CN102332087A - Face recognition method based on sparse representation - Google Patents

Abstract

The invention relates to a face recognition method based on sparse representation. The method comprises the following steps: (1) an original image can be restored when vectors of the original image obtained by being randomly projected satisfy certain conditions, namely, all the information of the original image is included in the projection vectors; (2) the practical distribution of training samples can be well reflected by utilizing a sorter system based on the sparse representation; the distance of a whole sub-space is utilized; and the sample distribution information in the sub-space is ignored, therefore, a face recognition technology is realized. In the process of selecting a template, according to the requirements in the sparse representation on dictionary non-relevance, the bigger the difference of similar images is, the higher the recognition rate is.

Description

A kind of face identification method based on rarefaction representation

Technical field

The present invention relates to the Image Processing and Pattern Recognition technical field, relate in particular to a kind of face identification method based on rarefaction representation.

Background technology

A kind of important identity recognizing technology based on biological characteristic is not only in recognition of face, and significance is also arranged on the academic research field simultaneously.The research of recognition of face relates to scientific research fields such as Flame Image Process, pattern-recognition, computer vision, artificial intelligence, brain cognition.The further investigation of recognition of face plays great function to promoting these subject development.Face identification system mainly comprises two large problems at present:

1) feature extraction

Feature extraction is meant and from facial image, extracts the differentiation characteristic that is used to distinguish Different Individual that the characteristic that requires to extract has stability for identical people, has otherness for different people.Traditional concept is thought: feature extraction is an of paramount importance part in the recognition of face, and its quality is the final recognition performance of decision directly.And research shows recently: good sorter can decrease to the requirement of feature extraction.

2) Classification and Identification

The main task of people's face classification is the characteristic according to the people's face to be identified that extracts, and itself and the facial image in the database are compared, and confirms its identity.This process new breakthrough also occurring in the research recently.

In recent years, obtained extensive concern, become the chief component of face identification method gradually based on the face characteristic extraction algorithm of subspace.According to the difference of mapping mode, subspace method is divided into linear and non-linear two big types.The linear subspaces method comprises methods such as principal component analysis (PCA) (PCA), independent component analysis (ICA), nonnegative matrix decomposition; Non-linear subspace method comprises based on methods such as the non-linear subspace method of nuclear mapping, manifold learnings.Though the characteristic of PCA gained has realized the original sample compression, only decorrelation on the meaning of second order, decorrelation is not thorough; And represent to have destroyed the original space structure of two dimensional image relation with one-dimensional vector; Be the optimal mapping vector under the meaning of best reconstruct original signal because of PCA again, so the characteristic of gained not optimum concerning classification.ICA utilizes the second order and the higher order statistical information of signal; Make signal decorrelation on all rank statistical significances, the directivity of representation feature better, but it is difficult to the invariant feature in the mining data; Can't measure the order relation between the isolated component, it calculates complicated than PCA.Non-linear subspace method geometric meaning based on the nuclear mapping is indeterminate, and parameters of choice does not have standard in the kernel function, and dependence experience is mostly chosen parameter, is not suitable for the situation of big training sample.Manifold learning is nonparametric technique, does not need the parameter of convection current shape to suppose, has embodied nonlinear feature, more can embody the essence of real data.But manifold learning is owing to rely on the local neighbor relation, and smaller error just possibly cause the change of neighbour's geometry, also has a segment distance from practicality.

Though the time based on the classifying identification method of subspace proposes is longer, effect is unsatisfactory.1976, Grenander pointed out that the mode class subspace can use the algebraically projection operator to describe, and has proposed linear regression model (LRM) method (SIMCA) based on the method for assumed statistical inspection; 1978, Kittler proposed the orthogonal subspaces method, and Kohonen has then proposed the notion of Learning Subspace Method, utilized the pattern sample established pattern subspace to be revised sequentially; Nineteen eighty-two, Oja has proposed the notion of average Learning Subspace Method, makes with the learning sequence of training sample irrelevantly, has improved discrimination; 1989, nineteen ninety T.D.Sanger, S.Y.Kung proposed the study dual subspace method based on neural network.

Obviously feature extraction and the classifying identification method based on the subspace still making constant progress, though its application in recognition of face is a lot, recognition effect is also bad, in reality, is difficult to the performance that reaches satisfied.

Summary of the invention

The technical matters that the present invention solved is: a kind of face identification method based on rarefaction representation is provided, to solve the problem in the background technology.

A kind of face identification method based on rarefaction representation comprises:

(1) vector that utilizes accidental projection to obtain to original image can recover original image when satisfying certain condition, and promptly projection vector has comprised all information of original image;

(2) consider variation and other errors that people's face portion expresses one's feelings; The distribution of facial image possibly be non-linear or multi-model; Utilization reflects the actual distribution of training sample better based on the classifier system of rarefaction representation; Use the distance of whole subspace and ignored the sample distribution information in the subspace, often this distributed intelligence is even more important to discerning, and therefore utilizes the actual distribution that reflects training sample based on the classifier system of rarefaction representation better; Therefore classification capacity is stronger when multiclass, thereby has realized a kind of recognition efficiency and the higher face recognition technology of recognition accuracy.

Definition 1: to any positive integer S=1,2 ..., n, the limited equidistance constant of definition matrix A is for satisfying the minimum δ of following condition _S:

sets up (3) to all S sparse vector x

If δ _S∈ (0,1) and be not very near 1, we just say that matrix A satisfies S rank RIP.

Sensing matrix below analyzing:

1. at unit ball R ^mOn evenly extract n column vector at random;

2. be that 0 variance is that the normal distribution sample of 1/m carries out the iid sampling to obeying average;

3. the iid sampling is carried out in Bernoulli Jacob's distribution or other accurate Gaussian distribution samples.

Document has proved that on very big probability all these matrixes are all followed RIP and needed only

M >=CSlog (n/S) sets up (4) to certain constant C

Further, if Φ is the measurement matrix of m * n of from a suitable distribution, obtaining at random, and Ψ is an orthogonal basis arbitrarily, and RIP also can satisfy sensing matrix A=Φ Ψ so under certain condition.

Theorem 2: suppose y=Ax+e, A=Φ Ψ, ‖ e ‖ ₂≤ε, δ _1.5S+ θ _{S, 1.5S}＜1, so to any η>=ε, following linear programming method can provide the accurate reconstruct of x

to meet

in the case (5)

And

Satisfy Wherein

With $C_1=\frac{\sqrt{2}(1+{\mathrm{\δ}}_{1.5S})}{1-{\mathrm{\δ}}_{1.5S}-{\mathrm{\θ}}_{S,1.5S}}.$

By above-mentioned theorem; We know; The vector that utilizes accidental projection to obtain to original image can recover original image when satisfying certain condition, and this just explains that this projection vector has comprised all information of original image, therefore can consider directly to use the characteristic of this projection vector as original image; This just obtains very simple feature extracting method, is called at random " subspace " here.Experiment shows that for top sorter based on rarefaction representation, as long as intrinsic dimensionality reaches certain requirement, characteristic is not very big to the influence of recognition effect.Document is pointed out: as long as intrinsic dimensionality satisfies following formula

d≥2Klog(N/d)，K＝‖x‖ ₀(6)

Do not need special feature extracting method so, utilize the projection vector of image on " subspace " at random can obtain recognition effect preferably as characteristic.Utilize shown in the various characteristics that compression sensing method extracts.

2, based on the sorter of rarefaction representation

Theorem 1: to linear system Ax=b (A ∈ R ^{M * N}Be non-singular matrix, M＜N), satisfy if x is separated in existence

${\left|\right|x\left|\right|}_0=\#\{i:x_i\&NotEqual;0\}<\frac{1}{2}(1+\frac{1}{{\mathrm{\&mu;}}_1\left(A\right)})---\left(1\right)$

μ wherein ₁(A) be the simple crosscorrelation of matrix A

So this to separate be the unique solution of following formula

$\underset{x}{\min }{\left|\right|x\left|\right|}_1\mathrm{subject\; to\; b}=\mathrm{Ax}({\left|\right|x\left|\right|}_1=\underset{i}{\mathrm{\&Sigma;}}|x_i\left|\right)---\left(2\right)$

This theorem shows if we can find dictionary A, makes b on A, have individual rarefaction representation and this expression enough sparse, and this unique expression can minimize through 1 norm and try to achieve so.Make

and represent i people's face image pattern collection, then can carry out Classification and Identification to different people's faces through following algorithm.

A kind of face recognition algorithms that the embodiment of the invention provides based on rarefaction representation:

1. input:

2. each row to A carry out 2 norm normalization

3. find the solution 1 norm minimization problem

4. calculate dump energy

5. output:

When image by noise pollution or exist when blocking, the model in the above-mentioned sorter is carried out trickle improvement can obtain effect preferably, be i.e. order in algorithm 1

$A\&RightArrow;B=[A,I_e]\&Element;R^{M\&times;(N+N_e)}---\left(7\right)$

x→w＝[x，e] (8)

$r_i\left(y\right)={\left|\right|y-{\hat{e}}_1-A{\mathrm{\&delta;}}_i\left({\hat{x}}_1\right)\left|\right|}_2---\left(9\right)$

Noise or the influence of blocking.

3, the advantage of rarefaction representation sorter

It is approximate that the subspace of known each type is of distributing of facial image; In fact; Because variation and other errors of facial expression; The distribution of facial image possibly be non-linear or multi-model, uses the distance of whole subspace and has ignored the sample distribution information in the subspace, and often this distributed intelligence is even more important to discerning.Even if test sample book can be passed through a simple statistical model y=A _iα _i+ z _iGenerate (α wherein _iAnd z _iFor independent Gauss's), the sufficient statistic of any one optimum classifier is by ‖ α _i‖ ₂With ‖ z _i‖ ₂Decision, rather than by ‖ z _i‖ ₂Determine separately.Although based on the minimized sorter of 1 norm also is suboptimal under this model, it has contained α really _iIn information because it has punished the α of big norm _i, when representing test sample book, not only be partial to little ‖ z with training sample based on the minimized sorter of 1 norm _i‖ ₂And be partial to little ‖ α _i‖ ₁

Further, possibly cross the expression test sample book, when separating of following formula by all training samples

y＝A _iα _i+z _i，‖z _i‖ ₂≤ε(10)

When not unique; 1 norm minimizes separate

that can find out the most sparse separating

rather than 2 norms minimum and that is to say; It is that sample with minimum number is represented test sample book that 1 norm minimizes, and obtains a little error.What we are illustrated as through following two kinds of situation need be represented test sample book with sparse solution.

Suppose training sample and in the subspace, be nonlinear Distribution,, only need with the just linear expression preferably of two training samples to the test sample book of red marker because human face posture changes; For the test sample book of blueness sign,, obviously departed from the distribution of data sample although it also drops in the subspace that all samples open.And among the figure on the right; A certain type training sample is distributed on two low n-dimensional subspace ns; Situation when this situation can be represented facial image simultaneously by illumination and expression influence to the test sample book of red marker, only needs the just linear expression preferably of a small amount of training sample equally; But when we use the subspace that all samples open, will be easy to the sample of other types of the blue sign of expression.

Can find out that from what has been discussed above norm minimizes sorter and can work under the condition widely, it is at arest neighbors and found a good balance between the subspace recently.In order to prevent to owe expression, it utilized all kinds of in a plurality of training samples test sample book is carried out linear extrapolation, but its simultaneously again restriction use minimum sample number to prevent expression.To any one test sample book, the training sample number that needs minimizes automatic decision by 1 norm, because seeking sparse solution x ₀Aspect, 1 norm minimize and are equivalent to 0 norm and minimize.Therefore, this sorter can reflect the actual distribution of training sample better, and therefore classification capacity is stronger when multiclass.

Utilization is extracted characteristic based on the method for compressed sensing, has comprised all information of original image.The method

Realize Classification and Identification through the rarefaction representation sorter, can work under the condition widely that it is at arest neighbors and found a good balance between the subspace recently to people's face.In order to prevent to owe expression, it utilized all kinds of in a plurality of training samples test sample book is carried out linear extrapolation, but its simultaneously again restriction use minimum sample number to prevent expression.Therefore, this sorter can reflect the actual distribution of training sample better, and therefore classification capacity is stronger when multiclass.

Beneficial effect:

The present invention has many advantageous properties through adopting a kind of feature extracting method based on compressed sensing commonly used in the pattern-recognition, utilizes the projection vector of image on " subspace " at random can obtain recognition effect preferably as characteristic; Sorting technique based on rarefaction representation can worked under the condition widely, and it is at arest neighbors and found a good balance between the subspace recently.In order to prevent to owe expression, it utilized all kinds of in a plurality of training samples test sample book is carried out linear extrapolation, but its simultaneously again restriction use minimum sample number to prevent expression, greatly improved the recognition performance of whole algorithm.Instance of the present invention is classified after image cut apart again and can be improved discrimination to a great extent when having noise pollution or blocking.Carrying out template when choosing, according in the rarefaction representation to the requirement of dictionary non-correlation, similar image difference is big more, then discrimination is just higher.

Embodiment

For technological means, creation characteristic that the present invention is realized, reach purpose and effect and be easy to understand and understand, below in conjunction with specific embodiment, further set forth the present invention.

The embodiment of the invention is carried out initialization operation in advance, promptly collects facial image to be trained, and utilizes the method for compressed sensing to extract the facial image characteristic then.At first introduce the method for following compressed sensing below:

Definition 1: to any positive integer S=1,2 ..., n, the limited equidistance constant of definition matrix A is for satisfying the minimum δ of following condition _S:

sets up (3) to all S sparse vector x

If δ _S∈ (0,1) and be not very near 1, we just say that matrix A satisfies S rank PIP.

Sensing matrix below analyzing:

4. at unit ball R ^mOn evenly extract n column vector at random;

5. be that 0 variance is that the normal distribution sample of 1/m carries out the iid sampling to obeying average;

6. the iid sampling is carried out in Bernoulli Jacob's distribution

or other accurate Gaussian distribution samples.

Document has proved that on very big probability all these matrixes are all followed RIP and needed only

M >=CSlog (n/S) sets up (4) to certain constant C

Further, if Φ is the measurement matrix of m * n of from a suitable distribution, obtaining at random,

And Ψ is an orthogonal basis arbitrarily, and RIP also can satisfy sensing matrix A=Φ Ψ so under certain condition.

Theorem 2: suppose y=Ax+e, A=Φ Ψ, ‖ e ‖ ₂≤ε, δ _1.5S+ θ _{S, 1.5S}＜1, so to any η>=ε, following linear programming method can provide the accurate reconstruct of x

to meet

in the case (5)

And

Satisfy Wherein

With $C_1=\frac{\sqrt{2}(1+{\mathrm{\&delta;}}_{1.5S})}{1-{\mathrm{\&delta;}}_{1.5S}-{\mathrm{\&theta;}}_{S,1.5S}}.$

By above-mentioned theorem; We know; The vector that utilizes accidental projection to obtain to original image can recover original image when satisfying certain condition, and this just explains that this projection vector has comprised all information of original image, therefore can consider directly to use the characteristic of this projection vector as original image; This just obtains very simple feature extracting method, is called at random " subspace " here.Experiment shows that for top sorter based on rarefaction representation, as long as intrinsic dimensionality reaches certain requirement, characteristic is not very big to the influence of recognition effect.Document is pointed out: as long as intrinsic dimensionality satisfies following formula

d≥2Klog(N/d)，K＝‖x‖ ₀(6)

Do not need special feature extracting method so, utilize the projection vector of image on " subspace " at random can obtain recognition effect preferably as characteristic.Utilize shown in the various characteristics that compression sensing method extracts.

2, based on the sorter of rarefaction representation

Theorem 1: to linear system Ax=b (A ∈ R ^{M * N}Be non-singular matrix, M＜N), satisfy if x is separated in existence

${\left|\right|x\left|\right|}_0=\#\{i:x_i\&NotEqual;0\}<\frac{1}{2}(1+\frac{1}{{\mathrm{\&mu;}}_1\left(A\right)})---\left(1\right)$

μ wherein ₁(A) be the simple crosscorrelation of matrix A

So this to separate be the unique solution of following formula

$\underset{x}{\min }{\left|\right|x\left|\right|}_1\mathrm{subject\; to\; b}=\mathrm{Ax}({\left|\right|x\left|\right|}_1=\underset{i}{\mathrm{\&Sigma;}}|x_i\left|\right)---\left(2\right)$

This theorem shows if we can find dictionary A, makes b on A, have individual rarefaction representation and this expression enough sparse, and this unique expression can minimize through 1 norm and try to achieve so.Make

and represent i people's face image pattern collection, then can carry out Classification and Identification to different people's faces through following algorithm.

A kind of face recognition algorithms that the embodiment of the invention provides based on rarefaction representation:

1. input:

2. each row to A carry out 2 norm normalization

3. find the solution 1 norm minimization problem

4. calculate dump energy

5. output:

When image by noise pollution or exist when blocking, the model in the above-mentioned sorter is carried out trickle improvement can obtain effect preferably, be i.e. order in algorithm 1

$A\&RightArrow;B=[A,I_e]\&Element;R^{M\&times;(N+N_e)}---\left(7\right)$

x→w＝[x，e] (8)

$r_i\left(y\right)={\left|\right|y-{\hat{e}}_1-A{\mathrm{\&delta;}}_i\left({\hat{x}}_1\right)\left|\right|}_2---\left(9\right)$

Noise or the influence of blocking.

3, the advantage of rarefaction representation sorter

It is approximate that the subspace of known each type is of distributing of facial image; In fact; Because variation and other errors of facial expression; The distribution of facial image possibly be non-linear or multi-model, uses the distance of whole subspace and has ignored the sample distribution information in the subspace, and often this distributed intelligence is even more important to discerning.Even if test sample book can be passed through a simple statistical model y=A _iα _i+ z _iGenerate (α wherein _iAnd z _iFor independent Gauss's), the sufficient statistic of any one optimum classifier is by ‖ α _i‖ ₂With ‖ z _i‖ ₂Decision, rather than by ‖ z _i‖ ₂Determine separately.Although based on the minimized sorter of 1 norm also is suboptimal under this model, it has contained α really _iIn information because it has punished the α of big norm _i, when representing test sample book, not only be partial to little ‖ z with training sample based on the minimized sorter of 1 norm _i‖ ₂And be partial to little ‖ α _i‖ ₁

Further, possibly cross the expression test sample book, when separating of following formula by all training samples

y＝A _iα _i+z _i，‖z _i‖ ₂≤ε(10)

When not unique; 1 norm minimizes separate that can find out the most sparse separating

rather than 2 norms minimum and that is to say; It is that sample with minimum number is represented test sample book that 1 norm minimizes, and obtains a little error.What we are illustrated as through following two kinds of situation need be represented test sample book with sparse solution.

Suppose training sample and in the subspace, be nonlinear Distribution,, only need with the just linear expression preferably of two training samples to the test sample book of red marker because human face posture changes; For the test sample book of blueness sign,, obviously departed from the distribution of data sample although it also drops in the subspace that all samples open.And among the figure on the right; A certain type training sample is distributed on two low n-dimensional subspace ns; Situation when this situation can be represented facial image simultaneously by illumination and expression influence to the test sample book of red marker, only needs the just linear expression preferably of a small amount of training sample equally; But when we use the subspace that all samples open, will be easy to the sample of other types of the blue sign of expression.

Can find out that from what has been discussed above 1 norm minimizes sorter and can work under the condition widely, it is at arest neighbors and found a good balance between the subspace recently.In order to prevent to owe expression, it utilized all kinds of in a plurality of training samples test sample book is carried out linear extrapolation, but its simultaneously again restriction use minimum sample number to prevent expression.To any one test sample book, the training sample number that needs minimizes automatic decision by 1 norm, because seeking sparse solution x ₀Aspect, 1 norm minimize and are equivalent to 0 norm and minimize.Therefore, this sorter can reflect the actual distribution of training sample better, and therefore classification capacity is stronger when multiclass.

Obviously, those skilled in the art can carry out various changes and modification to the present invention and not break away from the spirit and scope of the present invention.Like this, belong within the scope of claim of the present invention and equivalent technologies thereof if of the present invention these are revised with modification, then the present invention also is intended to comprise these changes and modification interior.

The above only is a preferred implementation of the present invention, and protection scope of the present invention also not only is confined to the foregoing description, and all technical schemes that belongs under the thinking of the present invention all belong to protection scope of the present invention.Should be pointed out that for those skilled in the art in the some improvement and the retouching that do not break away under the principle of the invention prerequisite, these improvement and retouching also should be regarded as protection scope of the present invention.

Claims (1)

1. the face identification method based on rarefaction representation is characterized in that, may further comprise the steps:

(1) vector that utilizes accidental projection to obtain to original image can recover original image when satisfying certain condition, and promptly projection vector has comprised all information of original image;

(2) utilize the actual distribution that reflects training sample based on the classifier system of rarefaction representation better, use the distance of whole subspace and ignored the sample distribution information in the subspace, thereby realized face recognition technology.