CN109522841A - A kind of face identification method restored based on group's rarefaction representation and low-rank matrix - Google Patents
A kind of face identification method restored based on group's rarefaction representation and low-rank matrix Download PDFInfo
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Abstract
The present invention provides one kind to block face identification method, belongs to pattern-recognition, field of face identification.There is illumination, block, the recognition of face when noise pollution in this method, propose a kind of to block face identification method based on what group's rarefaction representation and low-rank matrix restored for training set and test set sample standard deviation.Method includes: to obtain target occlusion facial image;Target occlusion facial image is pre-processed, obtains the sample data of target occlusion facial image as test sample data;By training sample human face data by spatial transform to log-domain, restore every subclass training sample by low-rank matrix recovery algorithms;Learn the low-rank mapping relations matrix between the low-rank ingredient and original training data that restore, test sample is mapped under its potential subspace using the matrix, removes error percentage present in test sample;Group rarefaction representation of the test sample restored on the training set of recovery is calculated, and class association reconstructed residual is combined to be identified with class incidence coefficient.Thus, it is possible to improve the discrimination and robustness for blocking face.
Description
Technical field
The invention belongs to pattern-recognitions, technical field of face recognition, are related to a kind of based on group's rarefaction representation and low-rank matrix
The face identification method method of recovery.
Background technique
With the universal of modern terminal and application, face recognition technology is because its is convenient, fast, safety, non-reproduction etc.
Feature becomes the research hotspot of image procossing, area of pattern recognition at this stage, learning value with higher and extensive market
Application prospect is a challenging job.It by scholars' years of researches and explores, face recognition technology is at present
Great successes are achieved, but most of research is all built upon and controls in stringent environment, is not suitable for the complicated modern times
The application scenarios of change.With smart phone, digital camera and intelligent monitor system being widely used in real life, face
Research of the recognition result under complex condition, without constraint environment is known as hot topic.
Recognition of face has a wide range of applications as a kind of ideal authentication means, human face data sample class
It is not more, but the sample number of every class is relatively fewer, simultaneously because the similitude in different faces structure, so that human face data has greatly
Class in divergence and small class scatter, this is numerous scholar institute facing challenges for being engaged in face recognition study.Rarefaction representation
It is the popular research direction of current field of face identification, proposes this method for facial image training image linear expression to be identified,
Then it identifies that is substantially taken is the presentation class strategy across classification to face using class association reconstructive residual error, can see
Work is that arest neighbors, the nearest feature line and arest neighbors characteristic face (are waited using the extension for indicating policy classifier in class, the theory
Frame excites the proposition of a series of innovatory algorithm, such as sparse representation method based on Gabor characteristic dictionary, robust sparse table
Show method, and the classification method etc. based on sparse-dense hybrid representation.
Sparse representation method is primarily present two problems.First, it is in ideal feelings that this method, which requires training sample,
Acquired under condition, and when exist in training facial image largely as blocking, variation caused by the factors such as expression, noise error
When, the facial image sample that can destroy same individual is located at this hypothesis of lower-dimensional subspace.Second, rarefaction representation is to pass through solution
One l1The linear regression model (LRM) of norm regularization constraint, due to the similitude between different faces mode, resulting expression coefficient
Although sparse, these sparse nonzero coefficients are often distributed in multiple classifications, are easy to cause misclassification.For sparse table
Show that the first problem of method, a solution route are to isolate distinctive from the training sample data that there is complicated variation
Identity information, such as current relatively broad Robust Principal Component Analysis algorithm used, which can be by contaminated sample data
Matrix decomposition is that a low-rank approaches the sum of matrix and a sparse error matrix.There is scholar to constrain structure non-correlation to introduce
Into low-rank matrix recovery, enhancing restores the taste of low-rank data, and low-rank representation and low-rank matrix are further restored skill
Art combines for restoring potential low-rank structure in data, and the original contamination data by learning and recovery low-rank number
Mapping relations matrix between corrects test sample.Solution for Second Problem is to solve test sample
When indicating coefficient, label supervision message is introduced, the expression coefficient acquired is concentrated on as much as possible in a small number of classifications, i.e.,
Obtain the sparse expression of group.
Summary of the invention
In view of this, the purpose of the present invention is to provide a kind of face knowledges restored based on group's rarefaction representation and low-rank matrix
Other method.This method restores every subclass by low-rank matrix recovery algorithms first by facial image by spatial transform to log-domain
Training sample.Then, study restores the low-rank mapping relations matrix between low-rank ingredient and original training data, and utilizes the square
Test sample is mapped under its potential subspace by battle array.Finally, calculating the test sample restored on the training set of recovery
Group's rarefaction representation, and identified.While reducing algorithm complexity as far as possible, solves training set and test set sample standard deviation is deposited
Illumination, block, noise pollution when recognition of face problem.
In order to achieve the above objectives, the invention provides the following technical scheme:
A kind of face identification method restored based on group's rarefaction representation and low-rank matrix, comprising the following steps:
Step 1) obtains target occlusion facial image;It is pre-processed, as test sample data;
Step 2) carries out log-domain transformation, restores every subclass training sample by low-rank matrix recovery algorithms;
Step 3) study restores the low-rank mapping relations matrix between low-rank ingredient and original training data, and utilizes the square
Test sample is mapped under its potential subspace by battle array;
Step 4) carries out PCA dimensionality reduction to the training sample data and test sample data of recovery, and does normalized;
Step 5) calculates group rarefaction representation coefficient and expression error of the test sample restored on the training set of recovery, weight
It builds test sample and is identified;
Further, the step 1) specifically includes the following steps:
Step 11) obtains target occlusion facial image.In the method, target occlusion facial image refers to be identified
Facial image under obstruction conditions, electronic equipment can obtain target occlusion facial image in several ways.
Step 12) pre-processes target occlusion facial image, obtains the sample data of target occlusion facial image, should
Sample data is as test sample data.
Step 2) described further specifically includes the following steps:
Step 21) is by facial image by spatial transform to log-domain.Pending data is transformed under log-domain by this method,
Then log-domain transformation model is
LogI (x, y)=logL (x, y)+logR (x, y)
Step 22) by low-rank matrix recovery algorithms restores every subclass training sample to reduce between each subclass low-rank ingredient
Correlation, enhancing restore the taste of data.On the basis of step 21), in low-rank matrix recovery process, it is non-to introduce structure
Correlation constraint enables the different classes of low-rank ingredient recovered as to keep independent as possible, keeps stronger taste.
Further, the step 22) specifically includes the following steps:
Step 23) is using augmented vector approach come by class solution procedure 22) model, it can be from contaminated data
D is restored low-rank data A, removes sparse noise error E.
Step 3) described further specifically includes the following steps:
Step 31) study restores the low-rank mapping relations matrix between low-rank ingredient and original training data.It is assumed that original
It pollutes training set D and there are potential mapping relations matrix P between the low-rank data A restored in D.Learn this herein potential to reflect
Penetrate relational matrix A=PD, and with the polluted test data of correction.
Step 32) removes it specifically includes the following steps: test data γ is mapped under its corresponding potential subspace
In error percentage obtain the test sample y=P γ of " clean ".
Step 4) described further specifically includes the following steps:
Step 41) carries out PCA dimensionality reduction to the training sample data and test sample data of recovery.
Step 42) is to the training sample data and test sample data after dimensionality reduction and is l2Norm normalized.
Step 5) described further specifically includes the following steps:
Step 51) calculates group rarefaction representation coefficient and expression error of the test sample restored on the training set of recovery:
Further, the step 51) specifically includes the following steps:
Step 511) uses augmented vector approach by the step step 51) model conversation are as follows:
Step 512) is to keep component separable, and problem is easier to solve, and introduces auxiliary variable u ∈ Rn, the step 511) mould
Type is equivalent to:
Step 513) is using the untethered optimization problem of equal value that ALM obtains step 512) described problem
Wherein μ is punishment parameter, α ∈ Rm, β ∈ RnFor Lagrange multiplier.
Step 514) takes the strategy of alternative optimization, optimizes respectively to x, e, u.The expression of available test sample
Coefficient x and expression error e.
Step 52) rebuilds test sample.It is represented by
Step 53) carries out recognition of face.It is defined as follows the recognition result that decision rule obtains test sample y
Wherein AiTo restore to correspond to the training sample subset of classification i, x in dataiTo indicate to correspond to classification i in coefficient x
Subrepresentation coefficient.
The beneficial effect of this method is: converting by log-domain, has stretched the dark pixel of facial image and had compressed bright
Pixel enhances picture contrast, and facial image illumination model is become additive model from multiplying property model, low-rank matrix is adapted to and restores
The basic assumption of technology, it is latent to combine illumination model with low-rank matrix recovery technology, the complicated feelings in reality can be coped with
Condition;It is as small as possible to constrain correlation between the inhomogeneous low-rank data restored, enhances the taste for restoring data;Study relationship
Mapping matrix restores contaminated test sample data, reduces algorithm complexity, to adapt to complicated face identification system.It is comprehensive
On, improve the accuracy rate and robustness of the identification of obstruction conditions human face.
Detailed description of the invention
In order to keep the purpose of the present invention, technical scheme and beneficial effects clearer, the present invention provides following attached drawing and carries out
Illustrate:
Fig. 1 is a kind of flow chart of the face identification method restored based on group's rarefaction representation and low-rank matrix of the present invention
Fig. 2 is present system important component illustraton of model
Specific embodiment
Below in conjunction with attached drawing, preferred embodiment of the invention is described in detail.
A kind of face identification method restored based on group's rarefaction representation and low-rank matrix provided by the invention, as shown in Figure 1,
Method includes the following steps: step 1) obtains target occlusion facial image;The target occlusion facial image is located in advance
Reason, obtains the sample data of the target occlusion facial image, the sample data is as test sample data;Step 2) is by face
Image restores every subclass training sample by spatial transform to log-domain, by low-rank matrix recovery algorithms to reduce each subclass low-rank
Correlation between ingredient, enhancing restore the taste of data;Step 3) study restores between low-rank ingredient and original training data
Low-rank mapping relations matrix, and test sample is mapped under its potential subspace using the matrix;Step 4) is to recovery
Training sample data and test sample data carry out PCA dimensionality reduction, and do normalized;Step 5) calculates what extensive calculating restored
Group rarefaction representation coefficient of the test sample on the training set of recovery and expression error, rebuild test sample and are simultaneously identified;
Finally obtained system important component is as shown in Figure 2.
Further, the step 1) specifically includes the following steps:
Step 11) obtains target occlusion facial image.In the method, target occlusion facial image refers to be identified
Facial image under obstruction conditions.Electronic equipment can obtain target occlusion facial image in several ways.For example, can be with
Target occlusion facial image is obtained by the way that camera on an electronic device is arranged, or obtains target from this map office and hides
Facial image is kept off, or obtains the target occlusion facial image etc. from another electronic equipment.In addition, circumstance of occlusion can be wrapped for example
Include but be not limited to: glasses, scarf, cap, mask etc. block face.
Step 12) pre-processes target occlusion facial image, obtains the sample data of target occlusion facial image, should
Sample data is as test sample data.It is as follows that pretreated process is carried out to target occlusion facial image: being hidden first in target
It keeps off on facial image, shearing and registration process is carried out centered on eyes, and do histogram equalization, by the target after equalization
The data matrix for blocking facial image becomes column vector by flattening operations, is l2Norm normalized, obtains target occlusion
The sample data of facial image, the sample data is as test sample data y.
Step 2) described further specifically includes the following steps:
Step 21) is by facial image by spatial transform to log-domain.Such as under illumination condition, widely used lambert's light
Assume that facial image I (x, y) is obtained by the product of reflecting component L (x, y) and illumination component R (x, y) according to the simple version of model
It arrives, i.e. I (x, y)=L (x, y) × R (x, y), wherein reflecting component can regard the stable inherent identity feature of facial image as,
For lineup's face image data from same people, reflecting component be it is relevant, have low-rank structure.It is our based on this
Pending data is transformed under log-domain by method, then log-domain transformation model is
LogI (x, y)=logL (x, y)+logR (x, y)
Step 22) by low-rank matrix recovery algorithms restores every subclass training sample to reduce between each subclass low-rank ingredient
Correlation, enhancing restore the taste of data.On the basis of step 21), in low-rank matrix recovery process, it is non-to introduce structure
Correlation constraint enables the different classes of low-rank ingredient recovered as to keep independent as possible, keeps stronger taste,
Model are as follows:
Wherein, first itemRestore operation for low-rank matrix, under log-domain, by every a kind of training
Sample data D is decomposed into the low-rank ingredient A for representing face substantive characteristicsiAnd represent the error percentage E of difference in classiThe sum of
Form.Section 2 is that correlation is as small as possible between the inhomogeneous low-rank data of constraint recovery, can enhance the mirror for restoring data
Other power.
Further, the step 22) specifically includes the following steps:
Step 221) is by class solution procedure 22) model, obtain following formula:
Step 222) is restoring data AiWhen, Aj(j≠i)It remains unchanged, passes through constraintIt minimizes, makes AiWith it
He restores data A at classj(j≠i)Between correlation it is as small as possible.To make problem be easier to solve, consider that there are relational expressionsStep 221) is described can to relax as following problem:
Step 223) is using augmented vector approach come by class solution procedure 222) model, it can be from contaminated number
It is restored low-rank data A according to D, removes sparse noise error E.
Step 3) described further specifically includes the following steps:
Step 31) study restores the low-rank mapping relations matrix between low-rank ingredient and original training data.It is assumed that original
It pollutes training set D and there are potential mapping relations matrix P between the low-rank data A restored in D.Learn this herein potential to reflect
Penetrate relational matrix A=PD, and with the polluted test data of correction, have following optimization problem
minP,A||P||*+ζ||E||1S.t.D=PD+E
Further, the step 31) specifically includes the following steps:
In the method, recovery data A error E has passed through step 223) solution and has obtained step 311), then step 31)
The model conversation is
minP||P||*S.t.A=PD
Step 312) can must be solved by the Singular-value Decomposition Solution step step 311) model are as follows:
WhereinIt is the pseudoinverse of D,U∑-1VTIt is the thin SVD of D, i.e., only retains the positive singular value of D.P is
For the mapping relations matrix between contamination data D and low-rank data A, it can be used for handling new band Contamination measurement data γ.
Step 32) removes it specifically includes the following steps: test data γ is mapped under its corresponding potential subspace
In error percentage obtain the test sample y=P γ of " clean ".
Step 4) described further specifically includes the following steps:
Step 41) carries out PCA dimensionality reduction to the training sample data and test sample data of recovery.
Step 42) is to the training sample data and test sample data after dimensionality reduction and is l2Norm normalized.
Step 5) described further specifically includes the following steps:
Step 51) calculates the extensive group's rarefaction representation coefficient and expression for calculating the test sample restored on the training set of recovery
Error.Group rarefaction representation coefficient of the y on A is solved, there is following optimization problem:
Wherein training sample label information is introduced into the learning process for indicating coefficient by Section 2, to applying l in class2Norm
Constraint, between applying l class1Norm constraint, so that the nonzero coefficient in the expression coefficient x acquired concentrates in a small number of classifications, tool
There is group sparsity structure.Meanwhile first item | | y-Ax | |1Utilize l1Norm measure indicates residual error, to error percentage more robust.
Further, the step 51) specifically includes the following steps:
Step 511) uses augmented vector approach by the step step 51) model conversation are as follows:
Step 512) is to keep component separable, and problem is easier to solve, and introduces auxiliary variable u ∈ Rn, the step 511) mould
Type is equivalent to:
Step 513) is using the untethered optimization problem of equal value that ALM obtains step 512) described problem
Wherein μ is punishment parameter, α ∈ Rm, β ∈ RnFor Lagrange multiplier, a kind of strategy of alternative optimization is taken, respectively
To x, e, u is optimized.
Step 514) fixed variable x, u, optimize e, and model conversation is
It is solved, can be obtained by soft-threshold operation operator
Wherein operator Sγ[χ]i=sign (χi)·max{|χi|-γ, 0 }, sign () is sign function.
Step 515) fixed variable x, e, optimize u, and model conversation is
It is through algebraic transformation
By one-dimensional contraction operator, obtaining closed solutions is
Wherein ri=xi+βi/ μ, i=1,2 ..., C,
Step 516) fixes e, u, optimizes x, and model conversation is
Objective function is to x derivation, and enabling it is 0, can be obtained
X=(μ ATA+μ·I)(μAy-μATe+ATα+μu-β)
Step 517) updates Lagrange multiplier and punishment parameter:
α=α+μ (y-Ax-e)
β=β+μ (x-u)
μ=min (ρ μ, μmax)
The punishment parameter obtained by above-mentioned transformation substitutes into step 514), the expression coefficient x of available test sample with
And indicate error e.
Step 52) rebuilds test sample.Pass through the expression coefficient x and expression error e of the test sample that step 52) obtains
For the test sample rebuild, it is represented by
Step 53) carries out recognition of face.It is defined as follows the recognition result that decision rule obtains test sample y
Wherein AiTo restore to correspond to the training sample subset of classification i, x in dataiTo indicate to correspond to classification i in coefficient x
Subrepresentation coefficient, due to xiIn also contain the identification information for being conducive to recognition of face classification, therefore this method is also by this
Partial information is taken into account.
By executing above step, it may be implemented in training set and test set sample standard deviation there are illumination, block, noise pollution
Deng in the case where, the accuracy rate and robustness for blocking face recognition algorithms are improved.
Finally, it should be noted that the above preferred embodiment example is only used to illustrate the technical scheme of the present invention and not to limit it,
Although the present invention has been described in detail by examples detailed above, it will be appreciated by those skilled in the art that, it can be in shape
Various changes are made in formula and to it in details, without departing from claims of the present invention limited range.
Claims (10)
1. a kind of face identification method restored based on group's rarefaction representation and low-rank matrix, it is characterised in that: this method include with
Lower step:
S1 target occlusion facial image) is obtained;
The target occlusion facial image is pre-processed, the sample data of the target occlusion facial image, the sample are obtained
Notebook data is as test sample data;
S2) by facial image by spatial transform to log-domain, by low-rank matrix recovery algorithms restore every subclass training sample with
The correlation between each subclass low-rank ingredient is reduced, enhancing restores the taste of data;
S3) study restores the low-rank mapping relations matrix between low-rank ingredient and original training data, and will be surveyed using the matrix
Sample is originally mapped under its potential subspace;
S4 PCA dimensionality reduction) is carried out to the training sample data of recovery and test sample data, and does normalized;
S5 it) calculates the extensive group's rarefaction representation coefficient for calculating the test sample restored on the training set of recovery and indicates error, weight
It builds test sample and is identified.
2. the method according to claim 1, wherein determine it is described will training facial image by spatial transform to pair
Number field restores every subclass training sample by low-rank matrix recovery algorithms, comprising:
Training sample human face data to be processed is transformed under log-domain, log-domain transformation model is constructed;
Between it is described restore every subclass training sample to reduce each subclass low-rank ingredient correlation so that the inhomogeneity recovered
Other low-rank ingredient can keep independent as far as possible, keep stronger taste.
3. according to the method described in claim 2, it is characterized in that, the log-domain transformation model are as follows:
LogI (x, y)=logL (x, y)+logR (x, y)
Wherein, I (x, y) indicates facial image;L (x, y) indicates the reflecting component of facial image, can regard facial image as and stablize
Inherent identity feature, have low-rank structure;R (x, y) indicates facial image illumination component.
4. according to the method described in claim 2, it is characterized in that, the every subclass training sample of recovery is low to reduce each subclass
Correlation between order ingredient introduces the constraint of structure non-correlation, so that the inhomogeneity recovered in low-rank matrix recovery process
Other low-rank ingredient can keep independent as far as possible, keep stronger taste, problem model are as follows:
Wherein,Restore operation for low-rank matrix, under log-domain, by every a kind of number of training according to D
It is decomposed into the low-rank ingredient A for representing face substantive characteristicsiAnd represent the error percentage E of difference in classiThe sum of form.
5. the method according to claim 1, wherein study restores between low-rank ingredient and original training data
Low-rank mapping relations matrix, and test sample is mapped under its potential subspace using the matrix and includes:
Study restores the low-rank mapping relations matrix between low-rank ingredient and original training data, it is assumed that original pollution training set D
With from, there are potential mapping relations matrix P, learn between the low-rank data A restored in D the potential mapping relations matrix A=
PD has following optimization problem:
minP||P||*S.t.A=PD
6. according to the method described in claim 5, having it is characterized in that, restoring test sample data using mapping relations matrix P
Following formula:
Y=P γ
7. the method according to claim 1, wherein further by the low-rank ingredient of the training sample data of recovery
A and test sample data y carries out PCA dimension-reduction treatment and presses l2Norm is normalized, obtain dimensionality reduction normalization after A and
y。
8. the method according to claim 1, wherein calculating the test sample restored on the training set of recovery
Group's rarefaction representation coefficient and expression error, rebuild test sample and are simultaneously identified there is following optimization problem:
9. according to the method described in claim 8, it is characterized in that, according to group's rarefaction representation coefficient and indicating error e, really
Surely the test sample rebuild can indicate are as follows:
10. according to the method described in claim 8, it is characterized in that, the decision rule of the recognition result are as follows:
Wherein, wherein AiTo restore to correspond to the training sample subset of classification i, x in dataiTo indicate to correspond to classification in coefficient x
The subrepresentation coefficient of i, due to xiIn also contain the identification information for being conducive to recognition of face classification, therefore this method is also by this
Partial information is taken into account.
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