CN106599787B - Single sample face recognition method based on semi-supervised sub-block joint regression - Google Patents
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Abstract
The invention discloses the single sample face recognition method based on semi-supervised sub-block joint regression, face is divided into multiple sub-blocks first by this method；Then it proposes based on semi-supervised sub-block joint regression model to make full use of label and the various change information of the facial image study facial image without label, and the distinctive for influencing model to avoid no label data away from all kinds of equidistant constraints in class label coordinate space without label facial image is added, using non-critical augmentation Lagrange multiplier solving model to obtain mapping matrix corresponding to each sub-block；Realize that the recurrence to test image block is classified by mapping matrix on this basis；Final determining classification results of voting finally are carried out to all test image blocks.Single sample face recognition method of the present invention is to expression, illumination variation and blocks etc. and to have good robustness, and accuracy of identification is high.
Description
Technical field
The present invention relates to single sample face recognition methods, only have a width training image more particularly to each object to be identified
The single sample face recognition method based on semi-supervised sub-block joint regression, belong to technical field of face recognition.
Background technique
In past 40 years, face recognition technology makes remarkable progress, and the face recognition technology under controlled condition is
It is mature on the whole.However under the conditions of non-controllable, due to being illuminated by the light, expression, posture, noise, the influence for the factors such as blocking, face is known
It is not still studying a question for a very challenging property.The most direct method solved these problems be exactly increase training sample, but
Such as identification of identity card identification, passport, the administration of justice confirms, in many practical applications of admission control in practical applications, usually only
One training sample can be acquired, and recognition of face problem in this case is referred to as single sample recognition of face problem
(Single Sample per Person, SSPP), be further exacerbated by it is non-controllable under the conditions of recognition of face difficulty.
Technically, single sample recognition of face has more highlighted the few lance between image data dimension height of training sample
Shield, so that many existing face recognition technologies or the serious performance of appearance decline or can not work at all, thus it is public
It is considered most challenging one of research topic.But said from practical standpoint, everyone single image itself but have acquisition be easy,
Storage cost is small, is convenient for many outstanding advantages such as a wide range of popularization.Therefore, single sample recognition of face problem not only has very strong
Research value, and be also that can not avoid, must solve the problems, such as during face identification system moves towards practical, it solves
This problem is of great immediate significance.
Variation is unable to estimate in class when in order to overcome the problems, such as single specimen discerning, general learning method (generic
Learning the general training set (generic set) containing everyone multiple faces) has been additionally introduced.Since face has
Variation in similar class, it is therefore possible to the facial image changing rules that will learn on generic set to be used to analyze single instruction
Practice the variation of facial image in sample set (gallery set).Based on it is above-mentioned it is assumed that Wang et al. first proposed one it is general
Frame (J.Wang, K.N.Plataniotis, J.Lu, A.N.Venetsanopoulos, " the On solving the of study
face recognition problem with one training sample per subject”.Pattern
Recognition, 2006,39 (9): 1746-1762), then Su (S.Yu, S.Shan, X.Chen, W.Gao, " Adaptive
Generic Learning for Face Recognition from a Single Sample per Person”IEEE
Computer Vision and Pattern Recognition.San Francisco,CA,June 2010:2699-2706)
Adaptive universal study (Adaptive Generic Learning, AGL) method of proposition attempts to use one from general training
The prediction model acquired on collection further improves the hypothesis.Kan et al. (M.Kan, S.Shan, Y.Su, et al. " Adaptive
discriminant learning for face recognition”.Pattern Recognition,2013,46(9):
2497-2509) adaptive discriminant analysis (the Adaptive Discriminant Analysis) method proposed is then based on above-mentioned
The thought of adaptive universal study goes estimation test sample using several training samples in the generic set neighbouring with test sample
Class in Scatter Matrix.Recently, to solve the problems, such as single specimen discerning, document (B.Wang, F.Zhou, W.Li, Z.Li, Q.Liao
“Combining Specific Learning and Generic Learning for Single-Sample Face
Recognition,”5th International Congress on Image and Signal Processing,
Chongqing, Oct.2012:1219-1223) it will specifically learn (Specific Learning) and general study (Generic
Learning it) combines, and Deng et al. (W.Deng, J.Hu, X.Zhou, et al. " Equidistant prototypes
embedding for single sample based face recognition with generic learning and
Incremental learning, " Pattern Recognition, 2014,47 (12): 3738-3749) then based on " equidistant former
Principle proposes a kind of linear regression analysis (linear regression Analysis, LRA) method, and introduces for type insertion "
It is general to learn to promote the generalization ability of this method.
In recent years, although variation is unable to estimate in class when general learning method can alleviate single specimen discerning to a certain extent
Predicament, but its foundation generally assume that not be all suitable in all cases, such as when two set in Genus Homo in not
With race or with the different colours of skin or when the age, and when in the class in generic set variation can not all cover
In class in gallery set when variation.Therefore variation in class in gallery set can more preferably be covered by how finding one
Generic set, and how effectively to excavate changing rule in the class in two set between sample is all that further research needs
Consider the problems of.
Summary of the invention
The technical problems to be solved by the present invention are: providing single sample recognition of face based on semi-supervised sub-block joint regression
Method provides a kind of simple and effective solution for list sample recognition of face problem.
The present invention uses following technical scheme to solve above-mentioned technical problem:
Based on the single sample face recognition method of semi-supervised sub-block joint regression, include the following steps:
Step 1, the training facial image of all classes and test facial image are carried out with equal-sized square window
Piecemeal, square window slip over each pixel of image, and a corresponding pros are obtained at each pixel of image
Shape block, vector corresponding to the square block at the training facial image pixel i of k-th of class are expressed asK=1 ..., K, K table
Show trained facial image total number or total classification number；
Step 2, corresponding square block structure block training sample set at the training facial image pixel i of all classes is utilizedClass label matrix corresponding to it isUtilize all tests
Corresponding square block structure block test sample collection Z at facial image pixel iiIf the class label matrix corresponding to it isN indicates the total number of test facial image；Set block training sample set XiIt is tested with block
Sample set ZiTo its class label matrix Y and YunlabeledMapping matrix be Wi, combine corresponding piece of trained sample at all pixels i
This collection and block test sample collection, to obtain based on semi-supervised joint regression model；
Step 3, by non-critical augmentation Lagrange multiplier solution procedure 2 based on semi-supervised joint regression model,
Obtain the block training sample set and the corresponding mapping matrix W of block test sample collection at all pixels ii；
Step 4, according to mapping matrix Wi, classify to each square block of each test facial image；
Step 5, after the classification for identifying each square block of each test facial image, test is determined by way of ballot
Classification belonging to facial image.
As a preferred solution of the present invention, the detailed process of the step 1 are as follows:
It 1.1 defines in images centered on any one pixel i, the square that radius r, size are (2r+1) × (2r+1)
Block is as the corresponding square block of pixel i；
1.2 using the methods processing image of edge pixel border pictures edge pixel, obtain with the edge pixel of image be
The square block of the heart.
As a preferred solution of the present invention, based on semi-supervised joint regression model described in step 2 are as follows:
Wherein,Indicate block test sample collection ZiBe mapped to [1,
1,…,1]T∈RKWhen the error that generates, E=[E1；E2；…；EM], EiIndicate error, W=[W1；W2；…；WM], α is indicatedError term coefficient, i=1 ..., M, M indicates each trained facial image or tests the square that is divided into of facial image
The total block data of block, λ are indicated | | W | |2,1Regularization coefficient, | | | |2,1Indicate 2,1 norm, T indicates transposition.
As a preferred solution of the present invention, the detailed process of the step 3 are as follows:
Step 2 is following form based on semi-supervised joint regression model conversation by 3.1:
Wherein,W=[W1；W2；…；WM], Yα=[Y, α Yu],i
=1 ..., M, M indicate each trained facial image or test the total block data for the square block that facial image is divided into, and λ is indicated | | W | |2,1
Regularization coefficient, | | | |2,1Indicate 2,1 norm, T indicates transposition；
3.2 introduce an auxiliary variable J for 3.1 objective function, obtain:
3.2 objective function is converted to Augmented Lagrangian Functions L by 3.3:
Wherein, J=[J1；J2；…；JM], G, H indicate Lagrange multiplier, G=[G1；G2；…；GM], H=[H1；
H2；…；HM], the mark of Tr () representing matrix, | | | |FIndicate F norm, μ is the punishment parameter greater than 0；
3.4Eα, J, W, G, H are initialized as 0, μ=0.5, fix other unknown numbers, update W, then the objective function of model turns
Turn to the objective function for seeking W as follows:
The more new formula that 3.5 objective functions for solving 3.4 obtain W is as follows:
Wherein, t indicates the number of iterations, and I is unit battle array；
3.6 fix other unknown numbers, update J, obtain following Lagrangian subproblem:
The objective function is converted toForm, wherein S=J；It has following closed solution:
3.7 fix other unknown numbers, update E in the following wayα:
Objective function is decomposed into M following subproblem in 3.8 above-mentioned 3.7:
The objective function is converted toForm, whereinIt has following closed solution:
3.9 update Lagrange multiplier:
3.10 μ: μ=min of undated parameter (ρ μ, μmax), wherein ρ=1.1, μmax=1010；
3.11 check whether and meet the following condition of convergence:
||Jt+1-Wt+1||∞<ε
Wherein, ε=10-8, when being unsatisfactory for the above-mentioned condition of convergence, 3.4-3.11 is repeated, until meeting the condition of convergence.
As a preferred solution of the present invention, the formula of classification described in step 4 are as follows:
Wherein, z indicates a test facial image, ziIndicate the corresponding square block of test facial image pixel i to
Amount expression, label (zi) indicate ziAffiliated class label,It indicates to utilize corresponding mapping square at pixel i
Battle array WiBy ziIt is mapped to the categorization vector corresponding to it, and takes the maximum class label the most final of categorization vector intermediate value,
K=1,2 ..., K, K indicate that the total number of training facial image or total classification number, T indicate transposition.
The invention adopts the above technical scheme compared with prior art, has following technical effect that
1, on the one hand single sample face recognition method of the present invention is portrayed in class due to introducing more unlabeled exemplars
Variation to expression, illumination variation and blocks etc. and to have good robustness, thus accuracy of identification with higher；On the other hand
Since the sample of no label is mapped to [1,1 ..., 1]T∈RK, distance is every a kind of in Tag Coordinate Space is equidistant,
It will not influence the discriminating power of model.
2, single sample face recognition method of the present invention is not necessarily to feature extraction, classifies simple and easy；And mark is taken full advantage of
The information of label and unlabeled exemplars.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow charts of the single sample face recognition method of semi-supervised sub-block joint regression.
Fig. 2 is that the present invention is based on image blocks in the single sample face recognition method of semi-supervised sub-block joint regression to illustrate
Figure.
Fig. 3 is that the present invention is based on the test specimens without label in the single sample face recognition method of semi-supervised sub-block joint regression
Originally the geometric interpretation schematic diagram in Tag Coordinate Space.
Specific embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the accompanying drawings.Below by
The embodiment being described with reference to the drawings is exemplary, and for explaining only the invention, and is not construed as limiting the claims.
Face change information is actually contained in the test facial image of no label, therefore in single sample recognition of face
It fully considers the test facial image of no label, can effectively learn facial image variation, to avoid general learning method pair
The dependence and limitation of general training sample set.Based on this idea, the present invention proposes that one kind is combined back based on semi-supervised sub-block
The single sample face recognition method returned.
As shown in Figure 1, the present invention is based on the single sample face recognition method of semi-supervised sub-block joint regression, including following step
It is rapid:
1, piecemeal is carried out to the training facial image of all classes and test facial image with equal-sized square window,
Square window slips over each pixel of image, and a corresponding square block is obtained at each pixel of image,
It is specific as follows:
(1) facial image of all one training samples and test sample is divided into the block of multiple overlappings, each piece of center
One pixel of correspondence image, centered on the pixel, radius for r square window carry out piecemeal.That is scheme
As any one pixel i, corresponding one be (2r+1) × (2r+1) by center size of the pixel square block, be expressed as to
Amount form isWherein k indicates the sample of kth class.Above-mentioned fixation is used to all trained facial images and test facial image
The square block of size carries out piecemeal, the pixel in the correspondence image of block center, as shown in Figure 2.
(2) it for image edge pixels, is handled using the method for edge pixel border picture due to bulk is beyond image border
The phenomenon that causing its interior section pixel value to lack, obtain the bulk centered on image edge pixels.
2, corresponding square block structure block training sample set X at the training facial image pixel i of all classes is utilizedi,
Corresponding class label isY∈RK×K, RK×KIndicate the space of K × K, it is assumed that
Block training set XiMapping matrix to its class label matrix Y is Wi, reflected by the way that all sub-blocks of regression model joint solution are corresponding
Penetrate matrix Wi, the specific steps are as follows:
(1) block training sample setWhereinIt indicates k-th or class training facial image is in pixel
Corresponding square block at i, k=1,2 ..., K, K indicate to train the total number of facial image or total classification number；
(2) by block training sample setCorresponding class label is defined asY∈RK×K, it is assumed that block training set XiTo the mapping matrix of its class label matrix Y
For Wi, the corresponding regression model of the sub-block can indicate are as follows: YT=(Xi)TWi+Ei, wherein EiIndicate error；
(3) the mapping matrix W of all sub-blocks is solved using following objective function jointi:
Wherein, E=[E1；E2；…；EM], W=[W1；W2；…；WM], i=1,2 ..., M, M indicate sub-block number, and λ is indicated |
|W||2,1Regularization coefficient, | | | |2,1It indicates 2,1 norm, can effectively inhibit noise and outlier.
3, take whether there is or not the test samples of label at pixel i and in training sample same size sub-block, constitute block
Test sample collection Zi, the class label of these test samples is unknown, but due in step 2 regression model only used uniquely
One training sample, be unable to fully the change information that face is arrived in study, therefore the present invention is by block test set ZiIt is mapped toTo obtain based on semi-supervised joint regression model, which can make full use of people
The change information of face, while all test samples are mapped to [1,1 ..., 1]T∈RKIt can guarantee that the test sample of no label exists
The distance of the every one kind of distance is equal in Tag Coordinate Space, in this way can while making full use of face change information guarantor
Demonstrate,prove these samples without tag attributes, the geometric interpretation in Tag Coordinate Space is as shown in Figure 3.This is based on semi-supervised son
Block joint regression model is as follows:
Wherein,N indicates test sample number,Indicate block test set ZiBe mapped to [1,1 ..., 1]T∈RKWhen generate
Error, α are indicated | | Eunlabeled||2,1Error term coefficient.
4, by the semi-supervised joint regression model of non-critical augmentation Lagrange multiplier solution procedure 3, owned
The corresponding mapping matrix W of sub-blocki, the specific steps are as follows:
(1) it is following form based on semi-supervised joint regression model conversation by step 3:
Wherein, Yα=[Y, α Yunlabeled],W=[W1；W2；…；
WM], λ is indicated | | W | |2,1Regularization coefficient, | | | |2,1Indicate 2,1 norms；
(2) an auxiliary variable J is introduced for the objective function of (1):
(3) objective function of (2) is converted into Augmented Lagrangian Functions L:
Wherein, the mark of Tr () representing matrix, J=[J1；J2；…；JM], G, H indicate Lagrange multiplier, G=[G1；
G2；…；GM], H=[H1；H2；…；HM], T indicates that transposition, μ are the punishment parameter greater than 0；
(4) first by Eα, J, W, G, H are initialized as 0, μ=0.5, μmax=1010, ρ=1.1, ε=10-8；
(5) E is updated using alternating minimizationα, J, W, G, H fix other unknown numbers, update W, then the target letter of model
Number can be converted into the objective function for seeking W as follows:
(6) solve (5) objective function can obtain W more new formula it is as follows:
Wherein I is unit battle array, and t indicates the number of iterations；
(7) other unknown numbers are fixed, following Lagrangian subproblem can be obtained:
The objective function can be converted toForm, wherein S=J；It has following closed solution:
J is updated by above-mentioned formula；
(8) other unknown numbers are fixed, update E in the following wayα:
(9) objective function can be decomposed into M following subproblem in above-mentioned (8):
The objective function also can be convertedForm, whereinThere is following closed solution:
(10) Lagrange multiplier is updated:
Gt+1=Gt+μ(Jt+1-Wt+1)
(11) μ: μ=min of undated parameter (ρ μ, μmax)；
(12) it checks whether and meets the following condition of convergence:
||Jt+1-Wt+1||∞<ε
Wherein, ε=10-8, when being unsatisfactory for the above-mentioned condition of convergence, repeat (5)-(12), until meeting the condition of convergence.
5, according to the mapping matrix W of each sub-block locationsi, each square block of each test facial image is divided
Class, classification formula are as follows:
Wherein, z indicates a test sample, ziIndicate the vector of the corresponding square block of pixel i of test facial image
It indicates, label (zi) indicate ziAffiliated class label,It indicates to utilize corresponding mapping square at pixel i
Battle array WiBy ziIt maps with the categorization vector corresponding to it, and takes the maximum class label the most final of categorization vector intermediate value.
6, it after the classification for identifying each test face block, is finally determined belonging to test facial image by the method for ballot
Classification.
The present invention is based on the single sample face recognition method of semi-supervised sub-block joint regression, every piece of classification can grasp parallel
Make, the method for the present invention has very strong robustness to illumination variation, can be under conditions of independent of additional training sample set
Still obtain preferable performance, at the same to illumination, expression, block, time change all has good robustness.
The above examples only illustrate the technical idea of the present invention, and this does not limit the scope of protection of the present invention, all
According to the technical idea provided by the invention, any changes made on the basis of the technical scheme each falls within the scope of the present invention
Within.
Claims (4)
1. the single sample face recognition method based on semi-supervised sub-block joint regression, which comprises the steps of:
Step 1, piecemeal is carried out to the training facial image of all classes and test facial image with equal-sized square window,
Square window slips over each pixel of image, and a corresponding square block is obtained at each pixel of image,
Vector corresponding to square block at the training facial image pixel i of k-th of class is expressed asK indicates instruction
The total number of white silk facial image or total classification number；
Step 2, corresponding square block structure block training sample set at the training facial image pixel i of all classes is utilizedClass label matrix corresponding to it isY∈RK×K；Utilize all tests
Corresponding square block structure block test sample collection Z at facial image pixel iiIf the class label matrix corresponding to it isN indicates the total number of test facial image；Set block training sample set XiIt is tested with block
Sample set ZiTo its class label matrix Y and YunlabeledMapping matrix be Wi, combine corresponding piece of trained sample at all pixels i
This collection and block test sample collection, to obtain based on semi-supervised joint regression model；
It is described based on semi-supervised joint regression model are as follows:
Wherein,Indicate block test sample collection ZiBe mapped to [1,1 ..., 1]T
∈RKWhen the error that generates, E=[E1；E2；…；EM], EiIndicate error, W=[W1；W2；…；WM], α is indicated's
Error term coefficient, i=1 ..., M, M indicate the total block data for the square block that each trained facial image or test facial image are divided into,
λ is indicated | | W | |2,1Regularization coefficient, | | | |2,1Indicate 2,1 norm, T indicates transposition；
Step 3, it is obtained by non-critical augmentation Lagrange multiplier solution procedure 2 based on semi-supervised joint regression model
The corresponding mapping matrix W of block training sample set and block test sample collection at all pixels ii；
Step 4, according to mapping matrix Wi, classify to each square block of each test facial image；
Step 5, after the classification for identifying each square block of each test facial image, test face is determined by way of ballot
Classification belonging to image.
2. the single sample face recognition method according to claim 1 based on semi-supervised sub-block joint regression, which is characterized in that
The detailed process of the step 1 are as follows:
1.1 define in images centered on any one pixel i, the square block that radius r, size are (2r+1) × (2r+1) is made
For the corresponding square block of pixel i；
1.2 handle the edge pixel of image using the method for edge pixel border picture, obtain centered on the edge pixel of image
Square block.
3. the single sample face recognition method according to claim 1 based on semi-supervised sub-block joint regression, which is characterized in that
The detailed process of the step 3 are as follows:
Step 2 is following form based on semi-supervised joint regression model conversation by 3.1:
Wherein,W=[W1；W2；…；WM], Yα=[Y, α Yu],I=
1 ..., M, M indicate each trained facial image or test the total block data for the square block that facial image is divided into, and λ is indicated | | W | |2,1's
Regularization coefficient, | | | |2,1Indicate 2,1 norm, T indicates transposition；
3.2 introduce an auxiliary variable J for 3.1 objective function, obtain:
3.2 objective function is converted to Augmented Lagrangian Functions L by 3.3:
Wherein, J=[J1；J2；…；JM], G, H indicate Lagrange multiplier, G=[G1；G2；…；GM], H=[H1；H2；…；
HM], the mark of Tr () representing matrix, | | | |FIndicate F norm, μ is the punishment parameter greater than 0；
3.4Eα, J, W, G, H are initialized as 0, μ=0.5, fix other unknown numbers, update W, then the objective function of model is converted into
The objective function of W is sought as follows:
The more new formula that 3.5 objective functions for solving 3.4 obtain W is as follows:
Wherein, t indicates the number of iterations, and I is unit battle array；
3.6 fix other unknown numbers, update J, obtain following Lagrangian subproblem:
The objective function is converted toForm, wherein S=J；It has following closed solution:
3.7 fix other unknown numbers, update E in the following wayα:
Objective function is decomposed into M following subproblem in 3.8 above-mentioned 3.7:
The objective function is converted toForm, whereinIt has following closed solution:
3.9 update Lagrange multiplier:
3.10 μ: μ=min of undated parameter (ρ μ, μmax), wherein ρ=1.1, μmax=1010；
3.11 check whether and meet the following condition of convergence:
||Jt+1-Wt+1||∞<ε
Wherein, ε=10-8, when being unsatisfactory for the above-mentioned condition of convergence, 3.4-3.11 is repeated, until meeting the condition of convergence.
4. the single sample face recognition method according to claim 1 based on semi-supervised sub-block joint regression, which is characterized in that
The formula of classification described in step 4 are as follows:
Wherein, z indicates a test facial image, ziIndicate the vector table of the corresponding square block of test facial image pixel i
Show, label (zi) indicate ziAffiliated class label,It indicates to utilize corresponding mapping matrix W at pixel ii
By ziIt is mapped to the categorization vector corresponding to it, and takes the maximum class label the most final of categorization vector intermediate value, k=
1,2 ..., K, K indicate that the total number of training facial image or total classification number, T indicate transposition.
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| CN109241827B (en) * | 2018-07-23 | 2021-07-20 | 江苏大学 | Face recognition method based on multi-core integration regression |
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