CN110097022A - 2DPCA facial image recognition method based on the enhancing of two-way interpolation - Google Patents
2DPCA facial image recognition method based on the enhancing of two-way interpolation Download PDFInfo
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Abstract
The present invention relates to a kind of 2DPCA facial image recognition method based on the enhancing of two-way interpolation, the present invention first is divided into training sample and test sample ORL face database；Then PCA method, 2DPCA method, (2D) are used respectively2PCA method extracts characteristic value and feature vector to training sample.The method for reusing interpolation carries out interpolation to extracted feature vector.Finally identified using norm distance method and support vector machine method.The present invention, it is expected to improve the display degree of characteristic information, improves the accuracy of identification of image by being inserted into new vector between the feature vector of high value under the premise of not increasing bigger computation complexity.
Description
Technical field
The invention belongs to field of image processings, are related to a kind of 2DPCA facial image identification side based on the enhancing of two-way interpolation
Method.
Background technique
Recognition of face, which is that one in area of pattern recognition is active, to study a question, in fast-developing intelligent information
The effect in generation, recognition of face is increasing.There are many kinds of the methods of recognition of face, and principal component analysis (PCA) is to extract eigenface
One of main method.
It is mutually orthogonal between each principal component that PCA algorithm extracts, influencing each other between initial data ingredient can be eliminated, and think
Think simply, to be easy to realize on computers.It require that converting one-dimensional vector for image array, covariance matrix is caused to be tieed up
Number is excessive, and calculation amount is too big, and the symmetry without utilizing facial image.
Then 2DPCA is suggested, and different based on one-dimensional vector from PCA method, 2DPCA is direct using original image matrix
Covariance matrix is constructed, and extracts principal eigenvector, substantially increases recognition efficiency.Although 2DPCA ratio PCA has higher
Accuracy of identification, but a major issue of 2DPCA is that it needs coefficients more more than PCA to indicate image.2DPCA is substantially
It is to work on the column direction of image, the dimension on line direction is not reduced, and complexity is still very high, therefore has promoted simultaneously
Consider the 2DPCA in row and column direction, i.e., (2D)2PCA.Although compressing while on row and column direction, recognition speed is improved,
Precision has different degrees of reduction.Analysis shows caused since Information Compression is excessive, it is on the other hand, capable and row
Between, be all between the column and the column it is orthogonal, without redundancy, make it difficult to the maximal projection direction for representing projection properties vector.
Summary of the invention
The purpose of the present invention is in view of the deficienciess of the prior art, propose a kind of 2DPCA based on the enhancing of two-way interpolation
Facial image recognition method.Key point is the present invention based on theory of marking the price, by between the feature vector of high value
It is inserted into new vector, it is expected to improve the display degree of characteristic information, is improved under the premise of not increasing bigger computation complexity
The accuracy of identification of image.
The method of the present invention includes 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
The method of extraction characteristic value and feature vector described in step 3, step 2 need to convert image array to it is one-dimensional to
Amount, causes covariance matrix dimension excessive, calculation amount is too big, to solve this problem, using 2DPCA to the training sample in step 1
This extraction characteristic value and feature vector.
The method of extraction characteristic value and feature vector described in step 4, step 3 is worked on the column direction of image,
Dimension on line direction is not reduced, and complexity is still very high, to solve this problem, is used (2D)2PCA is to the instruction in step 1
Practice sample extraction characteristic value and feature vector.
Step 5, using the method for interpolation to step 2, step 3, the extracted feature vector of step 4 carries out interpolation.
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 with
Angle is α between axis of projection u1；G point is any point on V vector, is projected from G point to two axis of projection u1, u2, projected length
Respectively 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 between vector W and the V vector of insertion
α's is gradually reduced, and projected length is gradually increased, and the feature implied gradually highlights.
Step 6 is identified using norm distance method or support vector machine method.
Beneficial effects of the present invention: the present invention between the feature vector of high value by being inserted into new vector, with expectation
The display degree for improving characteristic information, improves the accuracy of identification of image under the premise of not increasing bigger computation complexity.
Detailed description of the invention
Fig. 1: interpolation method schematic diagram；
Fig. 2: support vector cassification schematic diagram；
Fig. 3: flow chart of the present invention.
Specific embodiment
The present invention is further detailed with reference to the accompanying drawing.
As shown in figure 3, the present invention tool first respectively by principal component analysis (PCA), two-dimensional principal component analysis (2DPCA) and pair
To two-dimensional principal component analysis ((2D2) PCA) extract characteristic value and feature vector.Then using interpolation method shown in FIG. 1 to spy
Sign vector is enhanced, and is identified, is specifically included following finally by norm distance and support vector machine method shown in Fig. 2
Step:
ORL face database is divided into training sample and test sample by step 1.
Step 2 extracts characteristic value and feature vector
Step 2.1 extracts characteristic value to the training sample in step 1 with PCA method and feature vector, algorithm are as follows:
If there is the facial image of N number of people in a face database, everyone has niThe image of a different perspectives, is denoted as
Aij∈Rm×n, i=1,2 ..., N；J=1,2 ..., ni (1)
Wherein R represents set set of real numbers, and facial image matrix size is m × n.M and n respectively represents facial image matrix
Line number and columns.
R before being selected from everyone imageiA image is as training, and remaining image is as test.By each people
Face image AijOne-dimensional vector a is converted into according to identical put in orderij∈R1×mn.Each vector is 1 row mn column.
aij=[aij(1),aij(2),…,aij(mn)] (2)
Everyone training sample set is denoted as in this way:
Training sample set is denoted as:
Facial image is converted into the mean value of the one-dimensional vector of formula (2) such as and is denoted as in training sample:
The Mean Matrix of training sample is denoted as:
Wherein
?Reproduction matrix mn column are denoted asMatrix.
Deviation matrix is denoted as:
The covariance matrix of training sample set is denoted as:
Seek the preceding d characteristic value (λ of covariance matrix1≥λ2≥…≥λd) and corresponding feature vector (u1,u2,…,
ud)。
The matrix for being transformed into low-dimensional is denoted as:
Yi=[yi1,yi2,…,yik,…,yij], j=1,2 ..., ni (10)
Wherein
yij=UTaij (11)
U=[u1,u2,…,ur]T (12)
Step 2.2 extracts characteristic value and feature vector to the training sample in step 1 with 2DPCA.
If it is best projection direction that x, which is column direction, after any one sample image A is projected to x, feature after must projecting to
Amount.
It is denoted as:
yij=AijX, i=1,2 ..., N；J=1,2 ..., ri (13)
It determines best projection axis now, introduces the covariance matrix G of sample image At, the association side of projection properties vector Y
Poor matrix Sx, matrix SxMark tr (Sx).By seeking the maximum value of mark, to ask best projection direction.Its criterion are as follows:
J (X)=tr (Sx) (14)
It enables:
Formula 15 is substituted into formula 14 to obtain:
It enables:
Formula 17 is substituted into formula 16 to obtain:
J (X)=xTGtx (20)
The criterion is population variance degree criterion.
To GtSingular value decomposition is done, eigenvalue λ is obtainedi(i=1,2 ..., n), and λ1≥λ2≥…≥λn, singular vector is
ui(i=1,2 ..., n), U=[u1,u2,…,un].So
Formula 18 is substituted into formula 17 to obtain:
In general, it is inadequate for taking a best projection axis, so d main feature before selecting, singular vector ud(i
=1,2 ..., d), eigenvalue λd(i=1,2 ..., d), so Ud=[u1,u2,…,ud], d≤n.
Only work as eigenvalue λ in formula 20iWhen being maximized, corresponding feature vector uiObtain maximum value, uiOn X
Projection just obtain maximum value so that tr (Sx) obtain maximum value.
After seeking best projection axis, any sample image A is projected on axis of projection
yk=Axk, k=1,2 ..., d (24)
Wherein, x1,x2,…,xdFor best projection axis；Projection properties vector y1,y2,…,ydReferred to as sample image A it is main at
Divide vector.
Step 2.3 uses (2D)2PCA method extracts characteristic value and feature vector to the training sample in step 1.
Column mapping equation:
yij=Aijxk, k=1,2 ..., d (25)
Wherein i=1,2 ..., N；J=1,2 ..., ri, yij∈Rm×d。
Row mapping equation:
cij=vTAij, i=1,2 ..., N；J=1,2 ..., ri (26)
Joint Mapping formula:
zij=vTAijX, i=1,2 ..., N；J=1,2 ..., ri (27)
The enhancing of step 3 interpolation method
The method of step 3.1 interpolation method enhancing is as described below:
In Fig. 1,It is the vector at 30 ° of angles, u1 and u2 are two axis of projections.Point z and point o are respectivelyG point arrives on vector
Subpoint on two axis of projections, the length of subpoint to origin are respectively 5,Note
If
Then?On be projected as
For the vector of 45° angle, with vectorBetween angle be 15 °, highlighted hiding feature.
IfWithBetween continue interpolation, be denoted as
Then?On be projected as
WithAngle be 22.5 °,WithAngle be 7.5 °.It can make hiding feature further convex in this way
It shows and.As the density of interpolation increases, so that projecting direction is gradually to direction approximation to be projected, therefore, feature highlights degree
It is more and more obvious.
If arbitrary projection properties vector ui, it is denoted as:
ui=(a, b)T, i=1 ..., d (32)
Maximum projecting direction is determined by seeking s value.So corresponding vector is inserted between any combination in the plane,
Hiding feature can be highlighted to varying degrees.
Step 3.2 respectively carries out formula 11, formula 24 and formula 27 using the method for interpolation described in step 3.1 slotting
Value.
Step 4 identification
It is identified using the method for support vector machines or norm distance.
The identification of 4.1 norm Furthest Neighbors, principle are as follows:
Norm distance definition are as follows:
Difference between two projection properties matrixes of a ' expression.For the training sample projection matrix extracted in step 1,
For test sample projection matrix in step 1.Work as m=1, when, D is PCA projection matrix；As m=2, D represents 2DPCA projection square
Battle array；As m=3, D is (2D) 2PCA projection matrix.
4.2 support vector machines principles are as shown in Figure 2
Model=svmtrain (train_label, train_data, options) (36)
[predict, accuracy]=svmpredict (test_label, test_data, model) (37)
Call svmtrain and svmpredict function.Train_label is training sample label, and train_data is instruction
Practice sample data；Test_label is test sample label, and test_data is test sample data.Predict is the class of prediction
Not, accuracy is precision of prediction.
To sum up: the present invention can improve the accuracy of identification of image under the premise of not increasing bigger computation complexity, tool
There is 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.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111832467A (en) * | 2020-07-09 | 2020-10-27 | 杭州电子科技大学 | Face recognition method combining feature enhancement and network parameter optimization |
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| CN104951774A (en) * | 2015-07-10 | 2015-09-30 | 浙江工业大学 | Palm vein feature extracting and matching method based on integration of two sub-spaces |
| CN108564061A (en) * | 2018-04-28 | 2018-09-21 | 河南工业大学 | A kind of image-recognizing method and system based on two-dimensional principal component analysis |
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| US20030165260A1 (en) * | 2002-03-04 | 2003-09-04 | Samsung Electronics Co, Ltd. | Method and apparatus of recognizing face using 2nd-order independent component analysis (ICA)/principal component analysis (PCA) |
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| CN104951774A (en) * | 2015-07-10 | 2015-09-30 | 浙江工业大学 | Palm vein feature extracting and matching method based on integration of two sub-spaces |
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| CN111832467B (en) * | 2020-07-09 | 2022-06-14 | 杭州电子科技大学 | Face recognition method combining feature enhancement and network parameter optimization |
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