CN107506694B - Robust face recognition method based on local median representation - Google Patents

Abstract

The invention provides a robust face recognition method based on local median representation, which comprises the following steps: (1) the method comprises the steps of obtaining a face image training sample set, (2) obtaining neighbor samples of samples to be recognized in each class of training samples, (3) calculating a median value according to the neighbor samples of the samples to be recognized in each class, (4) calculating a reconstruction representation coefficient of the samples to be recognized according to the median value, and (5) determining class labels of the samples to be recognized according to the size of the reconstruction representation coefficient. The invention utilizes the neighborhood information of the sample, and the obtained median value can effectively process various changes in the face image, such as changes in facial expression, posture, illumination, shielding and the like, thereby meeting the high-precision requirement on face identification in practical application.

Description

Robust face recognition method based on local median representation

Technical Field

The invention relates to an image recognition method, in particular to a robust face recognition method based on local median representation, and belongs to the technical field of image recognition.

Background

The face recognition is an important method for identity authentication, and has wide application prospects in the fields of file management systems, security verification systems, credit card verification, criminal identity recognition of public security systems, bank and customs monitoring, man-machine interaction and the like. In general, the step of face recognition can be divided into three parts: firstly, detecting and segmenting human faces from a complex scene; secondly, extracting face features from the found face image; thirdly, matching and recognizing the human face by adopting a proper algorithm according to the extracted human face features.

The existing face feature extraction and identification method comprises the following steps:

(1) eigenfaces (Eigenfaces), i.e. face recognition methods based on Principal Component Analysis (PCA), are described in m.turn and a.pentland in 1991, in Journal of Cognitive Neuroscience, volume 3, pages 1, 71-86, Eigenfaces for recognition, which aim to find a projection direction so that the total divergence after projection of a face sample is maximized.

(2) Fisher face (fisherface), a face recognition method based on Linear Discriminant Analysis (LDA), is described in IEEE Transactions on Pattern Analysis and Machine Analysis, volume 19, page 7, 711 and 720 of IEEE Transactions on facial Analysis and Machine Analysis, d.j.kriegman, 1997 in eigenface vs. first face of fisher, which uses the class information of a sample to delineate the identification structure contained in the sample.

(3) Laplacian Face (laplacian Face), a Face recognition method based on Local Preserving Projection (LPP), is described in "Face recognizing faces" published by IEEE Transactions on Pattern Analysis and Machine Intelligence, volume 27, page 3, 328 and 340, of x.he, s.yan, y.hu et al, 2005.

(4) Sparse Representation Classifier (SRC), described in J.Wright, A.Y.Yang, A.Ganesh, S.Satry, Y.Ma, 2008 in IEEE Transactions on Pattern Analysis and Machine integrity, volume 31, phase 2, 210, 227, is a classification method that first represents the samples to be identified as linear combinations of other samples, solves the linear reconstruction coefficients by solving the L1 norm optimization problem, and finally determines the class labels of the samples to be identified according to the reconstruction residuals of the samples to be identified.

(5) A Linear Regression Classifier (LRC), described in i.naseem, r.togneri, m.bennamoun, Linear regression for surface recognition, published 2010 at IEEE Transactions on pattern analysis and machine analysis, volume 32, page 11, 2106, 2112, is similar to SRC, and is a classification method, which assumes that samples of the same type are located in the same Linear space, linearly represents the samples to be recognized as a Linear combination of samples of a certain type, then solves reconstruction coefficients by a least square method, and finally determines the class label of the samples to be recognized by the size of the reconstruction residual of the samples to be recognized.

In the above face recognition method, the PCA, the LDA, and the LPP belong to a feature extraction method, wherein the PCA does not consider an identification structure of a sample, so the robustness is poor, the LDA does not consider class membership of the sample, so the face recognition problem cannot be robustly processed, and the LPP belongs to an unsupervised method although considering a local structure of the sample, and does not consider a class structure of the sample. The SRC and the LRC both belong to a classification method based on expression learning, the problems of occlusion, illumination change and the like can be effectively processed, the robustness is high, however, the SRC needs to solve the L1 norm optimization problem, the required time is long, the LRC does not fully utilize prior information of a sample, such as neighborhood information, and when the number of the sample is small, the face features cannot be robustly expressed.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: a robust face recognition method based on local median representation is designed, so that a plurality of changes in a face image can be effectively processed, and the high-precision requirement on face recognition in practical application is met.

The invention adopts the following technical scheme for solving the technical problems:

the invention provides a robust face recognition method based on local median representation, which comprises the following steps:

step 1, acquiring a face image training sample set, wherein the training sample set comprises C different classes, normalizing each training sample and sample to be identified in the training sample set, and performing preprocessing by using Principal Component Analysis (PCA) to reduce data dimension;

step 2: acquiring K adjacent points of a sample to be identified in each type of training sample;

and step 3: calculating a median value according to K neighbor points of the sample to be recognized in each type of training sample;

and 4, step 4: linearly reconstructing the sample to be identified by using the C median values of the sample to be identified obtained in the step 3, and calculating a reconstruction coefficient according to a least square method;

and 5: and judging the class mark of the sample to be identified by utilizing the maximum similarity principle.

Further, the robust face recognition method based on local median representation of the present invention specifically includes the following steps:

assuming that the size of the image is w x h, the training sample comes from C image classes, and matrix vectorization operation is carried out on each facial image to obtain the ith facial image as x_i∈R^DWherein D ═ w × h;

denote the training sample set as X ═ X₁,x₂,...,x_n]The sample to be identified is denoted x_testN, n represents the number of face image training samples;

for training sample x_iThe normalization operation modulo 1 is performed:

x_i＝x_i/||x_i||₂，

also for test sample x_testNormalization is also performed:

x_test＝x_test/||x_test||₂，

the normalized samples are preprocessed using PCA to reduce the data dimensionality.

Furthermore, the robust face recognition method based on local median representation of the invention uses X ═ X₁,x₂,…,x_n]And x_testRepresenting a training sample set after PCA preprocessing and a sample to be identified, preprocessing the normalized sample by using PCA in step 1 to reduce the data dimension, and the steps are as follows:

(1) let Z be [ x ]₁-m,x₂-m,…,x_n-m]Calculating

The characteristic vector corresponding to the first d non-zero characteristic values, let λ₁>λ₂…>λ_dIs composed of

First d non-zero maximum eigenvalues, v₁,v₂,…,v_dIs the corresponding feature vector;

(2) expressing the PCA projection vector as:

(3) let A_PCA＝[a₁,a₂,…,a_d]And obtaining the data after PCA pretreatment as follows:

x_i＝A_PCA ^Tx_i,

x_test＝A_PCA ^Tx_test

wherein, i is 1,2, n, n represents the number of face image training samples.

Further, in the robust face recognition method based on local median representation of the present invention, the step 2 of obtaining K neighboring points of the sample to be recognized in each type of training sample specifically includes:

order to

Representing class c samples, calculating x_testAnd X_cEuclidean distance of each training sample:

screening the obtained distances according to the sequence from small to large to obtain the distance x in the class c training sample_testThe most recent K training sample sets:

X_{test_c_K}＝[x_{c_1},x_{c_2},...,x_{c_K}],

wherein, C is 1, 2.

Further, in the robust face recognition method based on local median representation of the present invention, step 3, according to K neighbor points of the sample to be recognized in each class of training samples, calculating the median specifically is:

class c training samples from x_testThe most recent K training sample sets are represented as:

let M_c＝[M_c,1,M_c,2,...,M_c,D]^T∈R^DRepresents X_{test_c_K}The median vector of (1), then M_cIs denoted as mean (x)_{c_1,j},x_{c_2,j},...,x_{c_K,j})；

X is to be_{c_1,j},x_{c_2,j},...,x_{c_K,j}Arranged in order from small to large, assuming x_{c_1,j}＜x_{c_2,j}＜...＜x_{c_K,j}Then mean (x)_{c_1,j},x_{c_2,j},...,x_{c_K,j}) The calculation formula is as follows:

further, the robust face recognition method based on local median representation of the present invention includes the following specific steps in step 4:

assuming that C median values of the samples to be identified obtained in step 3 are M ═ M₁,M₂,...,M_C]Then linearly expressing the sample to be identified as:

x_test＝Mw

wherein w ═ w₁,w₂,...,w_C]^T∈R^CTo linearly reconstruct the coefficient vector, it can be solved using the least squares method:

w＝(M^TM)^-1M^Tx_test。

further, in the robust face recognition method based on local median representation of the present invention, in step 5, the sample class mark to be recognized is discriminated according to the following criteria: if it is not

Where C is 1, 2.. and C, the sample to be identified belongs to the s-th class.

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

the method comprises the steps of calculating a median value according to the neighbors of a sample to be recognized in each class of training samples, linearly representing the sample to be recognized by the median value, calculating a linear reconstruction coefficient according to a least square method, and finally judging the class mark of the sample to be recognized according to a maximum similarity principle. The method utilizes neighborhood information of the sample, and the obtained median value can effectively process various changes in the face image, such as changes in facial expression, posture, illumination, shielding and the like, thereby meeting the high-precision requirement on face identification in practical application.

Drawings

FIG. 1 is a flowchart of the overall method of the present invention.

Detailed Description

The technical scheme of the invention is further explained in detail by combining the attached drawings:

it will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

The invention provides a robust face recognition method based on local median representation, and a specific flow is shown in figure 1.

Firstly, a training sample set is obtained.

Assuming that the size of the image is w x h, the training sample comes from C image classes, and matrix vectorization operation is carried out on each facial image to obtain the ith facial image as x_i∈R^DWherein D ═ w × h. The training sample set may be represented as X ═ X₁,x₂,...,x_n]The sample to be identified can be represented as x_testAnd n represents the number of training samples of the face image.

For training sample x_iThe normalization operation modulo 1 is performed:

x_i＝x_i/||x_i||₂,(i＝1,2,...,n)

also for test sample x_testNormalization is also performed:

x_test＝x_test/||x_test||₂

the normalized samples are preprocessed by PCA to reduce the data dimensionality, again using X ═ X for convenience₁,x₂,…,x_n]And x_testRepresenting the training sample set after PCA pretreatment and the sample to be identified, the calculation steps are as follows:

(1) let Z be [ x ]₁-m,x₂-m,…,x_n-m]Calculating

And the feature vectors corresponding to the first d non-zero feature values. Let lambda₁>λ₂…>λ_dIs composed of

First d non-zero maximum eigenvalues, v₁,v₂,…,v_dM represents the mean of the ensemble of training samples for the corresponding feature vector.

(2) The PCA projection vector can be expressed as:

(3) let A_PCA＝[a₁,a₂,…,a_d]Then the data after PCA pretreatment can be obtained as:

x_i＝A_PCA ^Tx_i,(i＝1,2,...,n)

x_test＝A_PCA ^Tx_test

and (II) acquiring K adjacent points of the sample to be identified in each type of training sample.

Order to

Representing class c samples, calculating x_testAnd X_cEuclidean distance of each training sample:

the obtained distances are screened from small to large to obtain the distance x in the class c training sample_testThe most recent K training sample sets:

X_{test_c_K}＝[x_{c_1},x_{c_2},…,x_{c_K}],c＝1,2,...,C

and (III) calculating a median value according to K neighbor points of the sample to be identified in each type of training sample.

Class c training samples from x_testThe most recent K training sample sets can be represented as:

let M_c＝[M_c,1,M_c,2,…,M_c,D]^T∈R^DRepresents X_{test_c_K}The median vector of (1), then M_cThe jth element of (a) can be represented as mean (x)_{c_1,j},x_{c_2,j},…,x_{c_K,j})。

Calculating mean (x)_{c_1,j},x_{c_2,j},…,x_{c_K,j}) It is necessary to first x_{c_1,j},x_{c_2,j},…,x_{c_K,j}Arranged in order from small to large, where for convenience we assume x_{c_1,j}＜x_{c_2,j}＜...＜x_{c_K,j}Then mean (x)_{c_1,j},x_{c_2,j},...,x_{c_K,j}) The calculation formula is as follows:

and (IV) linearly reconstructing the sample to be identified by using the C median values of the sample to be identified, which are obtained in the step (3), and calculating a reconstruction coefficient according to a least square method.

Assuming that C median values of the samples to be identified obtained in step 3 are M ═ M₁,M₂,...,M_C]So that the sample to be identified can be linearExpressed as:

x_test＝Mw

wherein w ═ w₁,w₂,...,w_C]^T∈R^CTo linearly reconstruct the coefficient vector, it can be solved using the least squares method:

w＝(M^TM)^-1M^Tx_test

and (V) judging the class mark of the sample to be identified by utilizing the maximum similarity principle.

The sample class mark to be identified can be distinguished according to the following criteria:

if it is not

The sample to be identified belongs to the s-th class.

The foregoing is only a partial embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (2)

1. A robust face recognition method based on local median representation comprises the following steps:

step 1, acquiring a face image training sample set, wherein the training sample set comprises C different classes, normalizing each training sample and sample to be identified in the training sample set, and performing preprocessing by using Principal Component Analysis (PCA) to reduce data dimension; the method comprises the following specific steps:

assuming that the size of the image is w x h, the training sample comes from C image classes, and matrix vectorization operation is carried out on each facial image to obtain the ith facial image as x_i∈R^DWherein D ═ w × h;

denote the training sample set as X ═ X₁,x₂,...,x_n]The sample to be identified is denoted x_testN, n represents the number of face image training samples;

for training sample x_iThe normalization operation modulo 1 is performed:

x_i＝x_i/||x_i||₂，

also for test sample x_testNormalization is also performed:

x_test＝x_test/||x_test||₂，

preprocessing the normalized sample by utilizing PCA to reduce the data dimension;

step 2, obtaining K adjacent points of a sample to be identified in each type of training sample; the method specifically comprises the following steps:

order to

Representing class c samples, calculating x_testAnd X_cEuclidean distance of each training sample:

screening the obtained distances according to the sequence from small to large to obtain the distance x in the class c training sample_testThe most recent K training sample sets:

X_{test_c_K}＝[x_{c_1},x_{c_2},...,x_{c_K}],

wherein, C is 1, 2.., C;

step 3, calculating a median value according to K neighbor points of the sample to be recognized in each type of training sample; the method specifically comprises the following steps:

class c training samples from x_testThe most recent K training sample sets are represented as:

let M_c＝[M_c,1,M_c,2,...,M_c,D]^T∈R^DRepresents X_{test_c_K}The median vector of (1), then M_cIs denoted as median(x_{c_1,j},x_{c_2,j},...,x_{c_K,j})；

X is to be_{c_1,j},x_{c_2,j},...,x_{c_K,j}Arranged in order from small to large, assuming x_{c_1,j}＜x_{c_2,j}＜...＜x_{c_K,j}Then mean (x)_{c_1,j},x_{c_2,j},...,x_{c_K,j}) The calculation formula is as follows:

step 4, linearly reconstructing the sample to be identified by using the C median values of the sample to be identified obtained in the step 3, and calculating a reconstruction coefficient according to a least square method; the method specifically comprises the following steps:

assuming that C median values of the samples to be identified obtained in step 3 are M ═ M₁,M₂,...,M_C]Then linearly expressing the sample to be identified as:

x_test＝Mw

wherein w ═ w₁,w₂,...,w_C]^T∈R^CTo linearly reconstruct the coefficient vector, it can be solved using the least squares method:

w＝(M^TM)^-1M^Tx_test；

step 5, judging the class mark of the sample to be identified by utilizing the maximum similarity principle; specifically, the judgment is carried out according to the following criteria: if it is not

Where C is 1, 2.. and C, the sample to be identified belongs to the s-th class.

2. The method of claim 1, wherein X ═ X is used₁,x₂,...,x_n]And x_testRepresenting a training sample set after PCA preprocessing and a sample to be identified, preprocessing the normalized sample by using PCA in step 1 to reduce the data dimension, and the steps are as follows:

(1) let Z be [ x ]₁-m,x₂-m,…,x_n-m]Calculating

The characteristic vector corresponding to the first d non-zero characteristic values, let λ₁>λ₂…>λ_dIs composed of

First d non-zero maximum eigenvalues, v₁,v₂,…,v_dM is the mean value of the whole training sample;

(2) the PCA projection vector is represented as:

(3) let A_PCA＝[a₁,a₂,…,a_d]And obtaining the data after PCA pretreatment as follows:

x_i＝A_PCA ^Tx_i,

x_test＝A_PCA ^Tx_test

wherein, i is 1,2, n, n represents the number of face image training samples.

Images