CN1700240A - Face recognition method based on random sampling - Google Patents

Abstract

LDA is a common feature extraction technology used in face recognition. However, it usually meets small sample problem as processing high-dimension face data. Fisher face and null space LDA (N-LDA) are two common methods for dealing with the problem.However, in many states, the LDA classifier exerts over-fit to training set, and discards some useful recognition information. The present invention raises a method which uses combination of random subspace and random sample to repectively improve the different over-fit problems of two LDA classifiers by analyzing the same. The invention builds plural stable Fisher face and N-LDA classifiers by random sampling for proper vector and training sample. The two kinds of complementary type classifiers can be synthesized in fusion manner thereby almost being able to store all recognition information. The method can also be applied on other features to build face recognition system of robustness which integrally concerns shape, vein and Gabor reaction.

Description

Face recognition method based on stochastic sampling

Technical field

The present invention relates to be used for the Feature Extraction Technology of face recognition, relate in particular to the face recognition method that utilizes stochastic sampling.

Background technology

Linear discriminant analysis (LDA) is a kind of common Feature Extraction Technology that is used for face recognition.According to taking house standard (Fisher criteria), LDA has determined one group of projection vector, and this group projection vector makes the scatter matrix maximization between class in the projection properties space, and the scatter matrix in the class is minimized.Because usually for each class people face, only have a small amount of sample to be used for training, scatter matrix can not be estimated well in the class of same classification, and may become singular matrix, therefore the LDA sorter has deviation usually, and very responsive for the minor alteration of training set.

The LDA face identification method of following brief description principal component analysis (PCA) (PCA) method and two kinds of routines promptly takes rounding off face (Fisherface) and kernel N-LDA method.

At first need explanation, in this manual, the implication of term " class " is meant the individuality (people) among training set and reference picture storehouse (Gallery).

For recognition of face based on presentation, the vector that it is N that the facial image of a 2D is considered the length in the higher-dimension image space.Training set comprises and belongs to L independent classification { X _j} _J=1 ^LM sample

The I.PCA method

The PCA method is to utilize the Karhunen-Loeve conversion to realize face description and identification.Calculate the eigenface set from the proper vector of the whole covariance matrix of training set, wherein covariance matrix is calculated by following formula: $C=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}({\stackrel{\→}{x}}_i-\stackrel{\→}{m}){({\stackrel{\→}{x}}_i-\stackrel{\→}{m})}^T---\left(1\right)$

Wherein Be the average of all samples,

$\stackrel{\→}{m}=\frac{1}{m}{\mathrm{\Σ}}_{i=1}^M{\stackrel{\→}{x}}_i---\left(2\right)$

There is M-1 the eigenface that nonzero eigenvalue is arranged at most.Usually, select K maximum eigenface (K the eigenface that eigenvalue of maximum is arranged), $U={[\stackrel{\→}{u}}_1,\·\·\·{\stackrel{\→}{u}}_K],$ Be used to form the PCA subspace.Because at the K dimension space, these eigenface can be rebuild people's face figure under the reconstructed error of minimum.By with people's face data Project to the PCA subspace and can extract the face characteristic of low-dimensional,

$\stackrel{\→}{w}=U^T(\stackrel{\→}{x}-\stackrel{\→}{m})---\left(3\right)$

The feature of different characteristic face is incoherent, and when people's face sample distribution met Gaussian distribution, these features were independently.

In other researchs, selected different subspace dimensions.At list of references 1, be H.Monn, " the Analysis of PCA-Based Face Recognition Algorithms " that is shown with P.J.Phillips (based on the analysis of the face recognition algorithm of PCA), publish in Empirical Evaluation Techniques inComputer Vision (the empirical evaluation technology of computer vision, K.W.Bowyer and P.J.Phillips edit, IEEE Computer Society Press (IEEE ACM (Association of Computing Machinery) publishing house), Los Alamitos, California, 1998) in, the dimension of PCA subspace is chosen as 40% of eigenface sum.

At list of references 2, be that " the Using DiscriminantEigenfeatures for Image Retrieval " that D.Swets and J.Weng show (uses in image retrieval and differentiate feature, IEEE Trans.on PAMI (IEEE is about the proceedings of PAMI), the 16th volume, the 8th phase, the 831-836 page or leaf, in August, 1996) in, the eigenface of selecting contains 95% of gross energy.They have abandoned little eigenwert characteristic of correspondence face.

II. take rounding off face method

LDA attempts to find a projection vector set W can discern different classes of best.According to taking the house standard, by making scatter matrix S between class _bThe value of determinant and class in scatter matrix S _wThe value of determinant between the ratio maximization, can realize this point:

$W=\arg \max \left|\frac{W^T{S}_{b}W}{W^T{S}_{w}W}\right|---\left(4\right)$

S wherein _bAnd S _wBe defined as,

$S_w=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\underset{{\stackrel{\→}{x}}_k\∈X_i}{\mathrm{\Σ}}({\stackrel{\→}{x}}_k-{\stackrel{\→}{m}}_i){({\stackrel{\→}{x}}_k-{\stackrel{\→}{m}}_i)}^T---\left(5\right)$

$S_b=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{n}_i({\stackrel{\→}{m}}_i-\stackrel{\→}{m}){({\stackrel{\→}{m}}_i-\stackrel{\→}{m})}^T---\left(6\right)$

Wherein Be to have n _iThe classification X of individual sample _iPeople's face average.W can be by S _w ^-1S _bProper vector calculate (" Introduction to StatisticalPattern Recognition " (introduction of statistics pattern identification of being shown referring to list of references 3:K.Fukunnaga, Academic Press (publishing house of institute), second edition, 1991).S _wOrder be M-L to the maximum.But in recognition of face, each classification only has a small amount of sample usually, and M-L is very little with respect to people's face vector length N.So S _wMay become singular matrix, thereby make s _w ^-1Be difficult to calculate.

In order to solve the problem of above-mentioned existing LDA sorter, a kind of two stage PCA+LDA method has been proposed, promptly take rounding off face (Fisherface) method.By PCA, high-dimensional people's face data have been mapped to the feature space of a low dimension, carry out LDA subsequently and handle in the PCA subspace of low dimension.Usually, in the PCA subspace, the eigenface with less eigenwert is removed.Because these eigenface also may comprise the identifying information that some are useful, they remove the loss that may bring discriminant information.For making up a stable LDA sorter, the dimension of PCA subspace depends on the size of training set.When the dimension of PCA subspace was higher relatively, constructed LDA sorter had deviation and instability usually.The slight noise disturbance of training set just may cause the bigger change of projection vector.Therefore, for making up a stable LDA sorter, when training set hour, some discriminant informations have to be dropped.

Referring to list of references 4, be V.Belhumeur, J.Hespanda, shown with D.Kiregeman, " Eigenfaces vs.Fisherfaces:Recognition Using Class Specific Linear Projection " (comparison of eigenface and expense rounding off face: use classes specific linear projection discern, IEEE Trans.on PAMI (IEEE is about the proceedings of PAMI), the 19th volume, the 7th phase, the 711-720 page or leaf, in July, 1997), in taking rounding off face method, at first, the PCA subspace that people's face data projection to is opened by M-L maximum eigenface.Subsequently, in the M-L n-dimensional subspace n, carry out LDA, make S _wBecome nonsingular.But under many circumstances, the M-L dimension is still too high with respect to training set.When training set hour, S _wCan not be estimated well.The slight noise dither of training set will change S greatly _wInverse matrix.Therefore, the LDA sorter has deviation and instability usually.

III. kernel LDA

At list of references 5, be L.Chen, H.Liao, M.Ko, J.Liin, (the 33rd rolls up " the ANew LDA-based Face Recognition System Which can Solve the Small SampleSize Problem " that is shown with G Yu for a kind of new facial-recognition security systems based on LDA that can solve small sample scale problem, Pattern Recognition (pattern identification), the 10th phase, the 1713-1726 page or leaf, in October, 2000) in, proposed to satisfy W ^TS _wThe kernel S of W=o _wA lot of discriminant informations have also been comprised.Might find out some projection vector W and satisfy W ^TS _wW=0 and W ^TS _bW ≠ 0, the expense house criterion in this pattern (4) must reach its maximal value.Like this, just proposed at kernel S _wThe LDA method of last application.At first, kernel S _wBe calculated as

V ^TS _wV＝0????????(7)

Scatter matrix is projected to kernel S between class _w,

${\tilde{S}}_b=V^T{S}_{b}V---\left(8\right)$

The LDA projection vector is defined as W=V Φ, and wherein Φ contains

In before several eigenvalue of maximum characteristic of correspondence vectors.

N-LDA also can produce over-fitting to training set.S _wOrder r (S _w) be subjected to min (M-L, restriction N).Since the existence of noise, r (S _w) this boundary no better than.The dimension of kernel be max (0, N-M+L).Shown in the test in the list of references 4, when the training sample number is big, kernel S _wDiminish, will cause the too much discriminant information beyond kernel to be lost like this.Opposite extreme situations be when training set very big so that M-L=N.Like this, in this space, can not obtain any information, because the dimension of kernel is zero.

In sum, expense rounding off face method and kernel LDA method have all met with the problem of over-fitting because of different reasons.That is, in taking rounding off face method, compare with the high dimensional feature vector less the time when training set, over-fitting will take place.Rounding off face method is opposite with taking, and in N-LDA, the over-fitting problem takes place when number of training is big, does not contain enough discriminant informations because kernel is too small.

Summary of the invention

In view of the problems referred to above of prior art, the purpose of this invention is to provide a kind of method of the face recognition based on LDA, overcome existing expense rounding off face method and the existing above-mentioned defective of kernel LDA method by introducing stochastic sampling.

Face identification method based on LDA according to the present invention comprises: facial training set is carried out stochastic sampling; Result according to described stochastic sampling trains a plurality of LDA sorters; The face data that will be identified inputs to described a plurality of LDA sorter; With output fusion with described a plurality of LDA sorters.

In the method for the invention,, training set is repeatedly sampled, to reduce the contradiction between number of training and the proper vector length for the LDA sorter of construction of stable.Utilize the method for this stochastic sampling, can construct a plurality of stable LDA sorters.By these Multiple Classifier Fusion being constructed a more powerful sorter, it can cover whole feature space and not lose discriminant information.

According to a kind of embodiment of the present invention, adopt the method for stochastic subspace that the recognition methods of doing at the sacrifice of dignity based on expense is improved.This method comprises: the facial characteristics value in the facial training set is carried out stochastic sampling, produce a plurality of stochastic subspaces; Train a plurality of LDA sorters respectively by described a plurality of stochastic subspaces; The face data that will be identified inputs to this a plurality of LDA sorters; According to predetermined rule the output of described a plurality of LDA sorters is merged at last.

Preferably, in said method, the facial training set with M training sample is carried out PCA earlier handle, remove eigenface, keep the candidate of M-1 eigenface as the described stochastic subspace of structure with zero eigenvalue.M-1 eigenface to described facial training set carried out stochastic sampling, produces a plurality of stochastic subspaces.

Preferably, in said method, each stochastic subspace comprises a plurality of eigenface that have eigenvalue of maximum in the described facial training set successively, and a plurality of eigenface with further feature value at random of described facial training set.

Method of the present invention is applied to stochastic subspace the face recognition problem domain first.The present invention can Direct Sampling primitive characteristics vector, and preferred mode is facial training set to be handled in the PCA subspace that the back forms through PCA sample.Like this, the dimension of feature space has been reduced widely, and does not lose discriminant information.After carrying out the PCA processing, different characteristic feature on the face is incoherent, thereby more independent, thereby can obtain better accuracy rate.In addition, the stochastic subspace among the present invention can not be a completely random.The dimension of stochastic subspace is fixed, promptly by training set decision, so that the LDA sorter is stable.Each stochastic subspace is by N ₀+ N ₁Individual dimension opens, wherein, and preceding N ₀Individual fixed in dimension is N in the training set ₀Individual have peaked eigenface, thereby comprised most human face structure information.Remaining N ₁Individual dimension is other M-1-N from training set randomly ₀Select in the individual eigenface.

According to another embodiment of the present invention, at kernel LDA exist when the quantity of training sample kernel problem of smaller greatly the time, sampling generates stochastic sampling collection (bootstrap replica) to training set can to make up (Bagging) by random sample, and each stochastic sampling collection all has the training sample than peanut like this.Based on this strategy, of the present inventionly make up the method that strengthens based on the recognition of face of kernel LDA by random sample and can comprise the following step:

M the training sample that facial training set is comprised carries out stochastic sampling, produces a plurality of stochastic sampling collection, and each stochastic sampling collection contains the L that selects at random from L the class that described facial training set comprises ₁The training sample of individual class, wherein L ₁＜L; Train a plurality of random sample combination N-LDA sorters respectively by described a plurality of stochastic sampling collection; The face data that will be identified inputs to this a plurality of random sample combination N-LDA sorters; At last according to of the output combination of predetermined fusion rule with described a plurality of N-LDA sorters.

Preferably, in said method, before described training sample is carried out described stochastic sampling, described training set is carried out PCA earlier handle, all face datas of described facial training set are projected to M-1 have the eigenface of nonzero eigenvalue.Then, the facial training set after the described PCA processing is carried out the stochastic sampling of described training sample.

The method according to this invention can be sampled to classification randomly, but the sample in each class is not sampled randomly.This is because have a large amount of classification (people) usually in recognition of face, but has only a spot of sample (if abundant sample is arranged, also can attempt stochastic sampling data in each class in each classification) in each classification.For example, in test picture library (hereinafter will illustrate), 295 people are arranged and everyone has only two samples for training usefulness.By stochastic sampling collection T _iThe N-LDA of structure not only can be sorted in the L that this stochastic sampling is concentrated effectively ₁Individuality, and can distinguish T _iPeople in addition is because the inherence of people's face share similar changes.Use K sorter can cover L all in a training set classification better.

According to a preferred version of the present invention, can above-mentioned two kinds of embodiments (being the method for stochastic subspace and the method for random sample combination (Bagging)) are integrated, realize recognition of face based on LDA.

Expense rounding off face is from S _wPrincipal subspace calculate, satisfy W ^TS _wW ≠ 0; And N-LDA calculates from its orthogonal subspaces, satisfies W ^TS _wW=0.The both has abandoned some discriminant information.But, because the information that is kept by two kinds of sorters is complementary.Like this, a plurality of LDA sorters by the stochastic sampling generation that can make up this two classes complementation are constructed final sorter.

Description of drawings

Fig. 1 has shown the synoptic diagram according to a preferred implementation of the present invention, will integrate by the expense rounding off face method and the N-LDA method of stochastic sampling method improvement;

Fig. 2 is the synoptic diagram of people's face graphics template;

Fig. 3 is the same people's that takes at four different times in the XM2VTS database a facial image;

Fig. 4 has shown the recognition correct rate of sorter of the expense rounding off face of the PCA eigenface of utilizing varying number in the PCA subspace of reducing;

Fig. 5 has shown use majority rule voting rule, makes up 20 recognition correct rates by the LDA sorter of stochastic subspace structure.Each stochastic subspace is selected 100 eigenface at random from the eigenface of 589 nonzero eigenvalues;

Fig. 6 has shown use majority rule voting rule, makes up the recognition correct rate by the LDA sorter of stochastic subspace structure of different numbers.Each stochastic subspace is selected 100 eigenface at random from the eigenface of 589 nonzero eigenvalues;

The majority rule that is to use that Fig. 7 shows is voted and sum rule, makes up 20 recognition correct rates by the LDA sorter of stochastic subspace structure.At each stochastic subspace, be 50 eigenface with preceding 50 fixed in dimension with eigenvalue of maximum, from remaining 539 eigenface, select other 50 at random then;

Fig. 8 has shown and has made up 20 recognition accuracies by the N-LDA sorter of stochastic subspace structure;

Fig. 9 has shown ballot of use majority rule and sum rule, makes up 20 recognition accuracies by the N-LDA sorter of random sample combining random sampling set structure.Wherein each stochastic sampling collection contains 150 training of human;

What Figure 10 showed is the recognition accuracy of combination by 20 expense rounding off face sorters of the random sample combining random sampling set structure of the training of human that contains different numbers (L).The PCA space is opened by 100 maximum eigenface.The rule of combination is the majority rule ballot.

Embodiment

Below with reference to description of drawings the specific embodiment of the present invention.

Though the dimension of image space is very high,, have only segment space (subspace) to comprise discriminant information.These subspaces are to be opened by the vector of the nonzero eigenvalue characteristic of correspondence among the covariance C.The covariance matrix that calculates from M training sample is up to M-1 nonzero eigenvalue characteristic of correspondence vector.In remaining and zero eigenvalue characteristic of correspondence vector, all training samples have zero projection, and do not comprise discriminant information.Therefore, two kinds of LDA algorithms among the present invention all are earlier the view data of higher-dimension to be projected to the PCA subspace of M-1 dimension, and then carry out stochastic sampling.Certainly, also can not carry out PCA and handle, directly on former data, carry out stochastic sampling.

Stochastic subspace and random sample combination are the random sampling techniques that is used to strengthen Weak Classifier of two kinds of routines.Can be referring to following list of references about the stochastic subspace method:

" the The Random Subspace Method forConstructing Decision Forests " that list of references 6:T.Kam Ho is shown (being used to construct the stochastic subspace method of decision-making clump), IEEETrans.on PAMI (IEEE is about the proceedings of PAMI), the 20th volume, the 8th phase, the 832-844 page or leaf, in August, 1998.

" Nearest Neighbor in Random Subspace " (the nearest neighbours in the stochastic subspace) that list of references 7:T.Kam Ho is shown, Intelligent Data Analysis (intelligent data analysis), 3, the 191-209 pages or leaves, 1999 years.

Can be referring to following list of references about random sample combination:

" the Bagging Predictors " that list of references 8:L.Breiman is shown (random sample combination prediction device), Machine Learning (machine learning), the 24th volume, the 2nd phase, 123-140 page or leaf, 1996 years.

In the method for stochastic subspace,, from original high dimensional feature vector, produce one group low n-dimensional subspace n by stochastic sampling.In conclusive judgement, a plurality of sorters that are structured in the low n-dimensional subspace n that is produced by stochastic sampling are merged.In the random sample combination, by the stochastic sampling generation stochastic sampling collection at random to training set, and the output result of all sorters is finally merged.

As mentioned above, in taking rounding off face method, when training set with respect to high-dimensional proper vector an over-fitting hour takes place.This problem can solve with the method for the dimension of minimizing proper vector by adopting stochastic subspace.In the N-LDA method, kernel is less when the quantity of training sample is big.Because each stochastic sampling collection comprises training sample still less, this problem can make up by random sample and weaken.Expense rounding off face method and N-LDA method have all abandoned some discriminant informations.But, because this two classes sorter calculates in the subspace of quadrature each other at two, they complement one another, and can they be made up by fusion rule, as shown in Figure 1.

One embodiment of the invention at first are described below.In this scheme, expense rounding off face method is improved by the stochastic subspace method.

In this embodiment, at first the facial training set that contains M sample is carried out PCA and handle, remove the eigenface that all have zero eigenvalue, keep M-1 eigenface U _t={ u ₁..., u _M-1As the candidate of constructing stochastic subspace.Then, this M-1 eigenface is carried out stochastic sampling, produce K stochastic subspace { S _i} _I=1 ^KEach stochastic subspace S _iBy N ₀+ N ₁Individual dimension opens, wherein, and preceding N ₀Individual fixed in dimension is U _tMiddle N ₀Individual eigenface with eigenvalue of maximum, remaining N ₁Individual dimension is randomly from U _tIn other M-1-N ₀Select in the individual eigenface.

Stochastic subspace is made up of two parts.Preceding N ₀Individual maximum eigenface has comprised most human face structure information.If they are not comprised in the stochastic subspace, then the accuracy rate of LDA sorter can be low excessively.Strengthen Weak Classifier although proposed many multiple Classifiers Combination systems, if each independent LDA sorter is very poor, fusion method will be more complicated.In the method for the invention, the LDA sorter in each stochastic subspace all has gratifying accuracy rate.And N ₁Individual dimension has at random covered most of remaining less eigenface.Like this, whole set of classifiers also has mistake diversity (error diversity) to a certain degree.The recognition performance that simple fusion rule such as use such as majority rule ballot just can be obtained.

Train K LDA sorter { C from K stochastic subspace according to the method for routine _i(x) }.Here, " training " in the sorting technique of subspace refers to calculate with the data training set process of projection vector (matrix characteristic vector) set of respective subspace method.For example, for the PCA method, promptly from the proper vector of the whole covariance matrix of training set, calculate the eigenface set.

At last, the face data of input is sent into K LDA sorter concurrently, and the output of K LDA sorter is merged.

In such scheme, the selection of K value can be determined by identification test repeatedly, according to K value of selecting in each test and resulting recognition result, selects used K value in the highest test of accuracy rate.Equally, N ₀And N ₁Value also can adopt this mode to select.

Method about the output of a plurality of sorters is merged has had many existing technology to use, for example the technology that is proposed in list of references 2 and the following document:

List of references 9:J.Kittler and F.Roli edit: Multiple Classifier Systems (multi-classifier system).

" Information Fusion in Biometrics " (information fusion in the biological characteristic) that list of references 10:A.Ross and A.Jain are shown, Pattern Recognition Letters (pattern identification journal), the 2115-2125 page or leaf, the 24th volume, 2003 years.

" the Integrating Faces andFingerprints for Personal Identification " that list of references 11:L.Hong and A.K.Jain are shown (being used for the integrated of individual face of differentiating and fingerprint), IEEE Trans.on PAMI (IEEE is about the proceedings of PAMI), the 20th volume, the 12nd phase, the 1295-1307 page or leaf, 1998.

" the Combination ofMultiple Classifier Using Local Accuracy Estimates " that list of references 12:W.P.Kegelmeyer and K.Bowyer are shown (utilizing the combination of the multi-categorizer that local accuracy estimates), IEEE Trans.on PAMI (IEEE is about the proceedings of PAMI), the 19th volume, the 4th phase, the 405-410 page or leaf, 1997.

" Switching Between Selection andFusion in Combining Classifiers:An Experiment " (switching of in the combination of sorter, selecting and merge a: experiment) that list of references 13:L.I.Kuncheva is shown, IEEE Trans.on Systems, Man, and Cybemetics, Part B (IEEE is about system, the mankind and cybernatic proceedings, B part), the 32nd volume, the 2nd phase, in April, 2002.

List of references 14:S.B.Yacoub, Y.Abdeljaoud, " the Fusionof Face and Speech Data for Person Identity Verification " that is shown with E.Mayoraz (being used for face and voice that personal identification differentiates merges), IEEE Transactions on Neural Networks (IEEE is about the proceedings of neuroid), the 1065-1074 page or leaf, the 10th volume, the 5th phase, in September, 1999.

The Multiple Classifier Fusion method of being introduced in the above-mentioned list of references all can be used for the present invention.

According to one embodiment of present invention, can use the fusion rule of majority rule ballot to make up the LDA sorter.

In this embodiment, each LDA sorter C _k(x)=i distributes a class label to give people's face data C of input _k(x)=and i, be a binary function with this representations of events

By the majority rule ballot, final classification is selected as

$\mathrm{\β}\left(x\right)=\underset{x_i}{\arg \max }\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{T}_k(x\∈X_i)---\left(10\right)$

According to another embodiment, also can adopt sum rule to make up the LDA sorter.

Suppose P (X _i| C _k(x)) be at LDA sorter C _k(x) x belongs to X under the measurement _iProbability.According to sum rule, the classification of conclusive judgement is selected as

$\mathrm{\β}\left(x\right)=\underset{X_i}{\arg \max }\underset{k=1}{\overset{K}{\mathrm{\Σ}}}P\left(X_i\right|C_k\left(x\right))---\left(11\right)$

P (X _i| C _k(x)) can estimate from the output of LDA sorter.And for LDA sorter C _k(x), classification X _iCenter m _iX is projected to LDA vector W with input people face data _k,

$w_k^i=W_k^T{m}_i---\left(12\right)$

$w_k^x=W_k^{T}x---\left(13\right)$

Estimate P (X as follows _i| C _k(x)):

$\hat{P}\left(X_i\right|C_k\left(x\right))=(1+\frac{{\left(w_k^x\right)}^T\left(w_k^i\right)}{\left|\right|w_k^x\left|\right|\·\left|\right|w_k^i\left|\right|})/2---\left(14\right)$

It is arrived [0,1] by normalizing.

In a preferred embodiment of the invention, above-mentioned stochastic sampling LDA method can be used for the integrated a plurality of features that comprise shape, texture and Gabor response.

Other many features integrated systems of great majority are based on the matching similarity level or the judgement level merges, and integrated approach of the present invention is from the eigenwert level.Carry out the integrated the abundantest information of having transmitted at the eigenwert layer, but owing to following two its realizations of reason are more difficult.The first, different types of feature is incompatible on yardstick.The second, new assemblage characteristic vector has higher dimension, and this has increased the weight of the problem of small sample.Method of the present invention has solved this two problems.With different feature normalization, solved the problem of small sample by PCA by stochastic sampling.

The following describes the object lesson that in the XM2VTS face database, uses method of the present invention.Can be about the XM2VTS face database referring to list of references 17, K.Messer, J.Matas, J.Kittler, J.Luettin, " the XM2VTSDB:The Extended M2VTS Database " that is shown with G.Matitre (XM2VTSDB: the M2VTS database of expansion), Second International Conference onAVBPA (second international AVBPA symposial), in March, 1999.

In this database, have 295 people, everyone has four full faces in different time sections.Fig. 3 has shown some examples.In this embodiment, two mug shots of every people's face classification are selected to come out to do training and reference, and remaining two be used for test.The identification test protocol that employing is used in the FERET test.Can be about the FERET test referring to list of references 18, be P.J.Phillips, H.Moon, S.A.Rizvi, " The FERET Evaluation Methodology for FaceRecognition Algorithms " (to the FERET evaluation method opinion of face recognition algorithm) of being shown with P.J.Rauss, IEEETrans.on Pattern Analysis and Machine Intelligence (IEEE pattern analysis and machine intelligence proceedings), the 22nd volume, the 10th phase, the 1090-1104 page or leaf, in October, 2000.During test, be confirmed to be in the reference set with the most alike image of test pattern be object, differentiate the class (individuality) of this image accuracy identical as the foundation of evaluating and testing with the method for discrimination of being estimated with the class of test pattern.

At first relatively stochastic subspace LDA and traditional use global feature takes rounding off face method.In pre-service, handle and carry out normalization by face images (all images that promptly comprises training set, picture library and test set) as shown in Figure 3 being carried out conventional translation, rotation and convergent-divergent, make that the eyes center separately of people's face is in same position in all images.(mask) removes most background with 46 * 81 friskets.The dimension of image space is 46 * 81=3726 like this.Utilize histogram to carry out the light equilibrium treatment.

Fig. 4 has shown the accuracy rate by single LDA sorter of the eigenface PCA subspace structure with different numbers.Because 295 classifications are arranged in training set, totally 590 facial images are so there are 589 eigenface with nonzero eigenvalue.According to taking rounding off face method, PCA subspace dimension is M-L=295.Yet the result has shown that the accuracy rate of using by single expense rounding off face sorter of 295 eigenface structures has only 79%, and this is that this dimension is too high because with respect to training set.As can be seen from the figure, when PCA subspace dimension was set to 100, the LDA sorter had better accuracy rate 92.88%.So for this data set, for the LDA sorter of construction of stable, the 100th, dimension more suitably.Therefore, below among the embodiment that will describe in detail, select 100 to construct compound LDA sorter as the dimension of stochastic subspace.Obviously, for different data sets, this dimension may be different.

At first, from the eigenface of 589 corresponding nonzero eigenvalues, select (stochastic sampling) 100 eigenface at random.Fig. 5 has provided the result who uses 20 LDA sorters of majority rule voting method combination.Obviously, the number K of LDA sorter is not restrictive.

Owing to be stochastic sampling, the accuracy rate of the LDA sorter that each is independent is very low, generally between 50% to 70%.Use above-mentioned majority rule voting method, Weak Classifier is strengthened greatly, can reach 87% accuracy rate.This shows that the LDA sorter by different stochastic subspace structures is complimentary to one another.In Fig. 6, along with the increase of the number K of sorter, the accuracy rate of the sorter of combination is improved, even more is better than accuracy rate the highest among Fig. 4.Certainly, can also further increase the sorter number and use more complicated fusion rule, thereby further improve performance.

According to a preferred embodiment of the present invention, improve the assembled classifier accuracy rate by the performance that improves each independent Weak Classifier.In order to improve the accuracy rate of each independent LDA sorter, can adopt method as previously described, at each stochastic subspace, be 50 eigenface with preceding 50 fixed in dimension with eigenvalue of maximum, from remaining 539 eigenface, select other 50 at random then.Obviously, for different databases, the number of the number of maximum eigenface and random character face can be different.

As shown in Figure 7, in this embodiment, the performance of single LDA sorter has been improved significantly.They are all similar to the LDA sorter based on preceding 100 eigenface.This shows { u ₅₁..., u ₁₀₀Must the eigenface littler not have more discriminant information than those eigenwerts.These sorters also are complimentary to one another, can obtain better accuracy rate so they are merged mutually.

When adopting kernel LDA (N-LDA) method to carry out face recognition, at kernel LDA exist when the quantity of training sample kernel problem of smaller greatly the time, can be by the method for random sample combination, promptly training set stochastic sampling and combination are generated at random independently stochastic sampling collection (bootstrap replica), each stochastic sampling collection all has the training sample than peanut like this.Therefore, according to a preferred embodiment of the invention, can comprise the following steps: by the method for stochastic sampling enhancing based on the recognition of face of N-LDA

At first, to have L class altogether the facial training set of M sample carry out PCA and handle, with everyone face data projection to the individual eigenface U of M-1 with nonzero eigenvalue _t={ u ₁..., u _M-1.Need explanation, the purpose of carrying out the PCA treatment step is to reduce the subsequent treatment data volume and raise the efficiency, but is not to be necessary.

Then, produce K stochastic sampling collection { T from described facial training set by stochastic sampling _i} _I=1 ^KEach stochastic sampling collection contains the L that selects at random from L class ₁The training sample of individual class (L wherein ₁＜L).The number K of stochastic sampling collection generally determines by identification test repeatedly, to find out the best or approaching best value.Equally, L ₁Value also be to determine like this.

In this embodiment of the present invention, produced 20 stochastic sampling collection, each stochastic sampling collection contains 150 classes and is used for training.

Concentrate N-LDA sorter of training from each stochastic sampling, and the output of using fusion rule to merge a plurality of sorters.

The independent N-LDA sorter of practicing from the training of each stochastic sampling is than the poor performance of original sorter based on whole training set.Yet when a plurality of sorters were merged, its recognition accuracy that brings was significantly improved, and better than existing N-LDA sorter.Combined method still can adopt aforesaid method, for example majority rule ballot or sum rule etc.Fig. 9 has shown the performance according to the N-LDA based on random sample combination of the present invention.

The following describes according to another preferred embodiment of the present invention, the N-LDA sorter that generates by the expense rounding off face sorter that will be generated by stochastic subspace with by the random sample combination is integrated, further improves recognition accuracy.Fig. 1 is the synoptic diagram of this scheme.

In a specific embodiment, make up 10 and take rounding off face sorter and 10 N-LDA sorters by random sample combined copy structure by stochastic subspace structure.Obviously, definite method of the number of sorter is the same, also is the best or approaching best number of finding out by test of many times.In addition, taking the number of rounding off face sorter and N-LDA sorter neither must be identical.

Utilize stochastic sampling, the LDA sorter of structure is stable, and the output fusion of sorter can be comprised most face characteristic space, therefore seldom loses discriminant information.This stochastic sampling method also can be applied to manifold comprehensive.For recognition of face, global feature and local feature all are crucial.

In another embodiment of the present invention, selected the feature of three quasi-representatives: shape, texture, the little wave response of local Gabor.These features through normalization and by the PCA decorrelation, have been formed comprehensive proper vector.Many LDA sorter has promptly formed a face identification system that has made up the robust of shape, texture and Gabor response by realizing from resultant vector and the training sample stochastic sampling that is used for discerning.

Utilize method (the list of references 15:A.Lanitis for example of conventional shape-variable model, C.J.Taylor, " the Automatic Interpretation and Coding of FaceImages Using Flexible Models " that is shown with T.F.Cootes (but utilize varying model opposite portion image automatic explanation and coding), IEEE Trans.on PAMI (IEEE is about the proceedings of PAMI), the 19th volume, the 7th phase, the 743-756 page or leaf, in July, 1997), facial image is decomposed into shape and texture.Shape vector Form by the coordinate that connects 35 reference points behind the aligning shown in Figure 2.Facial image is deformed into average people's face shape, obtains the texture vector by the normalized image of shape is sampled As with reference to zhang offering 16 (L.Wiskott, J.M.Fellous, " the Face Recognition by Elastic Bunch Graph Matching " that N.Krueger and C.von der Malsburg are shown (carrying out face recognition) by elasticity string figure coupling, IEEE Trans.on Pattern Analysis and Machine Intelligence (IEEE pattern analysis and machine intelligence proceedings), the 19th volume, the 7th phase, the 775-779 page or leaf, 1997) described in method, the Gabor of 8 directions of one group 5 yardsticks nuclear and the localized mass around each reference point are carried out convolution.Obtain the Gabor proper vector The texture of representing the face part with 35 * 40 Gabor response amplitude.

Like this, the method for this many features multi-categorizer face recognition comprises:

1. respectively to three feature vectors (feature vector) With Carry out PCA and handle compute matrix proper vector (eigenvector) U _s, U _t, U _gAnd eigenvalue _i ^s, λ _i ^t, λ _i ^gThe matrix characteristic vector of all corresponding zero eigenvalues all is removed.

2. for each facial image, every kind of feature is projected to corresponding proper vector, and by eigenwert is sued for peace they normalization, make them all have identical yardstick, concrete grammar is as follows:

${\stackrel{\→}{w}}_j=U_j^T{\stackrel{\→}{V}}_j/\sqrt{\mathrm{\Σ}{\mathrm{\λ}}_i^j},(j=s,t,g)---\left(15\right)$

3. will

Serial connection becomes a big proper vector successively.

4. use stochastic sampling method shown in Figure 1 and handle resulting big proper vector, to generate a plurality of LDA sorters.

In this embodiment, use sum rule to merge 20 sorters, obtained 99.83% recognition accuracy.Obviously, for different databases, the number of sorter can be different.For 590 test sample books, the method for this embodiment has only been discerned a class by mistake.

Table 1 has shown that the result based on the LDA of stochastic sampling and conventional method compares.Wherein, R-LDA (1) expression takes rounding off face method based on stochastic subspace, and R-LDA (2) expression is based on the N-LDA method of random sample combination; R-LDA (3) expression will be based on the integrated method of N-LDA method of taking rounding off face method and making up based on random sample of stochastic subspace.These listed in the table traditional methods comprise:

1, eigenface method, " FaceRecognition Using Eigenfaces " (the use characteristic face carries out face recognition) that document 19:M.Turk and A.Pentland shown sees reference, IEEEInternational Conference Computer Vision and Pattern Recognition (IEEE international computer vision and pattern identification meeting), the 586-591 page or leaf, 1991;

2, take rounding off face method, document 4 sees reference;

3, Bayesian analysis method, the document 20 that sees reference, B.Moghaddam, " Bayesian face recognition " (face recognition of Bayes's method) that T.Jebara and A.Pentland showed, PatternRecognition (pattern identification), the 33rd volume, 1771-1782 page or leaf, 2000 years;

Above-mentioned three kinds of methods all are based on the subspace face identification method of global feature.

4, elastic graph matching process (EBGM), document 16 sees reference.This method uses the correlativity of Gabor feature as the tolerance to similarity.

Table 1

Feature	Method	Accuracy rate
			Global feature	Eigenface	??85.59％
Take the rounding off face	??92.88％
		Bayes's method		??92.71％
??R-LDA(1)	??96.10％
		??R-LDA(2)		??95.59％
??R-LDA(3)	??97.63％
		Texture		Euclidean distance	??85.76％
Shape	Euclidean distance		??49.50％
		The Gabor feature		??EBGM	??95.76％
A plurality of features integrated	??R-LDA(3)		??99.83％

As can be seen from Table 1, method of the present invention has the performance that is better than existing recognition methods.

Although describe the present invention with reference to the preferred embodiments of the invention with describe, should be appreciated that, to one skilled in the art, can carry out various changes and modifications to the present invention without departing from the spirit and scope of the present invention.Scope of the present invention only is indicated in the appended claims.

Claims (10)

1. face recognition method based on stochastic sampling comprises:

Facial training set is carried out stochastic sampling;

Result according to described stochastic sampling trains a plurality of LDA sorters;

The face data that will be identified inputs to described a plurality of LDA sorter; With

The output of described a plurality of LDA sorters is merged.

2. method according to claim 1 is characterized in that, the step of the described LDA of training sorter comprises:

Facial characteristics value in the described facial training set is carried out stochastic sampling, produce a plurality of stochastic subspaces; With

Train a plurality of LDA sorters respectively by described a plurality of stochastic subspaces.

3. method according to claim 2, it is characterized in that, before described facial characteristics value is carried out described stochastic sampling, described facial training set is carried out PCA to be handled, remove eigenface, keep the candidate of M-1 eigenface, and a described M-1 eigenface is carried out stochastic sampling as the described stochastic subspace of structure with zero eigenvalue, produce a plurality of stochastic subspaces, wherein M is the number of sample in the facial training set.

4. method according to claim 3, it is characterized in that, each described stochastic subspace comprises a plurality of eigenface that have eigenvalue of maximum successively of described facial training set, and a plurality of eigenface with further feature value at random of described facial training set.

5. method according to claim 1 is characterized in that, the described step that trains a plurality of LDA sorters comprises:

M the training sample that described facial training set is comprised carries out stochastic sampling, produces a plurality of stochastic sampling collection, and each stochastic sampling collection contains the L that selects at random from L the class that described facial training set comprises ₁The training sample of individual class, wherein L ₁＜L; With

Train a plurality of random sample combination N-LDA sorters respectively by described a plurality of stochastic sampling collection.

6. method according to claim 5, it is characterized in that, before described training sample is carried out described stochastic sampling, described training set is carried out PCA to be handled, all face datas of described facial training set are projected to M-1 have the eigenface of nonzero eigenvalue, and the facial training set after described PCA handled carries out the stochastic sampling of described training sample.

7. method according to claim 1 is characterized in that,

The step of the described LDA of training sorter comprises:

Facial characteristics value in the described facial training set is carried out stochastic sampling, produce a plurality of stochastic subspaces;

Train a plurality of stochastic subspace LDA sorters respectively by described a plurality of stochastic subspaces, and

To have L class altogether the training sample of the facial training set of M sample carry out stochastic sampling, produce a plurality of stochastic sampling collection, each stochastic sampling collection contains the L that selects at random from a described L class ₁The training sample of individual class, wherein L ₁＜L;

Train a plurality of random sample combination N-LDA sorters respectively by described a plurality of stochastic sampling collection;

With described a plurality of stochastic subspace LDA sorters and a plurality of random sample combination N-LDA Multiple Classifier Fusion.

8. method according to claim 7 is characterized in that, further comprises: before described facial characteristics value and described training sample are carried out described stochastic sampling, described training set is carried out PCA handle, remove the eigenface with zero eigenvalue.

9. according to each described method of claim 1-8, it is characterized in that, described stochastic sampling to facial training set is that shape, texture, the little wave response of local Gabor as eigenwert are carried out, and described stochastic sampling to shape, texture, the little wave response of local Gabor comprises:

Respectively to the proper vector of shape, texture, the little wave response of local Gabor

With Carry out PCA and handle, obtain matrix characteristic vector U _s, U _t, U _gAnd eigenvalue _i ^s, λ _i ^t, λ _i ^g, and remove the matrix characteristic vector of all corresponding zero eigenvalues;

For each facial image, every kind of feature is projected to described matrix characteristic vector U _s, U _t, U _g, and carry out normalization, become a total characteristic vector with merging; With

Described total characteristic vector is carried out stochastic sampling.

10. according to each described method of claim 1 to 9, it is characterized in that, be used for the rule that the output of described a plurality of LDA sorters is merged is comprised: majority rule voting rule, sum rule.

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