CN104063715B - A kind of face classification method based on the nearest feature line - Google Patents

Abstract

The invention discloses a kind of face classification method based on the nearest feature line, with arest neighbors characteristic theory as foundation, define a kind of new weighted index, characteristic line method is simplified after proposing the criterion based on weighted index and improving, construct a kind of face classification device for being suitable for illumination and the various changes of attitude, there are lower computation complexity, less recognition time, and more preferably robustness compared to other graders.The grader extracts the feature of training storehouse image first by principal component analysis, builds training storehouse matrix and extracts sample image feature, builds test sample vector.Then weight coefficient is calculated, and dicision rules, the nearest feature line method that structure is simplified is formulated according to weight coefficient.It is in the case of various test result indicate that, below identical hardware environment, the grader has smaller computational complexity and more preferable robustness compared with other graders.

Description

Face classification method based on nearest neighbor characteristic line

Technical Field

The invention relates to a face classification method based on nearest neighbor characteristic lines, in particular to a method for realizing automatic classification and discrimination of faces by utilizing a computer technology, a digital image processing technology, a pattern recognition technology and the like, belonging to the technology about face feature extraction and recognition in the field of biological feature recognition.

Background

1. Face recognition technology

Face recognition has become an important research direction in biometric identification, and the key technology is the implementation of a feature vector extraction and classification method. Researchers have proposed a large number of face recognition methods, in which there are Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) that are popular for feature vector extraction; PCA is an unsupervised algorithm that obtains the principal components by solving eigenvalues of the covariance matrix of multivariate variables. As the classification method, a K-Nearest Neighbor (KNN) method, a Nearest Neighbor subspace method, a Support Vector Machine (SVM) method, a compressed sensing-based classifier (SRC) and the like are popular.

2. Principal component analysis

Principal component analysis, also known as KL transformation, computes a generator matrix ∑ of the KL transformation, which may be the overall step matrix S of the training sample_tOr the interspecies scattering matrix S of the training sample_bAnd so on, the scatter matrix is generated from the training set.

The overall scatter matrix can be expressed as:

if the total distribution matrix S is taken_tAs the generator matrix ∑, note that

Then Σ can be written as:

∑＝XX^T∈R^m×m

if the intra-class scatter matrix S_bThe generator matrix ∑, which is a KL transform, is:

where c is the number of pattern classes in the training sample set,the mean vector of all kinds of mode samples in the training sample set is recorded as follows:

the generator matrix Σ is:

∑＝XX^T∈R^n×n

finally, calculating the eigenvalue and the eigenvector of the generated matrix, constructing a subspace, projecting the training image and the test image into the eigenspace, and projecting each image into a point in the space corresponding to the subspace. And can be classified by the theory of pattern recognition.

3. Nearest neighbor characteristic line classifier

There is provided a class L pattern in which class k has N_kA sampleFor test samples y and N_kAny sample of the samplesDefining the distance:wherein,representing y to vectorHang enough toBy calculating y toThe distance of the feature line, the classification result is as follows, ifThen y belongs to class 1.

Disclosure of Invention

The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a face recognition method based on nearest neighbor characteristic lines, which has higher recognition rate and better robustness under the condition of maintaining the same computational complexity as the existing classifier.

The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:

a face distinguishing method based on nearest neighbor characteristic lines comprises the following steps:

(1) establishing a training library: extracting a characteristic value of a sample by using a PCA method, obtaining a base vector of a characteristic subspace by taking the extracted characteristic value as training data, and projecting the sample to the characteristic subspace according to the base vector to obtain a coordinate of the sample in the characteristic subspace; establishing a training base matrix A ═ A₁，A₂，...，A_k]∈R^m×nWherein m is the dimension of each sample after sampling by PCA method, n is the total number of samples in the training library, k is the total number of sample classes in the training library, A_kA set of training pictures of each type;

(2) projecting the picture to be detected to the feature subspace to obtain the coordinates of the picture to be detected in the feature subspace

(3) Calculating a weight coefficient w_jAnd performing preliminary judgment, comprising the following steps:

(31) defining an error functionIs provided with

Wherein,j is more than or equal to 1 and less than or equal to n, and j is a natural number;

(32) the local covariance matrix isThe weight coefficient is obtained by calculation

Wherein k is more than or equal to 1 and less than or equal to n, and k is a natural number; l is more than or equal to 1 and less than or equal to n, m is more than or equal to 1 and less than or equal to n, and l and m are natural numbers;

(33) calculating the w_jWeight coefficients corresponding to each sample class in the training library

(34) Calculating a weight vector discrimination index

(35) Designing a threshold value tau of a weight vector discriminant index:

wherein,

(36) comparing the weighted discrimination index W (x) with the threshold τ: if W (x) > tau, directly outputThe class corresponding to the maximum modulus is a classification result;

(4) if W (x) is less than or equal to tau, the following treatment is carried out:

(41) correcting a training library: sorting outThe largest X sample classes reestablish the training library matrix A' ═ A_max1，A_max2，...，A_maxX]∈R^m×n；

(42) Calculating a simplified characteristic line: any two images in the correction training library areObtaining a characteristic line in the characteristic space

(43) Calculating the coordinate of the picture to be measured in the feature subspace to the feature lineIs a distance ofWherein,

(44) according to the aboveIs classified to obtain

Wherein N is_kFor the number of samples in each class, k is more than or equal to 1 and less than or equal to n, k_cIs the number of class C samples.

Has the advantages that: according to the face distinguishing method based on the nearest neighbor characteristic line, a new weight coefficient W (x) is defined based on the nearest neighbor characteristic line theory, a face classifier suitable for illumination and various changes of postures is constructed based on the discrimination criterion of W (x) and a threshold value calculation method, and compared with other classifiers, the face distinguishing method based on the nearest neighbor characteristic line has the advantages of similar calculation complexity, higher recognition rate and better robustness; under the conditions of illumination change and multi-pose human faces, the recognition success rate of the method is more than 98 percent; the method can achieve higher recognition rate for various feature data (such as PCA, LDA, random sampling and the like), and can still achieve higher recognition rate under the condition of less sample feature dimensions, and the characteristic of the method can reduce the sampling requirement and reduce the data storage space, thereby reducing the cost of face recognition and being better suitable for software and hardware environments with limited resources (such as battery power supply, small storage capacity and the like); under the condition that noise interference and shielding are less than 50%, the method still has a good recognition rate, has a better recognition success rate and better robustness compared with the classical algorithms such as NFL and KNN, has good adaptability and effectiveness to face recognition in a severe environment, and greatly improves the operation complexity.

Drawings

FIG. 1 is a flow chart of the present invention;

fig. 2 shows the effect of classification when w (x) is 0.47;

fig. 3 shows the effect of classification when w (x) is 0.98;

FIG. 4 is an illustration of the impact of weight discrimination index on recognition success rate;

FIG. 5 is a comparison of the present algorithm with the NFL algorithm in the case of superimposed salt and pepper noise;

FIG. 6 is a comparison of the present algorithm with the NNL algorithm in the case of superimposed salt and pepper noise;

FIG. 7 is a comparison of the present algorithm with the KNN algorithm in the case of superimposed salt and pepper noise;

FIG. 8 is a comparison of the present algorithm with the NFL algorithm in the case of overlay block occlusion;

FIG. 9 is a comparison of the present algorithm with the NNL algorithm for the case of overlay patch occlusion;

fig. 10 is a comparison of the present algorithm with the KNN algorithm in the case of overlay patch occlusion.

Detailed Description

The present invention will be further described with reference to the accompanying drawings.

As shown in fig. 1, a face distinguishing method based on nearest neighbor feature lines includes the following steps:

(1) establishing a training library: extracting a characteristic value of a sample by using a PCA method, obtaining a base vector of a characteristic subspace by taking the extracted characteristic value as training data, and projecting the sample to the characteristic subspace according to the base vector to obtain a coordinate of the sample in the characteristic subspace; establishing a training base matrix A ═ A₁，A₂，...，A_k]∈R^m×nWherein m is the dimension of each sample after sampling by PCA method, n is the total number of samples in the training library, k is the total number of sample classes in the training library, A_kA set of training pictures of each type;

(2) projecting the picture to be detected to the feature subspace to obtain the picture to be detectedMeasuring the coordinates of the picture in the feature subspace

(3) Calculating a weight coefficient w_jAnd performing preliminary judgment, comprising the following steps:

(31) defining an error functionIs provided withWherein,j is more than or equal to 1 and less than or equal to n, and j is a natural number;

(32) the local covariance matrix isThe weight coefficient is obtained by calculationWherein k is more than or equal to 1 and less than or equal to n, and k is a natural number; l is more than or equal to 1 and less than or equal to n, m is more than or equal to 1 and less than or equal to n, and l and m are natural numbers;

(33) calculating the weight coefficient corresponding to each classIs a weight coefficient w_jA coefficient corresponding to each sample class in the training library;

(34) calculating a weighted discrimination index

(35) Making a judgment according to the magnitude of the calculated weight discrimination index W (x):

if W (x) is 1, max_i||_i(x)||₂/||x||₂1, the weight coefficients are basically distributed in only one type;

if W (x) is 0, thenIllustrating that the weight coefficients are distributed almost in each class;

therefore, a threshold τ e (0, 1) of the weight discrimination index can be designed to represent the distribution of the weight coefficient, and the specific design method is as follows:

wherein,

(36) comparing the weighted discrimination index W (x) with the threshold τ:

if W (x) is more than tau, the distribution of the weight coefficients is more concentrated, the classification effect is better, and the sample class with the minimum residual error can be directly output as a classification result;

if W (x) is less than or equal to tau, the weight coefficient is not well distributed, the classification effect is better, the classification effect is not good, the range of the training library needs to be reduced, and the classification is carried out again;

(4) if W (x) is less than tau, the following is performed:

(41) correcting a training library: sorting outThe largest X sample classes reestablish the training library matrix A' ═ A_max1，A_max2，...，A_maxX]∈R^m×n；

(42) Calculating a simplified characteristic line: any two images in the correction training library areObtaining a characteristic line in the characteristic space

(43) Calculating the coordinate of the picture to be measured in the feature subspace to the feature lineIs a distance ofWherein,

(44) according to the aboveIs classified to obtain

Wherein N is_kFor the number of samples in each class, k is more than or equal to 1 and less than or equal to n, k_cIs the number of class C samples.

The following describes some of the details of the present invention in its implementation.

1. The selected test databases are an ORL face database, a UMIST face database and an Extended YaleB face database, and the three databases all contain face images and mainly change directions and angles.

2. The PCA method is used for extracting features, and experiments show that the PCA has higher success rate compared with random sampling.

1) Reading in a face library, normalizing the face library, selecting a certain number of images from each person in the library to form a training set, and forming a test set by the rest of the images. Assuming that the normalized image is N × M, pixel points are connected in columns to form an N × M dimensional vector, which can be regarded as a point in N × M space, and this image can be described by a low dimensional subspace through KL transform.

2) Let N face images in the face image library be represented as X by vector₁，X₂，...，X_NCalculating the average image of the human face asFrom this, the mean difference of each image is obtained

3) Computing a covariance matrixCalculating the eigenvalues λ of the matrix C_kAnd corresponding feature vector mu_k. In actual calculation, the calculation amount is large, and in order to reduce the calculation amount, the mean deviation of each image is formed into a matrix: x' ═ X₁′，X₂′，...X_N′]Then the covariance matrix can be written asAccording to the linear algebraic theory, X '(X')^TCharacteristic value λ of_jAnd corresponding eigenvectors Φ_jConverts the problem of (2) into a calculation (X')^TCharacteristic value λ of X_jAnd corresponding eigenvectors Φ_j', obtaining phi_j' rear phi_jCan be prepared fromThus obtaining the product. Further, the eigenvalue lambda of the matrix C is obtained by SVD theorem_k。

4) Projecting the training image to a feature subspace, projecting the average differences of all N human face images in a human face library to the space to obtain respective projection vectors Y₁，Y₂，...，Y_N：

(Y_i)T＝[y_1i，y_2i，...，y_Mi]，i＝1，2，...，N

y_ji＝(u_j)^TX′_j，j＝1，2，...，M

Wherein u is_jIs a set of feature vectors, X'_jTo train the mean difference of the images.

Form a training matrix A ═ Y₁，Y₂，...，Y_N]The image vectors are arranged in a class order.

3. Classifying for the first time, projecting the given test picture into a characteristic subspace to obtain a characteristic coordinate vector

1) Calculating weight coefficient, making preliminary judgment, defining error functionIs provided withWherein,n training library samples are provided, j is more than or equal to 1 and less than or equal to n, and j is a natural number;

2) the local covariance matrix isThe weight coefficient is obtained by calculationWherein k is more than or equal to 1 and less than or equal to n, and k is a natural number; l is more than or equal to 1 and less than or equal to n, m is more than or equal to 1 and less than or equal to n, and l and m are natural numbers;

3) calculate each classCorresponding weight coefficientCorresponding the weight coefficient w to the coefficient of each sample class in the training library, and calculating the weight discrimination index

4. And designing a threshold value tau epsilon (0, 1) of the weight discrimination index to represent the distribution condition of the weight coefficient.

5. Design ofWhere k is the total number of sample classes in the training library:

if W (x) is more than tau, the weight coefficient distribution is more concentrated and the weight coefficient is directly outputThe class corresponding to the maximum modulus is a classification result;

if W (x) is less than or equal to tau, the weight coefficient is not well distributed, then the following treatment is carried out, the range of the training pants needs to be reduced, and the training pants are classified again;

6. the appropriate selection of τ can effectively improve the success rate of identification, as shown in fig. 4:

1) sorting outThe largest X classes rebuild a new smaller training library matrix A' ═ A_max1，A_max2，A_max3](ii) a In most cases, the correct classification is contained in the modified smaller training library, thus narrowing the recognition range, and X is given by

2) Calculating a simplified characteristic line: any two images in the correction training library areObtaining a characteristic line in the characteristic space

3) Calculating the coordinate of the picture to be measured in the feature subspace to the feature lineIs a distance ofWherein,

4) according to the aboveIs classified to obtain

Wherein N is_kFor the number of samples in each class, k is more than or equal to 1 and less than or equal to n, k_cIs the number of class C samples.

The experimental results of the present invention are explained in detail below:

1. the database adopted by the experiment of the invention is an international ORL, UMIST and Extended YaleB face database. The ORL library contains a total of 40 volunteers, each containing 10 pictures with 92 × 112 pixels, for a total of 400 pictures. We selected 5 images of each person as the training library and 5 more as the test images. For the UMIST library, a total of 20 volunteers each selected 18 images for use, with pixels 92 × 112, of which 3 were training images and the rest were test images. For the Extended YaleB library, a total of 38 volunteers were included, and 58 images were selected for each person, with 168 × 192 pixels.

2. Experiment one: FIG. 4 shows the effect of different values on test success and time at W (x), which is performed in the UMIST library. The abscissa represents the value of W (x), from 0 to 1. The left ordinate represents the recognition success rate, and the right ordinate represents time. Experiments show that with the increase of the value of W (x), after W (x) is more than 0.5, the algorithm can achieve a higher success rate than the NFL algorithm, and with the increase of W (x), the testing time is increased.

3. Experiment two: fig. 5-10 are experiments in which test images are superimposed with noise. The experiment is carried out on an ORL face library, and randomface, eigenface and fisherface are selected as a feature extraction mode. Fig. 6 shows an experiment of superimposing salt-pepper noise, and fig. 7 shows an experiment of superimposing random block occlusion. The abscissa represents the percentage of noise in the image, and the ordinate represents the success rate of recognition. Experiments show that the algorithm has a better recognition effect than NFL, KNN and NNL algorithms under the condition of noise superposition, and particularly when eigenface is selected as feature extraction, the algorithm can achieve improvement of the recognition success rate of nearly 20% under the condition of 50% noise ratio.

4. Experiment three: table 1 shows algorithm complexity tests, where the experiments are performed in Extended YaleB library, and 3 methods of feature extraction, namely randomface, eingentface, and fisherface, are selected, and the algorithm and the classical classification algorithm, such as KNN and NNL, have similar algorithm complexity, but the algorithm recognition success rate and robustness are better than those of the classical algorithm. Compared with other algorithms such as NFL, NFP and SVM, the test time of the algorithm is remarkably reduced.

TABLE 1 calculation time test(s)

	Randomfaces	Eigenfaces	Fisherfaces
				SFL	110.88	143.42	188.85
KNN	106.24	112.81	135.06
				NNL	107.95	133.76	175.51
NFL	598.23	639.03	789.35
				NFP	7890.06	9180.31	9862.89
SVM	1824.08	483.81	565.25

The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (1)

1. A face distinguishing method based on nearest neighbor characteristic lines is characterized in that: the method comprises the following steps:

(1) establishing a training library: extracting a characteristic value of a sample by using a PCA method, obtaining a base vector of a characteristic subspace by taking the extracted characteristic value as training data, and projecting the sample to the characteristic subspace according to the base vector to obtain a coordinate of the sample in the characteristic subspace; establishing a training base matrix A ═ A₁,A₂,...,A_k]∈R^m×nWherein m is the dimension of each sample after sampling by PCA method, and n is the sample in training libraryK is the total number of sample classes in the training library, A_kA set of k-th class training pictures;

(2) projecting the picture to be detected to the feature subspace to obtain the coordinates of the picture to be detected in the feature subspace

(3) Calculating a weight coefficient w_jAnd performing preliminary judgment, comprising the following steps:

(31) defining an error functionIs provided with

Wherein,j is more than or equal to 1 and less than or equal to n, and j is a natural number;

(32) the local covariance matrix isThe weight coefficient is obtained by calculation

Wherein z is more than or equal to 1 and less than or equal to n, and z is a natural number; l is more than or equal to 1 and less than or equal to n, m is more than or equal to 1 and less than or equal to n, and l and m are natural numbers;

(33) calculating the w_jWeight coefficients corresponding to each sample class in the training libraryi is 1 to k;

(34) calculating a weight vector discrimination index

(35) Designing a threshold value tau of a weight vector discriminant index:

$\mathrm{\τ}=\frac{\sqrt{k}\×(1-X/k)-1}{\sqrt{k}-1}$

wherein,

(36) comparing the weighted discrimination index W (x) with the threshold τ: if W (x) > tau, directly outputThe class corresponding to the maximum modulus is a classification result;

(4) if W (x) is less than or equal to tau, the following treatment is carried out:

(41) correcting a training library: sorting outReestablishing a training library matrix A' of the X sample classes with the maximum modulus as [ A ═ A_max1,A_max2,...,A_maxX]∈R^m×n；

(42) Calculating a simplified characteristic line: any two images in the correction training library areObtaining a characteristic line in the characteristic space

(43) Calculating the coordinate of the picture to be measured in the feature subspace to the feature lineIs a distance ofWherein,

(44) according to the aboveIs classified to obtain

Wherein k is_cIs the number of class C samples.