CN108921088A - A kind of face identification method based on discriminate target equation - Google Patents
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Abstract
The invention discloses a kind of face identification methods based on discriminate target equation, first with the first training sample come linear expression test sample, and construct first object equation, then first category corresponding to the least residual of test sample is calculated, carry out linear expression test sample again for first category corresponding to least residual as the second training sample, then the second target equation is constructed, second category corresponding to the least residual of test sample is obtained by calculating the second target equation, second category corresponding to least residual is classification belonging to test sample, method of the invention passes through the Quadric Representation of A to test sample and the calculating of residual error twice, reduce the design complexities during picture classification, face can more accurately be sorted out, and there is very strong robustness under different illumination and posture.
Description
Technical field
The present invention relates to image identification technical field, especially a kind of recognition of face side based on discriminate target equation
Method.
Background technique
Recognition of face is always the hot issue in the fields such as pattern-recognition, image procossing, computer vision, and rarefaction representation
Very big concern is just caused since being suggested for image classification, and rarefaction representation all has very strong property in many applications
Can, the sparse representation method for image classification can be divided into two kinds：Based on original training sample (thetraining
Sample-based) and it is based on dictionary (dictionary-based), the rarefaction representation based on original training sample directly utilizes
Original sample indicates test sample as atom, and the rarefaction representation based on dictionary uses algorithm and original training sample first
Dictionary is obtained, test sample is then indicated using dictionary, rarefaction representation is shown in many application programs due to its characteristic
High performance, however available sparse representation method still has some problems, such as computation complexity height, low efficiency, treats
When different illumination, facial expression and posture difference the disadvantages of poor robustness.
Summary of the invention
To solve the above problems, the purpose of the present invention is to provide a kind of recognition of face sides based on discriminate target equation
Method, by two step residual computations, for traditional rarefaction representation, design complexities are lower, can be more accurate point
Class goes out face, and has very strong robustness under different illumination and posture.
Technical solution used by the present invention solves the problems, such as it is：
A kind of face identification method based on discriminate target equation, includes the following steps：
A, face sample is divided into the first training sample and test sample, and with the first training sample linear expression test specimens
This；
B, constructing first object equation and solving first indicates coefficient；
C, first category corresponding to least residual is obtained according to the residual error that the first expression coefficient calculates test sample, it is minimum
First category corresponding to residual error is the second training sample；
D, with the second training sample linear expression test sample；
E, constructing the second target equation and solving second indicates coefficient；
F, second category corresponding to least residual is obtained according to the residual error that the second expression coefficient calculates test sample, it is minimum
Second category corresponding to residual error is classification belonging to test sample.
Further, the step A is in the first training sample linear expression test sample, the expression of the test sample
Formula：
Y=b1x1+b2x2+…+bNxN=BX；
Wherein y is test sample, x1, x1..., xNFor the first training sample, X=[x1, x1..., xN], b1, b2...,
bNCoefficient, B=[b are indicated for corresponding first1, b2..., bN]T, N is the first face sample, and N=n*L, L are people in face database
The quantity of face image, n are the quantity of difference photo possessed by each facial image, a secondary facial image containing x pixel
It is represented as a column vector xi∈Rx×1, test sample y is represented as column vector y ∈ Rx×1。
Further, the step B constructs first object equation and solves first and indicates in coefficient, the first object equation
Expression formula be：
Wherein δ is a normal number, and y is test sample, and X is the first training sample,
X=[x1, x2..., xN], B=[b1, b2..., bN]T,
Bi=[bn(i-1)+1, bn(i-1)+2..., bni]T,
Bj=[bn(j-1)+1, bn(j-1)+2..., bnj]T, (i=1 .., L；J=1 ..., n), L is L people in face database
Facial image, n are the quantity of difference photo possessed by each facial image；First object equation is calculated and is used in combinationTable
Show calculated result, wherein
XC=[x1, x2..., xn]。
Further, the step C is obtained corresponding to least residual according to the residual error that the first expression coefficient calculates test sample
First category the specific steps are：According to the residual error f between test sample and i-th the first training sample of classiIt is calculated s
First category corresponding to least residual, wherein residual error fiExpression formula be：
fi=| | y-bijxij‖2；
Wherein (i=1 .., L；J=1 ..., n), L is the quantity of facial image in face database, and n is each facial image institute
The quantity for the different photos having, bijFirst indicates coefficient, x corresponding to jth photo for i-th faceijIt is i-th
The jth of face photo.
Further, in the second training sample linear expression test sample, the test sample is the step D：
Y=d1z1+d2z2+…+drzr=DZ；
Wherein y is test sample, and r is the second face sample, and r=s*n, s are the Minimum Residual being calculated in the step C
The quantity of first category corresponding to difference, Z are the second training sample, Z=[z1, z2..., zr], n be each first category in not
With the quantity of photo, D is the second expression coefficient, D=[d1, d2..., dr]T。
Further, the step E constructs the second target equation and solves second and indicates in coefficient, the second target equation
For：
Wherein δ is a normal number, and y is test sample, and Z is the second training sample, Z=[z1, z2..., zr], D
Two indicate coefficient, D=[d1, d2..., dr]T, s is the quantity of first category corresponding to least residual；
Di=[dn(i-1)+1, dn(i-1)+2..., dni]T,
Dj=[dn(j-1)+1, dn(j-1)+2..., dnj]T, (i=1 .., s；J=1 ..., n), n is each of first category
The quantity of difference photo possessed by facial image；Second target equation is calculated and is used in combinationIndicate calculated result, wherein
Further, the step F is obtained corresponding to least residual according to the residual error that the second expression coefficient calculates test sample
Second category the specific steps are：According to the residual error g between test sample and i-th the second training sample of classiIt is calculated most
Second category corresponding to small residual error, wherein residual error giExpression formula be：
gi=| | y-dijzij||2；
Wherein (i=1 .., s；J=1 ..., n), dijSecond indicates system corresponding to jth photo for i-th face
Number, zijFor the jth photo of i-th face.
The beneficial effects of the invention are as follows：A kind of face identification method based on discriminate target equation that the present invention uses,
By constructing two kinds of target equations, Quadric Representation of A, and the calculating by carrying out residual error twice are carried out to test sample, reduce figure
Design complexities in piece assorting process can more accurately sort out face, and have under different illumination and posture
Very strong robustness.
Detailed description of the invention
The invention will be further described with example with reference to the accompanying drawing.
Fig. 1 is a kind of flow chart of the face identification method based on discriminate target equation of the present invention.
Specific embodiment
Referring to Fig.1, a kind of face identification method based on discriminate target equation of the invention, includes the following steps：
A, face sample is divided into the first training sample and test sample, and with the first training sample linear expression test specimens
This.
Assuming that there is the face of L people in face database, everyone has n different photos, therefore a total of N number of first face
Sample, wherein N=n*L, if a secondary facial image containing x pixel can be expressed as a column vector xi∈Rx×1, enable P=
[X1, X2..., XC..., XL], wherein XC=[x1, x2..., xn], (C=1,2 ..., L), test sample be represented as column to
Measure y ∈ Rx×1, therefore can be with the first training sample come linear expression test sample, wherein the expression formula of test sample is：
Y=b1x1+b2x2+…+bNxN=BX；
B is the first expression coefficient, B=[b in above formula1, b2..., bN]T, X is the first training sample, X=[x1, x1...,
xN]。
B, constructing first object equation and solving first indicates coefficient.
The expression formula of constructed first object equation is：
Wherein δ is a normal number, each section when it takes a suitable value, in the expression formula of test sample y
Good effect, B=[b can be obtained1, b2..., bN]T, Bi=[bn(i-1)+1, bn(i-1)+2..., bni]T；Bj=[bn(j-1)+1,
bn(j-1)+2..., bnj]T, wherein (i=1 .., L；J=1 ..., n), first object equation is calculated and is used in combinationIndicate meter
It calculates as a result, wherein
C, first category corresponding to least residual is obtained according to the residual error that the first expression coefficient calculates test sample, it is minimum
First category corresponding to residual error is the second training sample.
Assume initially that fiThe residual error between test sample y and i-th the first training sample of class is represented, residual error is smaller, represents examination
Sample y and i-th the first training sample of class are closer, by calculating residual error fiSize, corresponding to available s least residual
First category, residual error fiExpression formula be：
fi=| | y-bijxij||2；
Wherein (i=1 .., L；J=1 ..., n), bijFirst indicates system corresponding to jth photo for i-th face
Number, xijFor the jth photo of i-th face.
First category corresponding to obtained s least residual is the second training sample in step C.
D, with the second training sample linear expression test sample.
First category corresponding to s least residual a total of r the second face samples, wherein r=s*n, each first
There are n different photos in classification, it then can be with this r face sample come linear expression test sample, the table of test sample
It is up to formula：
Y=d1z1+d2z2+…+drzr=DZ；
Z is the second training sample, Z=[z1, z2..., zr], D is the second expression coefficient, D=[d1, d2..., dr]T, contain
There is the column vector z of classification corresponding to the least residual of z pixeli∈Rz×1It indicates, enables P1=[Z1, Z2..., ZE..., Zs],
Wherein ZE=[z1, z2..., zn], (E=1,2 ..., L).
E, constructing the second target equation and solving second indicates coefficient.
Wherein the expression formula of the second target equation is：
Wherein δ is a normal number, and y is test sample, D=[d1, d2..., dr]T, s is the corresponding to least residual
A kind of other quantity；
Di=[dn(i-1)+1, dn(i-1)+2..., dni]T,
Dj=[dn(j-1)+1, dn(j-1)+2..., dnj]T, (i=1 .., s；J=1 ..., n)；
Second target equation is calculated and is used in combinationIndicate calculated result, wherein
Wherein
F, second category corresponding to least residual is obtained according to the residual error that the second expression coefficient calculates test sample.
Assume initially that giThe residual error between test sample h and i-th the second training sample of class is represented, residual error is smaller, represents and surveys
This h of sample and i-th the second training sample of class are closer, by calculating residual error giSize, corresponding to available least residual
Second category, wherein residual error giExpression formula be：
gi=| | y-dijzij||2；
(i=1 .., s；J=1 ..., n), dijSecond indicates coefficient corresponding to jth photo for i-th face,
zijPhoto is opened for the jth of i-th face, second category corresponding to the smallest residual error is classification belonging to test sample, at this time
It is considered that the face in test sample belongs to that the smallest class facial image of residual error.
Method of the invention constructs target equation first with the first all training samples come linear expression test sample
(i.e. first object equation) finds first category corresponding to s least residual by solving residual error, then minimum by this s
First category corresponding to residual error carrys out linear expression test sample again, finally by new target equation (i.e. second mesh
Mark equation) solve second category corresponding to least residual, to realize the classification of face, biggest advantage of the present invention be using
New discriminate target equation, this new discriminate target equation directly strengthens the class inherited of sample, then passes through two
Residual computations are walked, face can be more accurately sorted out, reduce the design complexities in picture classification, and in different illumination
And have very strong robustness under posture.
Method of the invention generally includes two steps, and first step includes step A, B, C, and second step includes
Step D, E, F, previous step are the residual computations of the test sample for being indicated with the first training sample, are surveyed by calculating
The residual error of sample sheet obtains the second training sample, to reduce the scope, then indicates test specimens again with the second training sample
This, and the least residual of test sample is calculated, second category corresponding to finally obtained least residual is exactly test sample institute
The classification of category is considered that testing face belongs to that the smallest class facial image of residual error.
The present invention is tested by multiple authentication, when the quantity s=5 of the first category corresponding to the least residual, the present invention
Recognition correct rate highest.
In order to verify effectiveness of the invention, by method of the invention and CRC, L1LS, FISTA, INNC, FCM, LDA,
The methods of Homotopy, DALM are compared, and primary data is set as the face quantity L=40 in face database, everyone is different
The number of pictures n=10 of posture, so entire face database a total of 400 (40*10) face picture, takes each face respectively
2-6 different photos, that is, 80-240 photos are used as training sample in total, other remaining facial images are then as survey
Sample sheet, specific test result are as shown in table 1：
Table 1 (accuracy of method and other image-recognizing methods of the invention)
By the data in table 1 it is found that the quantity for the photo no matter method of the invention chooses each face is how many, this hair
The accuracy of bright method will be better than other methods, by table 1 statistics indicate that method of the invention and existing sparse table
Show that the method for image classification is higher compared to correctness, design is also simpler, and robustness and high efficiency are higher.
The above, only presently preferred embodiments of the present invention, the invention is not limited to above embodiment, as long as
It reaches technical effect of the invention with identical means, all should belong to protection scope of the present invention.
Claims (7)
1. a kind of face identification method based on discriminate target equation, it is characterised in that：Include the following steps：
A, face sample is divided into the first training sample and test sample, and with the first training sample linear expression test sample；
B, constructing first object equation and solving first indicates coefficient；
C, first category corresponding to least residual, least residual are obtained according to the residual error that the first expression coefficient calculates test sample
Corresponding first category is the second training sample；
D, with the second training sample linear expression test sample；
E, constructing the second target equation and solving second indicates coefficient；
F, second category corresponding to least residual, least residual are obtained according to the residual error that the second expression coefficient calculates test sample
Corresponding second category is classification belonging to test sample.
2. a kind of face identification method based on discriminate target equation according to claim 1, it is characterised in that：It is described
Step A is in the first training sample linear expression test sample, the expression formula of the test sample：
Y=b1x1+b2x2+…+bNxN=BX；
Wherein y is test sample, x1, x1..., xNFor the first training sample, X=[x1, x1..., xN], b1, b2..., bNFor
Corresponding first indicates coefficient, B=[b1, b2..., bN]T, N is the first face sample, and N=n*L, L are face figure in face database
The quantity of picture, n are the quantity of difference photo possessed by each facial image, and a secondary facial image containing x pixel is by table
It is shown as a column vector xi∈Rx×1, test sample y is represented as column vector y ∈ Rx×1。
3. a kind of face identification method based on discriminate target equation according to claim 1, it is characterised in that：It is described
Step B, which constructs first object equation and solves first, indicates in coefficient that the expression formula of the first object equation is：
Wherein δ is a normal number, and y is test sample, and X is the first training sample, X=[x1, x2..., xN], B is the first table
Show coefficient, B=[b1, b2..., bN]T,
Bi=[bn(i-1)+1, bn(i-1)+2..., bni]T,
Bj=[bn(j-1)+1, bn(j-1)+2..., bnj]T, (i=1 .., L；J=1 ..., n), L is the number of facial image in face database
Amount, n are the quantity of difference photo possessed by each facial image；First object equation is calculated and is used in combinationIt indicates to calculate
As a result, wherein
XC=[x1, x2..., xn]。
4. a kind of face identification method based on discriminate target equation according to claim 3, it is characterised in that：It is described
Step C obtains the specific steps of first category corresponding to least residual according to the residual error that the first expression coefficient calculates test sample
For：According to the residual error f between test sample and i-th the first training sample of classiIt is calculated first corresponding to s least residual
Classification, wherein residual error fiExpression formula be：
fi=| | y-bijxij||2；
Wherein (i=1 .., L；J=1 ..., n), L is the quantity of facial image in face database, and n is had by each facial image
Different photos quantity, bijFirst indicates coefficient, x corresponding to jth photo for i-th faceijFor i-th face
Jth photo.
5. a kind of face identification method based on discriminate target equation according to claim 1, it is characterised in that：It is described
With in the second training sample linear expression test sample, the test sample is step D：
Y=d1z1+d2z2+…+drzr=DZ；
Wherein y is test sample, and r is the second face sample, and r=s*n, s are the least residual institute that is calculated in the step C
The quantity of corresponding first category, Z are the second training sample, Z=[z1, z2..., zr], n is different in each first category shines
The quantity of piece, D are the second expression coefficient, D=[d1, d2..., dr]T。
6. a kind of face identification method based on discriminate target equation according to claim 1, it is characterised in that：It is described
Step E, which constructs the second target equation and solves second, indicates in coefficient that the second target equation is：
Wherein δ is a normal number, and y is test sample, and Z is the second training sample,
Z=[z1, z2..., zr], D is the second expression coefficient, D=[d1, d2..., dr]T, s is first corresponding to least residual
The quantity of classification；
Di=[dn(i-1)+1, dn(i-1)+2..., dni]T,
Dj=[dn(j-1)+1, dn(j-1)+2..., dnj]T, (i=1 .., s；J=1 ..., n), n is each of first category face
The quantity of difference photo possessed by image；Second target equation is calculated and is used in combinationIndicate calculated result, wherein
ZE=[z1, z2..., zn]。
7. a kind of face identification method based on discriminate target equation according to claim 6, it is characterised in that：It is described
Step F obtains the specific steps of second category corresponding to least residual according to the residual error that the second expression coefficient calculates test sample
For：According to the residual error g between test sample and i-th the second training sample of classiThe second class corresponding to least residual is calculated
Not, wherein residual error giExpression formula be：
gi=| | y-dijzij||2；
Wherein (i=1 .., s；J=1 ..., n), dijSecond indicates coefficient, z corresponding to jth photo for i-th faceij
For the jth photo of i-th face.
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