thereby identify the identity of everyone face.Face recognition technology relates to the knowledge of the subjects such as pattern-recognition, image processing, computer vision, physiology, cognitive science, and with the recognition methods of other biological feature and the research field of computer man-machine perception interactive close ties is arranged.Simultaneously recognition of face has the incomparable advantage of other biological characteristic recognition method (such as fingerprint, iris, DAN detection etc.) as a kind of living things feature recognition:

(1) non-infringement, obtaining of facial image do not need with the detected person Body contact to occur, and can identify letting alone in detected person's the situation;

(2) low-cost, easily installation, the picture pick-up device that face identification system only need to adopt common camera, Digital Video etc. to be widely used gets final product, and does not also have special installation requirement concerning the user;

(3) prosthetic participates in, and whole face recognition process does not need user or detected person's active to participate in, and computing machine can carry out according to setting in advance automatically of user.

Because face recognition technology has above advantage, face recognition technology is widely used a plurality of fields, such as the judicial department field, public security department can be by suspect's photo or facial characteristics, the human face photo of transferring rapidly in the archives economy is compared, and can improve the efficient of criminal investigation and case detection; Public safety field, AT STATION, the place that the crowd is dense such as airport, hotel, if it is very difficult wanting to find specific target, adopt face identification system to be connected with intelligent video monitoring system, just can find specific objective from the place that the crowd is dense very fast; Gate control system field, the identity recognizing technology of traditional gate control system exist forgery, falsely use equivalent risk, and a kind of as living things feature recognition of face identification system do not exist these risks, but also can bring more convenience to the user; Information security field, holder's authentication such as all kinds of bank cards, fiscard, and along with the development of Network Information, it is more and more frequent that e-bank is used, but the security mechanism of present e-bank mainly is to depend on account, password, digital certificate etc., these information are replicated easily, propagation, face recognition technology are a kind of safer reliable identity identifying technologies, so it is in information security, and civil field has ample scope for one's abilities.

Although the mankind do not distinguish a people by people's face in difficulty ground, but utilize computing machine to carry out fully automatically recognition of face and still have many difficulties, it shows: people's face is the natural structure target of the variations in detail of a class with very complex, the differences such as appearance, expression, the colour of skin; People's face changes with age growth; The decorations such as hair style, glasses, beard cause people's face and block; Image that people's face becomes is affected by illumination, imaging angle, image-forming range etc.The awareness of the development of Research on Face Recognition Technology and related discipline and human brain is closely related in addition, and this factors is rich in challenging problem so that recognition of face research becomes one.Therefore, if can find the method that addresses these problems, successfully construct automatic human face recognition system, will provide important enlightenment for solving other similar Complicated Problems of Pattern Recognition.

The subspace analysis method is the important method of a class in the statistical model identification, it is the method for a kind of feature extraction and selection in essence, and relatively typical method comprises principal component analysis (PCA) (PCA), linear discriminant analysis (LDA), independent component analysis (ICA), svd (SVD), the nonnegative matrix factor (NMF), local Preserving map (LPP) and analyzes etc. based on the nonlinear subspace of nuclear.In recent years, the mode identification method of subspace-based has obtained fast development, because it has the characteristics such as calculation cost is little, descriptive power is strong, separability is good, so that the method has obtained studying widely and using in the identification of recognition of face isotype and feature extraction.

Summary of the invention

The present invention is directed to the proposition of above problem, and development is based on the face identification method of PCA Image Reconstruction and LDA.

The technical scheme that the present invention takes is as follows;

1, the face identification method based on PCA Image Reconstruction and LDA comprises following several step:

Step 1, image pre-service

Step 2, choose at random image as training set from the ORL face database, remaining image reads training storehouse facial image and becomes the gray matrix form as test set, and training sample classified with the individual is stored as V _j

Step 3, with individual's facial image covariance matrix S _j=E[(X-μ _j) (X-μ _j) ^T] as producing matrix, adopt the PCA method to extract its proper subspace W _j

Step 4, repeating step two to three extract the proper subspace W of everyone face _{J, j}=1,2 ..., m, wherein m is for being used for training and knowing others face categorical measure

Step 5, with training image X _iAccording to formula H _Ij=(X _i-μ _j) * W _j, i=1,2 ..., N, j=1,2 ..., m extracts its feature H _Ij, described H _Ij=(X _i-μ _j) * W _j, i=1,2 ..., N, j=1,2 ..., m;

Step 6, with proper vector H _IjTo W _jCounter asking is according to formula Y _Ij=W _j* H _Ij+ μ _j, i=1,2 ..., N, j=1,2 ..., m reconstruct obtains new facial image Y _Ij

Step 7, from original image X _iIn deduct reconstructed image Y _Ij, obtain residual image

Namely

Step 8, in residual image, use linear discriminant analysis (LDA) method to carry out proper vector to extract, according to formula $W_{\mathrm{opt}}^T=W_{\mathrm{lda}}^T{W}_{\mathrm{pca}}^T,$ $W_{\mathrm{pca}}=\underset{W}{\arg \max }\left|W^T{S}_{t}W\right|,$ $W_{\mathrm{lda}}=\underset{W}{\arg \max }\frac{\left|W^T{W}_{\mathrm{pca}}^T{S}_b{W}_{\mathrm{pca}}W\right|}{\left|W^T{W}_{\mathrm{pca}}^T{S}_w{W}_{\mathrm{pca}}W\right|}$ Obtain matrix of coefficients, wherein, S _t, S _bAnd S _wBe respectively scatter matrix and the interior scatter matrix of class between total population scatter matrix, class.

Step 9, test pattern is mapped in the proper subspace, then to extract test pattern with the same step 5-8 of training image;

Step 10, calculation training image and the test pattern Euclidean distance between the corresponding point in the eigenface space is identified facial image as criterion with minimum Eustachian distance;

In the above step 3 with individual's facial image covariance matrix S _jThe eigenwert and the characteristic of correspondence that produce matrix are vectorial as producing matrix, calculating, and eigenwert order is from big to small sorted, and the characteristic of correspondence vector also sorts simultaneously, and then obtains all 40 people's facial image proper subspace W _j, j=1,2 ..., 40.

The acquisition process of reconstructed image obtains for single people's proper subspace in the above step 7, and its concrete grammar is, at first with training image X _iAccording to formula H _Ij=(X _i-μ _j) * W _jExtract its feature H _IjSecondly with proper vector H _IjTo W _jCounter asking is according to formula Y _Ij=W _j* H _Ij+ μ _jReconstruct obtains new facial image Y _IjAgain from original image X _iIn deduct reconstructed image Y _Ij, obtain residual image.

In the above step 8 the LDA method is applied to extract in people's face residual image the proper vector of facial image, and realizes the identification of facial image.

The present invention compared with prior art has the following advantages:

1, the method for traditional principal component analysis (PCA) (PCA) recognition of face, mostly be to adopt total population scatter matrix as producing matrix, what obtain like this is the common feature of people's face and ignored everyone different people's face characteristic mostly, although everyone face has certain similarity and rule, but different people's faces exists obvious difference, and the feature of different people's faces Useful Information in the recognition of face exactly.Therefore, based on Principal Component Analysis Algorithm, the face characteristic subspace that we obtain single people with covariance matrix in the class as the generation matrix, then image to be identified is shone upon the extraction feature to each proper subspace, and carry out Image Reconstruction with this eigenwert, then residual image is used the linear discriminant analysis method.We adopt the minimum distance classification recognizer to realize recognition of face at last, and the method is compared with proper subspace method in the past, can better extract the face characteristic of different people, effectively raises the recognition of face rate.

2, the method is with good expansibility; Because the eigenface of different people is relatively independent, when in face database, adding new people's face, only need to carry out to people's face of new interpolation the training of eigenface, and need not be as traditional proper subspace method training characteristics subspace again, so the method has better extensibility.

Description of drawings

Fig. 1 system flowchart of the present invention.

Embodiment

The present invention will be further described below in conjunction with accompanying drawing;

One embodiment of the present of invention:

As shown in Figure 1: this comprises the steps: clearly

Step 1, image pre-service

Facial image I(size is w * h) carry out certain pre-service, mainly comprises the normalized of image smoothing and gradation of image and variance, remove the adverse effect that the factors such as scale size, bright and dark light are brought to identifying as far as possible;

Image smoothing is for the removal of images noise, improves picture quality.The smoothing technique of digital picture is divided into two classes: a class is Global treatment, namely whole the or large piece of noise image is proofreaied and correct; Another kind of smoothing technique is that noise image is used Local Operator, when a certain pixel is carried out smoothing processing, and only to its in addition computing of some pixels in local little field, can be to a plurality of pixel parallel processings.The thought of smooth template is to remove the point of unexpected variation by any and the computing of several points on every side, thereby filters certain noise, generally speaking, eliminates different noises by selecting different masterplates, and template commonly used has:

$\frac{1}{4}\left[\begin{array}{ccc}0& 1& 0\\ 1& 1\·& 1\\ 0& 1& 0\end{array}\right],$ $\frac{1}{8}\left[\begin{array}{ccc}1& 1& 1\\ 1& 0\·& 1\\ 1& 1& 1\end{array}\right],$ $\frac{1}{9}\left[\begin{array}{ccc}1& 1& 1\\ 1& 1\·& 1\\ 1& 1& 1\end{array}\right],$ $\frac{1}{10}\left[\begin{array}{ccc}1& 1& 1\\ 1& 2\·& 1\\ 1& 1& 1\end{array}\right],$ $\frac{1}{16}\left[\begin{array}{ccc}1& 2& 1\\ 2& 4\·& 2\\ 1& 2& 1\end{array}\right].$

Normalized target is to obtain consistent size, standardization people face that the gray scale span is identical.In order to remove certain illumination to the impact of intensity profile, need to carry out gray scale normalization to target image, more typical a kind of gray scale normalization method is histogram equalization.

Histogram is that its horizontal ordinate is gray-scale value for the statistical graph of expressing the gradation of image distribution situation, and ordinate is the probability that this gray-scale value occurs.If the gray-scale value of image f (x, y) is r ₁, r ₁..., r _L-1, n (r _i) be r _iThe probability that gray-level pixels occurs, then image histogram is:

$p\left(r_i\right)=\frac{n\left(r_i\right)}{N},i=\mathrm{0,1},...,L-1---\left(1\right)$

In the formula, N is total pixel of piece image, and L is the number of greyscale levels of image pixel, and

$\underset{i}{\overset{L-1}{\mathrm{\Σ}}}p\left(r_i\right)=1---\left(2\right)$

The accumulated probability that this moment, image pixel distributed is

$P_f\left(r_i\right)=\underset{j=0}{\overset{i}{\mathrm{\Σ}}}p\left(r_j\right)---\left(3\right)$

Get accumulated probability P _f(r _i) as image pixel greyscale transformation function T (r _i), output image grey scale pixel value s then _iDetermined by following formula:

$s_i=T\left(r_i\right)=\underset{j=0}{\overset{i}{\mathrm{\Σ}}}p\left(r_j\right)=\underset{j=0}{\overset{i}{\mathrm{\Σ}}}\frac{n_j}{N},i=\mathrm{0,1,2},...,L-1;0\≤r_i\≤1---\left(4\right)$

Step 2, choose at random image as training set from the ORL face database, remaining image reads training storehouse facial image and becomes the gray matrix form as test set, and training sample classified with the individual is stored as V _j

Each width of cloth image array I of single people is launched into the vector x of n=w * h dimension by row or column, and go average value processing and albefaction to process the vector x, so that the variable covariance matrix after the albefaction is unit matrix, utilize covariance to carry out Eigenvalues Decomposition, i.e. E (xx ^T)=PEP ^T, wherein E is orthogonal matrix E (xx ^T) eigenwert, P is characteristic of correspondence vector, the albefaction matrix that obtains is:

M＝PE ^-1/2P ^T （5）

Obtain the data after the albefaction:

$\stackrel{\‾}{x}=\mathrm{Mx}---\left(6\right)$

Everyone face training image quantity of a people with n * s(s with all training images of individual) matrix V _jExpression.

Step 3, with individual's facial image covariance matrix S _j=E[(X-μ _j) (X-μ _j) ^T] as producing matrix, adopt the PCA method to extract its proper subspace W _j

Sample average in the training sample is

And covariance matrix S=E[(X-μ) (X-μ) ^T]=XX ^T

Generally, the dimension n of image column vector is all higher, directly calculate comparatively difficulty of its proper vector by sample covariance matrix, and comparatively speaking, training sample concentrates the number N of training sample but relatively less, according to the knowledge of matrix theory, and XX ^TAnd X ^TX has identical eigenwert, and XX ^TCorresponding to eigenvalue λ _iProper vector u _iWith X ^TThe corresponding proper vector v of X _iHave following relationship:

$u_i=\frac{1}{\sqrt{{\mathrm{\λ}}_i}}{\mathrm{Xv}}_i---\left(7\right)$

Therefore can utilize and find the solution product matrix X in N * N dimension ^TThe eigenvector of X comes the eigenvector of indirect calculation covariance matrix.According to Karhunen-Loeve transformation, the eigenwert of supposing S is λ _j(j=1,2 ..., n), and λ ₁〉=λ ₂〉=... 〉=λ _n〉=0, corresponding proper vector is μ _j, then to the sample x among any X _iCan be expressed as:

$x_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{y}_j{u}_j---\left(8\right)$

Y wherein _j=x _i ^Tu _j(j=1,2 ..., n), y=[y ₁, y ₂..., y _n] ^TChoose front d the component of y

As feature, then can demonstrate,prove

Be d component of variance maximum (being that energy is maximum), and

In all reconstruct with d the proper vector of S, have minimum square error, thereby

Be commonly called main composition, with

Corresponding subspace is called as signal subspace.

Calculate accordingly the eigenvalue λ of individual's facial image covariance matrix _jAnd characteristic of correspondence vector ω _j, and eigenwert order from big to small sorting, the characteristic of correspondence vector also sorts simultaneously, selects wherein a part of structural attitude subspace again.

Step 4, repeating step 2-3 extract the proper subspace W of everyone face _j, j=1,2 ..., m, wherein m trains and knows others face categorical measure for being used for, and it may further comprise the steps;

Each width of cloth facial image projects to after the subspace, and just corresponding to a point in the subspace, namely any point in the subspace is also corresponding to piece image.The later image of some reconstruct in these subspaces is the spitting image of " people's face ", so be called " eigenface ".Therefore, any facial image can be done projection and obtain one group of coordinate coefficient: y=W to eigenface ^TX, this group coefficient table understands the position of this image in the subspace, just can be used as the foundation of recognition of face, namely the eigenface feature of this facial image.

Step 5, with training image X _iExtract its feature H according to formula (9) _Ij

H _ij＝(X _i-μ _j)×W _j，i＝1,2,…,N,j＝1,2,…,m （9）

Step 6, with proper vector H _IjTo W _jCounter asking, reconstruct obtains new facial image Y according to formula (10) _Ij

Y _ij＝W _j×H _ij+μ _j，i＝1,2,…,N,j＝1,2,…,m （10）

Step 7, from original image X _iIn deduct reconstructed image Y _Ij, obtain residual image

Namely

Step 8, in residual image, use linear discriminant analysis (LDA) method, obtain matrix of coefficients according to formula (14) (15) (16);

The purpose of LDA is to seek a matrix W, so that in some sense, and the ratio of dispersion maximum in dispersion and the class between class, and a kind of simple scalar tolerance of dispersion is exactly the value of the determinant of scatter matrix.Therefore, if the interior scatter matrix S of class _wBe nonsingular, then can obtain optimum projection matrix and be:

$W_{\mathrm{opt}}=\underset{W}{\arg \max }\frac{\left|W^T{S}_{b}W\right|}{\left|W^T{S}_{w}W\right|}=\left[\begin{array}{cccc}{W}_1& W_2& ...& W_m\end{array}\right]---\left(11\right)$

Just can obtain optimum projection matrix, W by the eigenvalue problem of finding the solution following Generalized Characteristic Equation _Opt=[W ₁W ₂W _m] be the corresponding proper vector of eigenvalue of maximum of Generalized Characteristic Equation, namely

S _bW _j＝λ _jS _wW _j,j＝1,2,…,m （12）

Because S _wBe nonsingular, secular equation (8) can be converted into

$S_w^{-1}{S}_b{W}_j={\mathrm{\λ}}_j{W}_j,j=\mathrm{1,2},...,m---\left(13\right)$

But when LDA was used for the face characteristic extraction, the dimension of sample image caused S often much larger than sample number _wUnusual, so be difficult to find the solution optimum projection matrix according to secular equation (12).

For solving this small sample problem, the method that adopts PCA and LDA to combine utilizes first PCA that facial image is carried out dimensionality reduction, makes S _wFull rank uses LDA to carry out feature extraction again, and then realizes recognition of face, and the optimum projection matrix of finding the solution by the method can be described as:

$W_{\mathrm{opt}}^T=W_{\mathrm{lda}}^T{W}_{\mathrm{pca}}^T---\left(14\right)$

$W_{\mathrm{pca}}=\underset{W}{\arg \max }\left|W^T{S}_{t}W\right|---\left(15\right)$

$W_{\mathrm{lda}}=\underset{W}{\arg \max }\frac{\left|W^T{W}_{\mathrm{pca}}^T{S}_b{W}_{\mathrm{pca}}W\right|}{\left|W^T{W}_{\mathrm{pca}}^T{S}_w{W}_{\mathrm{pca}}W\right|}---\left(16\right)$

Wherein, S _t, S _bAnd S _wBe respectively scatter matrix and the interior scatter matrix of class between total population scatter matrix, class.

Step 9, test pattern is mapped in the proper subspace, then to extract test pattern with the same step 5-8 of training image;

Step 10, calculation training image and the test pattern Euclidean distance between the corresponding point in the eigenface space is identified facial image as criterion with minimum Eustachian distance.

Facial image is projected to proper subspace, obtain after the corresponding face characteristic vector, ensuing task is exactly how to differentiate the affiliated classification of test pattern.At first we will calculate the similarity between the image, select suitable sorter to carry out discriminant classification again.Here adopt minimum Eustachian distance between training image and the test pattern as criterion.Euclidean distance is also referred to as Euclidean distance, and the Euclidean distance between vectorial X and the Y is defined as:

$D(X,Y)=\sqrt{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(x_i-y_i)}^2}---\left(17\right)$

Suppose to have m classification, every class has N _iIndividual sample, then the discriminant function of i class is

$g_i\left(x\right)=\underset{k}{\min }\left|\right|X-X_i^k\left|\right|,k=\mathrm{1,2},...,N_i---\left(18\right)$

Be different from conventional P CA method with proprietary training image covariance matrix as producing matrix, the present invention is with individual's facial image covariance matrix S _jThe eigenwert and the characteristic of correspondence that produce matrix are vectorial as producing matrix, calculating, and eigenwert order is from big to small sorted, and the characteristic of correspondence vector also sorts simultaneously, and then obtains all 40 people's facial image proper subspace W _j, j=1,2 ..., 40.

The acquisition process of reconstructed image obtains for single people's proper subspace in the step 7, and its concrete grammar is, at first with training image X _iAccording to formula H _Ij=(X _i-μ _j) * W _jExtract its feature H _IjSecondly with proper vector H _IjTo W _jCounter asking is according to formula Y _Ij=W _j* H _Ij+ μ _jReconstruct obtains new facial image Y _IjAgain from original image X _iIn deduct reconstructed image Y _Ij, obtain residual image.

In the step 10 LDA method is applied to extract the facial image feature in people's face residual image claimed in claim 3, and realizes the identification of facial image.

Embodiment has adopted a public face database, the ORL face database of univ cambridge uk.The ORL storehouse comprises the facial image of 400 112 * 92 sizes of 40 people, everyone 10 width of cloth.These images are taken at different time, and the variations such as attitude, angle, yardstick, expression and glasses are arranged.Concrete face recognition process is summarized as follows:

1, image pre-service

Facial image to 112 * 92 sizes carries out pre-service, mainly comprises the normalized of the figure image intensifyings such as image smoothing and contrast correction and gradation of image and variance.Through after the pre-service, the gray scale of all images is unified to standard level, and gray-level is clearly more demarcated, and simultaneously, for time and the memory space of saving computing, we compress image to 24 * 24 sizes.

2, feature extraction

(1) we adopt direct access to be used for training according to half image in the storehouse, and second half is used for the way of identification, i.e. the way of everyone 5 sample training, and corresponding remaining sample is tested.At first people's face training image is processed, to obtain the original training sample matrix V in the former space _jPeople's face training image is stacked as the vector of 576 dimensions by windrow, and adopts and go average and albefaction processing that its value is normalized between 0 to 1.Form so altogether 576 * 5 * 40 training sample matrix V={ V ₁, V ₂..., V _j, j=1,2 ..., 40, V in the formula _jIt is 576 * 5 training sample matrix;

(2) corresponding to each V _jJ=1,2 ..., 40, as producing matrix, and then adopt the PCA method to produce proprietary personal characteristics face with the covariance matrix of same class sample, namely calculate the eigenwert and the characteristic of correspondence vector that produce matrix, and eigenwert order from big to small sorted, simultaneously the characteristic of correspondence vector also sorts, and selects wherein a part of structural attitude subspace again, and then obtains the proper subspace W of all 40 class facial images _j, j=1,2 ..., 40.

(3) with training image X _i, i=1,2 ..., 200 to W _jShine upon, extract it corresponding to the characteristics of image H of each proper subspace _Ij, i=1,2 ..., 200, afterwards, with H _Ij, i=1,2 ..., 200 to W _jThe anti-reconstructed image Y that asks to obtain himself _Ij

(4) from original image, deduct reconstructed image, obtain residual image, then in residual image, use the LDA method, obtain matrix of coefficients according to formula (14) (15) (16);

(5) test pattern is mapped to proper subspace, next with the step 3-4 extraction test pattern same with training image;

3, training and identification

Adopt minimum distance classifier, calculation training image and test pattern be the Euclidean distance between the corresponding point in the eigenface space, and the image of the Euclidean distance minimum in the training set and between test pattern is optimum matching, thereby realizes the identification to facial image.

For algorithm complexity better is described, we choose everyone 5 samples at random as training image, and remaining 5 samples are tested.This paper experiment will repeat 50 times, get the mean value of its discrimination as final experimental result.The method of this paper was with other the Comparison of experiment results of some face recognition methods in the ORL database was as shown in table 1 below in recent years.

Table 1: distinct methods compares the discrimination of ORL face database

Can find out that by table 1 in the face recognition experiment based on ORL, the correct recognition rata that face identification method in this paper obtains is 97.48%, be enhanced at discrimination than other typical face identification method.Experimental result has illustrated that the method can effectively in conjunction with PCA and LDA advantage separately, improve the accuracy rate of recognition of face

The above; only be the better embodiment of the present invention; but protection scope of the present invention is not limited to this; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses; be equal to replacement or change according to technical scheme of the present invention and inventive concept thereof, all should be encompassed within protection scope of the present invention.

Claims (4)

1. based on the face identification method of PCA Image Reconstruction and LDA, it is characterized in that: comprise following several step:

Step 1, image pre-service

To facial image I, described image I size is w * h, carries out certain pre-service, mainly comprises the normalized of image smoothing and gradation of image and variance, removes the adverse effect that the factors such as scale size, bright and dark light are brought to identifying;

Step 2, choose at random image as training set from the ORL face database, remaining image reads training storehouse facial image and becomes the gray matrix form as test set, and training sample classified with the individual is stored as V _j

Each width of cloth image array I of single people is launched into the vector x of n=w * h dimension by row or column, and go average value processing and albefaction to process the vector x, so that the variable covariance matrix after the albefaction is unit matrix, utilize covariance to carry out Eigenvalues Decomposition, i.e. E (xx ^T)=PEP ^T, wherein E is orthogonal matrix E (xx ^T) eigenwert, P is characteristic of correspondence vector, the albefaction matrix that obtains is:

M＝PE ^-1/2P ^T （1）

Obtain the data after the albefaction:

$\stackrel{\‾}{x}=\mathrm{Mx}---\left(2\right)$

Everyone face training image quantity of a people with n * s(s with all training images of individual) matrix V j represents.

Step 3, with individual's facial image covariance matrix S _j=E[(X-μ _j) (X-μ _j) ^T] as producing matrix, adopt the PCA method to extract its proper subspace W _j

Sample average in the training sample is

And covariance matrix S=E[(X-μ) (X-μ) ^T]=XX ^T

Calculate the eigenvalue λ of everyone facial image covariance matrix _jAnd characteristic of correspondence vector ω _j, and eigenwert order from big to small sorting, the characteristic of correspondence vector also sorts simultaneously, selects wherein a part of structural attitude subspace again.

Step 4, repeating step two extract the proper subspace W of everyone face to step 3 _j, j=1,2 ..., m, wherein m trains and knows others face categorical measure for being used for, and it may further comprise the steps;

Each width of cloth facial image projects to after the subspace, and just corresponding to a point in the subspace, namely any point in the subspace is also corresponding to piece image.The later image of some reconstruct in these subspaces is the spitting image of " people's face ", so be called " eigenface ".Therefore, any facial image can be done projection and obtain one group of coordinate coefficient: y=W to eigenface ^TX, this group coefficient table understands the position of this image in the subspace, just can be used as the foundation of recognition of face, namely the eigenface feature of this facial image.

Step 5, training image Xi is extracted its feature H according to formula (3) _Ij

H _ij＝(X _i-μ _j)×W _j，i＝1,2,…,N,j＝1,2,…,m （3）

Step 6, with proper vector H _IjTo W _jCounter asking, reconstruct obtains new facial image Y according to formula (4) _Ij

Y _ij＝W _j×H _ij+μ _j，i＝1,2,…,N,j＝1,2,…,m （4）

Step 7, from original image X _iIn deduct reconstructed image Y _Ij, obtain residual image

Namely

Step 8, in residual image, use linear discriminant analysis (LDA) method to carry out proper vector to extract, obtain matrix of coefficients according to formula (6) (7) (8);

But when LDA was used for the face characteristic extraction, the dimension of sample image caused S often much larger than sample number _wUnusual, so be difficult to according to secular equation

S _bW _j＝λ _jS _wW _j,j＝1,2,…,m （5）

Find the solution optimum projection matrix.

For solving this small sample problem, the method that adopts PCA and LDA to combine utilizes first PCA that facial image is carried out dimensionality reduction, makes S _wFull rank uses LDA to carry out feature extraction again, and then realizes recognition of face, and the optimum projection matrix of finding the solution by the method can be described as:

$W_{\mathrm{opt}}^T=W_{\mathrm{lda}}^T{W}_{\mathrm{pca}}^T---\left(6\right)$

$W_{\mathrm{pca}}=\underset{W}{\arg \max }\left|W^T{S}_{t}W\right|---\left(7\right)$

$W_{\mathrm{lda}}=\underset{W}{\arg \max }\frac{\left|W^T{W}_{\mathrm{pca}}^T{S}_b{W}_{\mathrm{pca}}W\right|}{\left|W^T{W}_{\mathrm{pca}}^T{S}_w{W}_{\mathrm{pca}}W\right|}---\left(8\right)$

Wherein, S _t, S _bAnd S _wBe respectively scatter matrix and the interior scatter matrix of class between total population scatter matrix, class.

Step 9, test pattern is mapped in the proper subspace, then to extract test pattern with the same step 5-8 of training image;

Step 10, calculation training image and the test pattern Euclidean distance between the corresponding point in the eigenface space is identified facial image as criterion with minimum Eustachian distance.

Facial image is projected to proper subspace, obtain after the corresponding face characteristic vector, we adopt minimum Eustachian distance between training image and the test pattern as criterion.Euclidean distance is also referred to as Euclidean distance, and the Euclidean distance between vectorial X and the Y is defined as:

$D(X,Y)=\sqrt{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(x_i-y_i)}^2}---\left(9\right)$

Suppose to have m classification, every class has N _iIndividual sample, then the discriminant function of i class is

$g_i\left(x\right)=\underset{k}{\min }\left|\right|X-X_i^k\left|\right|,k=\mathrm{1,2},...,N_i---\left(10\right)$

2. described face identification method based on PCA Image Reconstruction and LDA according to claim 1 is characterized in that: with individual's facial image covariance matrix S _jThe eigenwert and the characteristic of correspondence that produce matrix are vectorial as producing matrix, calculating, and eigenwert order is from big to small sorted, and the characteristic of correspondence vector also sorts simultaneously, and then obtains all 40 people's facial image proper subspace W _j, j=1,2 ..., 40.

3. the face identification method based on PCA Image Reconstruction and LDA according to claim 1, it is characterized in that: the acquisition process of reconstructed image obtains for single people's proper subspace in the step 7, and its concrete grammar is, at first with training image X _iAccording to formula H _Ij=(X _i-μ _j) * W _jExtract its feature H _IjSecondly with proper vector H _IjTo W _jCounter asking is according to formula Y _Ij=W _j* H _Ij+ μ _jReconstruct obtains new facial image Y _IjAgain from original image X _iIn deduct reconstructed image Y _Ij, obtain residual image.

4. the face identification method based on PCA Image Reconstruction and LDA according to claim 3 is characterized in that: in the step 8 LDA method is applied to extract in people's face residual image the proper vector of facial image, and realizes the identification of facial image.