CN107563334B - Face recognition method based on identification linear representation preserving projection - Google Patents

Abstract

The invention discloses a face recognition method based on identification linear representation preserving projection, which linearly represents each training sample by using other training samples of the same type and carries out identification analysis on all the training samples and the linear representations thereof. Compared with the prior art, the method can greatly reduce the calculation time and effectively improve the identification result.

Description

Face recognition method based on identification linear representation preserving projection

Technical Field

The invention particularly relates to a face recognition method based on identification linear representation preserving projection, and belongs to the technical field of face recognition.

Background

(1) Sparse preserving projection method (SPP, L.Qiao, S.Chen, X.Tan, "sparse rendering projects with Applications to Face registration", Pattern registration, vol.43, No.1, pp.331-341,2010):

let X ═ X₁,X₂,...,X_N]Representing a training sample set comprising N samples, x_i∈R^d(R^dA set of real vectors representing d dimensions) represents the ith training sample.

SPP first obtains a training sample x by solving the following problem_iCoefficient of sparsity α_i＝[α_1i,α_2i,…,α_Ni]^T∈R^N：

Where > 0 is a relatively small positive real number for controlling the error of the sparse reconstruction, E ∈ R^NIs a column vector with all element values 1, α_ii0. Then, SPP obtains the optimal linear projection vector u by solving the following problem:

(2) the shortcomings and improvements of the sparse reservation projection method are as follows:

the sparse preserving projection method has two problems: (a) the time complexity of calculating the sparse coefficient is very high, the calculation time increases exponentially along with the increase of the number of the training samples, and according to the principle of sparse representation, the number of the training samples at least needs to be closer to d, so that the condition that the requirement of | x is met under the condition of smaller number can be ensured_i-Xα_i||<However, d is usually a comparisonLarge numbers; (b) the sparse preservation projection method is an unsupervised linear projection method, and the recognition effect is generally lower than that of the supervised method.

Sparseness factor α_iThe non-zero coefficients in (1) mainly correspond to the training sample x_iOther training samples of the same class, which is the principle of sparse representation classification. Face recognition method based on identification linear representation preserving projection uses and trains sample x_iOther training samples of the same kind linearly represent the training sample x_iAnd performing a discriminant analysis on all training samples and their linear representations. Compared with a sparse preservation projection method, on one hand, the face recognition method based on the identification linear representation preservation projection only needs to calculate linear representation coefficients of a small number of similar training samples, so that the calculation time can be greatly reduced; on the other hand, the face recognition method based on the identification linear representation preserving projection uses a supervised identification analysis technology, and can effectively improve the recognition result.

Disclosure of Invention

The face recognition method based on the identification linear representation preserving projection linearly represents each training sample by using other training samples of the same type, and performs identification analysis on all the training samples and linear representations thereof. Compared with a sparse reservation projection method, the face recognition method based on the identification linear representation reservation projection can greatly reduce the calculation time and effectively improve the recognition result.

Simulation experiments were performed on Face Recognition Grade Challenge (FRGC) version 2Experiment 4 Face database (p.j.phillips, p.j.flynn, t.scruggs, k.bowyer, j.chang, k.hoffman, j.marques, j.min, w.work, "Overview of the Face Recognition grade Challenge", ieee conf.computer Vision and Pattern Recognition, vol.1, pp.947-954,2005), demonstrating that the effectiveness of the Face Recognition method of preserving projection is expressed based on discriminant linearity.

The technical scheme is as follows:

let X ═ X₁,X₂,...,X_c]Representing a training sample set containing c classes,

training sample set, X, representing the ith class_iContaining N_iA sample, x_ij∈R^dJ-th training sample, R, representing the i-th class^dA set of real vectors representing the d dimension,

represents the total number of samples of the training sample set, y ∈ R^dRepresenting a sample to be identified.

The steps of the face recognition method based on the identification linear representation preserving projection are as follows:

in a first step, a training sample x is obtained by solving the following problem_ijIs linear representation coefficient

Wherein, it is made

And secondly, carrying out differential analysis on the training sample and the linear representation thereof:

wherein, v ∈ R^dIs a linear projection vector;

equation (2) can be converted into

Wherein, P ═ I [ (NI-I)_c)+A(NI-I_c)A^T]-[(E-E_c)A^T+A(E-E_c)]，Q＝(I_c+AI_cA^T)-(E_cA^T+AE_c)，I∈R^N×NIs a unit array which is composed of a plurality of unit arrays,E∈R^N×Nis a square matrix with element values all being 1,

is a unit array which is composed of a plurality of unit arrays,

is a square matrix with element values all being 1,

satisfy the requirement of

Solution v of equation (3)^*By pair matrix (XQX)^T)^-1XPX^TPerforming characteristic decomposition to obtain;

third, when (XQX) has been obtained^T)^-1XPX^TEigenvectors v corresponding to the first m largest eigenvalues of the matrix_k(k-1, 2, …, m), where m is a tunable parameter, let V-V₁,v₂,…,v_m]Obtaining the training sample characteristic set after projection

Z_X＝V^TX (4)

And sample characteristics to be identified

Z_y＝V^Ty (5)

Calculating z_yThe distance to each training sample feature, assigns y to the class in which the training sample with the smallest distance is located.

Advantageous effects

Compared with the prior art, the invention adopting the technical scheme has the following beneficial effects:

the invention provides a face recognition method based on identification linear representation preserving projection, which is characterized in that other training samples of the same type are used for each training sample to linearly represent the training sample, and all the training samples and the linear representations thereof are subjected to identification analysis. Compared with the prior art, the method can greatly reduce the calculation time and effectively improve the identification result.

Drawings

FIG. 1 is an example picture of a human face;

fig. 2 is a graph showing the fluctuation of the recognition rate of 20 random tests.

Detailed Description

The technical solution of the present invention is specifically described below with reference to the accompanying drawings.

The Face Recognition Grand Challenge (FRGC) version 2 Experimental 4 Face database (P.J. Phillips, P.J. Flynn, T.Scruggs, K.Bowyer, J.Chang, K.Hoffman, J.Marques, J.Min, W.Worek, "Overview of the Face Recognition Grandchange", IEEE Conf.computer Vision and Pattern Recognition, vol.1, pp.947-954,2005) was selected for experimental verification. The database is large in size and comprises three sub-libraries of train, target and query, wherein the train sub-library comprises 12776 pictures of 222 persons, the target sub-library comprises 16028 pictures of 466 persons, and the query sub-library comprises 8014 pictures of 466 persons. The experiment selected 100 people from the training set, each with 36 images. All selected images are converted from original color images into gray images, corrected (the two eyes are in horizontal positions), scaled and cut, and each image sample only retains a face with the size of 60 multiplied by 60 and a nearby area. An example picture of a processed face is shown in fig. 1.

In an experimental database, 18 human face image samples are randomly selected from each category as training samples, the rest samples are used as samples to be identified, and random tests are carried out for 20 times.

Fig. 2 and table 1 show the recognition effect of the sparse preserving projection method (i.e., SPP method in graph) and the face recognition method based on discriminating linear representation preserving projection (i.e., DLRPP method in graph) 20 random tests. In fig. 2, the abscissa is the random test number, and the ordinate is the recognition rate (i.e., the number of correctly recognized samples to be recognized/the total number of samples to be recognized). Table 1 shows the recognition rate mean and standard deviation, and the average training time for 20 random tests in the two methods. Compared with a sparse preserving projection method, the face recognition method based on the identification linear representation preserving projection has the advantages that the recognition effect is remarkably improved, and the training time is greatly reduced. This verifies the effectiveness of face recognition methods that preserve projections based on discriminating linear representations.

TABLE 1

Name of method	Recognition rate (mean and standard deviation,%)	Average training time(s)
			SPP	76.52±4.60	3446.84
DLRPP	91.31±1.84	2.62

Claims (1)

1. A face recognition method based on discriminative linear representation preserving projection is characterized in that,

let X ═ X₁,X₂,...,X_c]Representing a training sample set containing c classes,

training sample set, X, representing the ith class_iContaining N_iA sample, x_ij∈R^dJ-th training sample, R, representing the i-th class^dA set of real vectors representing the d dimension,

represents the total number of samples of the training sample set, y ∈ R^dRepresenting a sample to be identified;

the method comprises the following specific steps:

in a first step, a training sample x is obtained by solving the following problem_ijIs linear representation coefficient

Wherein, it is made

And secondly, carrying out differential analysis on the training sample and the linear representation thereof:

wherein, v ∈ R^dIs a linear projection vector;

equation (2) to

Wherein, P ═ I [ (NI-I)_c)+A(NI-I_c)A^T]-[(E-E_c)A^T+A(E-E_c)]，Q＝(I_c+AI_cA^T)-(E_cA^T+AE_c)，I∈R^{N ×N}Is a unit array, E ∈ R^N×NIs a square matrix with element values all being 1,

is a unit array which is composed of a plurality of unit arrays,

is a square matrix with element values all being 1,

satisfy the requirement of

Solution v of equation (3)^*By pair matrix (XQX)^T)^-1XPX^TPerforming characteristic decomposition to obtain;

third, when (XQX) has been obtained^T)^-1XPX^TEigenvectors v corresponding to the first m largest eigenvalues of the matrix_k(k-1, 2, …, m), where m is a tunable parameter, let V-V₁,v₂,…,v_m]Obtaining the training sample characteristic set after projection

Z_X＝V^TX (4)

And sample characteristics to be identified

Z_y＝V^Ty (5)

Calculating z_yThe distance to each training sample feature, assigns y to the class in which the training sample with the smallest distance is located.

Images