CN110097022A - 2DPCA facial image recognition method based on the enhancing of two-way interpolation - Google Patents

Abstract

The present invention relates to a kind of 2DPCA face image recognition method based on two-way interpolation enhancement, the present invention first divides ORL face storehouse into training sample and test sample; Then use PCA method, 2DPCA method, (2D) ² PCA method to Extract eigenvalues and eigenvectors from the training samples. Then use the interpolation method to interpolate the extracted feature vectors. Finally, the norm distance method and the support vector machine method are used for identification. The present invention inserts new vectors between high-value feature vectors in order to increase the display degree of feature information, and improves image recognition accuracy without increasing computational complexity.

Description

2DPCA Face Image Recognition Method Based on Bidirectional Interpolation Enhancement

technical field

The invention belongs to the field of image processing and relates to a 2DPCA human face image recognition method based on bidirectional interpolation enhancement.

Background technique

Face recognition is an active research problem in the field of pattern recognition. In the rapidly developing intelligent information age, face recognition plays an increasingly important role. There are many methods for face recognition, principal component analysis (PCA) is one of the main methods to extract eigenfaces.

The principal components extracted by the PCA algorithm are orthogonal to each other, which can eliminate the mutual influence between the original data components, and the idea is simple and easy to implement on the computer. But it needs to convert the image matrix into a one-dimensional vector, resulting in too large covariance matrix dimension, too much calculation, and does not take advantage of the symmetry of the face image.

Then 2DPCA was proposed. Unlike the PCA method based on one-dimensional vectors, 2DPCA uses the original image matrix to directly construct the covariance matrix and extract the main feature vectors, which greatly improves the recognition efficiency. Although 2DPCA has higher recognition accuracy than PCA, an important problem with 2DPCA is that it requires more coefficients than PCA to represent the image. 2DPCA basically works in the column direction of the image, the dimensionality in the row direction is not reduced, and the complexity is still high, so the 2DPCA that considers the row and column directions at the same time is promoted, that is, (2D) ² PCA. Although the simultaneous compression in the row and column directions improves the recognition speed, but the accuracy is reduced to varying degrees. The analysis shows that, on the one hand, it is caused by excessive information compression; on the other hand, rows and rows, columns and columns are all orthogonal, and there is no redundancy, making it difficult to express the maximum projection direction of the projected feature vector .

Contents of the invention

Purpose of the present invention aims at the deficiency that prior art exists, has proposed a kind of 2DPCA people's face image recognition method based on two-way interpolation enhancement. The key point is that the present invention is based on the pricing theory. By inserting new vectors between high-value feature vectors, it is expected to improve the display of feature information and improve the recognition accuracy of images without increasing the computational complexity. .

Method of the present invention comprises the following steps:

Step 1. Divide the ORL face database into training samples and test samples.

Step 2, use the PCA method to extract eigenvalues and eigenvectors from the training samples in step 1

Step 3 and the method of extracting eigenvalues and eigenvectors described in step 2 need to convert the image matrix into a one-dimensional vector, resulting in too large a dimension of the covariance matrix and a large amount of calculation. In order to solve this problem, 2DPCA is used for step 1 Extract eigenvalues and eigenvectors from the training samples in .

The methods for extracting eigenvalues and eigenvectors described in step 4 and step 3 work in the column direction of the image, the dimensionality in the row direction is not reduced, and the complexity is still very high. To solve this problem, use (2D) ² PCA extracts eigenvalues and eigenvectors from the training samples in step 1.

Step 5, using an interpolation method to interpolate the feature vectors extracted in steps 2, 3 and 4.

The specific interpolation methods are as follows:

Let u1 and u2 be two projection axes, that is, two eigenvectors; V vector is any vector on the coordinate axis, and the angle between V vector and projection axis u1 is α; G point is any point on V vector, from G point Project to two projection axes u1, u2, the projection lengths are a, b, assuming a>b; insert a vector W between the V vector and the projection axis u1, and set the angle between the V vector and the W vector to be β , then β<α; the projection from point G to vector W is obviously longer than a, and as the angle α between the inserted vector W and vector V gradually decreases, the projection length gradually increases, implying that features gradually emerged.

Step 6 uses the norm distance method or the support vector machine method to identify.

Beneficial effects of the present invention: the present invention inserts new vectors between high-valued feature vectors in order to increase the display degree of feature information and improve image recognition accuracy without increasing computational complexity.

Description of drawings

Figure 1: Schematic diagram of interpolation method;

Figure 2: Schematic diagram of support vector machine classification;

Figure 3: Flowchart of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

As shown in FIG. 3 , the present invention extracts eigenvalues and eigenvectors through principal component analysis (PCA), two-dimensional principal component analysis (2DPCA) and two-way two-dimensional principal component analysis ((2D ² )PCA). Then use the interpolation method shown in Figure 1 to enhance the feature vector, and finally identify it through the norm distance and the support vector machine method shown in Figure 2, specifically including the following steps:

Step 1 divides the ORL face database into training samples and test samples.

Step 2 extract eigenvalues and eigenvectors

Step 2.1 Use the PCA method to extract eigenvalues and eigenvectors from the training samples in step 1, the algorithm is as follows:

Suppose there are face images of N people in a face database, and each person has n _i images from different perspectives, denoted as

A _ij ∈ R ^m×n , i=1,2,…,N; j=1,2,…,n _i (1)

Among them, R represents the set of real numbers, and the size of the face image matrix is m×n. m and n represent the number of rows and columns of the face image matrix, respectively.

From the images of each person, the first r _i images are selected for training and the remaining images for testing. Transform each face image A _ij into a one-dimensional vector a _ij ∈ R ^1×mn in the same order. Each vector is 1 row mn columns.

a _ij ＝[a _ij (1),a _ij (2),...,a _ij (mn)] (2)

In this way, each person's training sample set is recorded as:

The training sample set is recorded as:

The mean value of the face image in the training sample converted into a one-dimensional vector such as formula (2) is recorded as:

The mean matrix of the training samples is recorded as:

in

Bundle Matrix copy mn columns denoted as matrix.

The deviation matrix is written as:

The covariance matrix of the training sample set is recorded as:

Find the first d eigenvalues (λ ₁ ≥λ ₂ ≥…≥λ _d ) and corresponding eigenvectors (u ₁ ,u ₂ ,…,u _d ) of the covariance matrix.

The matrix converted to low dimension is recorded as:

Y _i =[y _i1 ,y _i2 ,...,y _ik ,...,y _ij ], j=1,2,...,n _i (10)

in

y _ij = U ^T a _ij (11)

U＝[u ₁ ,u ₂ ,…,u _r ] ^T (12)

Step 2.2 Use 2DPCA to extract eigenvalues and eigenvectors from the training samples in step 1.

Let x be the column direction is the best projection direction, after any sample image A is projected to x, the projected feature vector is obtained.

Recorded as:

y _ij =A _ij x, i=1,2,...,N; j=1,2,...,r _i (13)

Now to determine the optimal projection axis, introduce the covariance matrix G _t of the sample image A, the covariance matrix S _x of the projected feature vector Y, and the trace tr(S _x ) of the matrix S _x . Find the best projection direction by finding the maximum value of the trace. Its guidelines are:

J(X)＝tr(S _x ) (14)

make:

Substituting Equation 15 into Equation 14 gives:

make:

Substituting Equation 17 into Equation 16 gives:

J(X)＝x ^T G _t x (20)

This criterion is the total dispersion criterion.

Perform singular value decomposition on G _t to obtain eigenvalues λ _i (i=1,2,…,n), and λ ₁ ≥λ ₂ ≥…≥λ _n , and the singular vector is u _i (i=1,2,… ,n), U=[u ₁ ,u ₂ ,…,u _n ]. so

Substituting Equation 18 into Equation 17 gives:

In general, it is not enough to take an optimal projection axis, so choose the first d dominant features, singular vector u _d (i=1,2,…,d), eigenvalues λ _d (i=1,2,… ,d), so U _d =[u ₁ ,u ₂ ,…,u _d ], d≤n.

In formula 20, only when the eigenvalue λ _i takes the maximum value, the corresponding eigenvector u _i takes the maximum value, and the projection of u _i on X takes the maximum value, so that tr(S _x ) takes the maximum value.

After finding the best projection axis, project any sample image A on the projection axis

y _k =Ax _k , k=1,2,...,d (24)

Among them, x ₁ , x ₂ , ..., x _d are the optimal projection axes; the projection feature vectors y ₁ , y ₂ , ..., y _d are called principal component vectors of the sample image A.

Step 2.3 Use the (2D) ² PCA method to extract eigenvalues and eigenvectors from the training samples in step 1.

Column mapping formula:

y _ij =A _ij x _k , k=1,2,...,d (25)

where i=1,2,...,N; j=1,2,...,r _i , y _ij ∈R ^m×d .

Row mapping formula:

c _ij =v ^T A _ij ,i=1,2,…,N; j=1,2,…,r _i (26)

Joint mapping formula:

z _ij = v ^T A _ij x, i = 1, 2, ..., N; j = 1, 2, ..., r _i (27)

Step 3 Interpolation Enhancement

Step 3.1 The method of interpolation enhancement is as follows:

In Figure 1, is a vector at an angle of 30°, and u1 and u2 are two projection axes. Point z and point o are respectively The projection points from point G on the vector to the two projection axes, the lengths from the projection point to the origin are 5, remember

Assume

but exist The projection on

is a vector at an angle of 45°, and the vector The angle between them is 15°, highlighting hidden features.

if in and Continue to interpolate between them, denoted as

but exist The projection on

and The included angle is 22.5°, and The included angle is 7.5°. This can further highlight hidden features. As the density of interpolation increases, the projection direction gradually approaches the direction to be projected, so the feature prominence becomes more and more obvious.

Let any projected feature vector u _i be recorded as:

u _i =(a,b) ^T ,i=1,...,d (32)

Determine the maximum projection direction by calculating the value of s. Therefore, inserting the corresponding vector between any combination on the plane can highlight hidden features to varying degrees.

Step 3.2 uses the interpolation method described in step 3.1 to interpolate formula 11, formula 24 and formula 27 respectively.

Step 4 Identify

Use support vector machines or norm distance methods for identification.

4.1 Norm distance method identification, the principle is as follows:

The norm distance is defined as:

a' represents the difference between the two projected feature matrices. is the projection matrix for the training samples extracted in step 1, Projection matrix for the test sample in step 1. When m=1, D is a PCA projection matrix; when m=2, D represents a 2DPCA projection matrix; when m=3, D is a (2D)2PCA projection matrix.

4.2 The principle of support vector machine is shown in Figure 2

model=svmtrain(train_label, train_data, options) (36)

[predict,accuracy]=svmpredict(test_label,test_data,model) (37)

Call the svmtrain and svmpredict functions. train_label is the training sample label, train_data is the training sample data; test_label is the test sample label, and test_data is the test sample data. predict is the predicted category, and accuracy is the prediction accuracy.

To sum up: the present invention can improve image recognition accuracy without increasing computational complexity, and has important practical value.

Claims (1)

1. the 2DPCA facial image recognition method based on the enhancing of two-way interpolation, it is characterised in that method includes the following steps:

ORL face database is divided into training sample and test sample by step 1；

Step 2 extracts characteristic value and feature vector to the training sample in step 1 with PCA method；

Step 3 extracts characteristic value and feature vector to the training sample in step 1 with 2DPCA method；

Step 4, with (2D)²PCA method extracts characteristic value and feature vector to the training sample in step 1；

Step 5, using interpolation method respectively to step 2, step 3, the extracted feature vector of step 4 carries out interpolation；

Step 6 carries out facial image identification using norm distance method or support vector machine method；

The wherein interpolation method specifically:

If u1 and u2 is two axis of projections, i.e. two feature vectors；V vector is any vector in reference axis, if V vector and projection Angle is α between axis u1；G point is any point on V vector, is projected from G point to two axis of projection u1, u2, projected length difference For a, b, it is assumed that a > b；It is arbitrarily inserted into vector W between V vector sum axis of projection u1, if the angle between V vector and W vector is β, then β<α；It is projected from G point on W vector, it is clear that projected length is greater than a, with angle α between vector W and the V vector of insertion It is gradually reduced, projected length is gradually increased, and the feature implied gradually highlights.