CN101079103A - Human face posture identification method based on sparse Bayesian regression - Google Patents

Abstract

The invention discloses a face posture identification method based on rarefaction Bayesian regression in the image processing technique field, which comprises the following steps: extracting Gabor character for face posture image with Gabor filter; stacking the sampled character to one-dimensional vector after down sampling for Gabor character; acquiring the essential lower dimensional subspace of the face posture image and the corresponding projection matrix with the linear tangent space arrangement for the training sample; training the identification parameter with rarefaction Bayesian regression method in the lower dimensional subspace; mapping the projection matrix of every detecting sample to the lower dement ional subspace by training; proceeding the face posture identification with trained identification parameter. The invention can acquire the uncertain solution of the face posture, which reduces the wrong radio.

Description

Face posture identification method based on sparse Bayesian regression

Technical field

What the present invention relates to is a kind of method of technical field of image processing, specifically is a kind of face posture identification method based on sparse Bayesian regression.

Background technology

In the gatherer process of facial image,, thereby obtain facial image under the different visual angles because the relative visual angle of imaging device and people's face changes.Be presumed to as device coordinate system and fix, different imaging visual angles can be regarded as because different people's face directions obtains, and these different people's face directions are different face postures.At present, the recognition of face under the different gestures is one of hot issue in the recognition of face, and face posture identification accurately and rapidly is again a key link that addresses this problem.Face posture identification also plays important role and uses widely in computer vision and field of Computer Graphics, such as face tracking, human face expression identification and man-machine interaction etc.Because the information of the two-dimension human face image disappearance third dimension, so the change of face posture identification problem is very complicated.Also have many factors to increase the difficulty of head it off in addition, such as the variation of environment illumination, the quality of facial image, the variation of people's face identity etc.In the face posture identifying, also have a factor to need to consider, being exactly people's face rotates and the nonlinear deformation that brings at depth direction.

Method based on outward appearance is a kind of effective, and the low method that assesses the cost.But need the problem of solution also still many.Rotate at depth direction such as people's face, cause some nonlinearities change, use general dimension reduction method to be difficult to disclose essential structure in the data, and it is many to influence the factor of people's face outward appearance, also affects the solution of this problem such as factors such as the variation of illumination, picture qualities.In addition, in actual environment, the facial image that collects will be subjected to the influence of some factors, such as: the variation of surrounding environment illumination, the resolution of image capture device, expression shape change of people's face or the like.Therefore, it is far from being enough directly characterizing with original facial image pixel, needs to give new characterization image of original image, when embodying the posture otherness, restrains the above-mentioned adverse factors of mentioning.

Through the literature search of prior art is found, Xingliang Ge etc. are at " Optical Engineering " Vol.45, No.9,2006 (optical engineering, the 45th volume, the 9th phases, 2006) on, a kind of face posture identification method based on nonlinear discriminant has been proposed.This method is at first extracted face characteristic with the Gabor small echo, carries out dimensionality reduction with SLPP then, carries out the posture classification with support vector machine at last.The gesture recognition of this method is supervised, and that is to say, the face posture angle of final test sample book must be consistent with certain angle of training sample.If training sample is less, will there be bigger error so.Secondly, support vector machine needs more support vector, can have influence on the real-time of method.

Summary of the invention

The objective of the invention is to overcome deficiency of the prior art, a kind of face posture identification method based on sparse Bayesian regression is proposed, making it can access the non-of face posture determines to separate, reduce error rate, secondly, the sparse Bayesian regression method is used less support vector, has improved the real-time of invention.In addition, the present invention adopts Gabor wave filter behaviour face gesture recognition to extract the Gabor feature, suppresses unfavorable factor; Use linear tangent space aligning method can survey the essential low dimensional structures of face posture image.

The present invention is achieved by the following technical solutions, and concrete steps of the present invention are as follows:

(1) adopt Gabor wave filter behaviour face posturography picture to extract the Gabor feature.

(2) the Gabor feature is carried out down-sampling, the feature windrow after will sampling then is stacked as one-dimensional vector, and forms sample set.

(3) the linear tangent space of utilization aligning method on training sample obtains the low n-dimensional subspace n of essence of face posture image, and obtains corresponding projection matrix.

(4) at low n-dimensional subspace n utilization sparse Bayesian regression method training identification parameter.

(5) projection matrix that each test sample book is obtained by training is mapped to low n-dimensional subspace n, and the identification parameter that the utilization training obtains carries out face posture identification.

Described extraction Gabor feature is meant: new people's face that the convolution of facial image and one group of Gabor transformation kernel is obtained characterizes.Suppose that (x y) is a width of cloth facial image, ψ to I _{μ, v}(x y) is the Gabor transformation kernel, and its Gabor transform definition is as follows: O _{μ v}(x, y)=I (x, y) * ψ _{μ, v}(x, y).Wherein, * represents convolution algorithm, and (x y) is convolution results to the Gabor transformation kernel on μ direction and the ν yardstick to O, and (x y) is facial image I (x, Gabor feature y) to O.

Described linear tangent space aligning method is meant: raw data is projected to lower dimensional space obtain corresponding low-dimensional face posture data thereby try to achieve a projection matrix A on training sample.This method is divided into four key steps: the supposition lower dimensional space is the d dimension,

1. for each high dimensional data point x _i, search out its k nearest neighbor point.This local neighborhood is designated as X _i

2. to X _iH carries out SVD and decomposes, wherein H _KBe the centralization matrix.Make V _iBe the right singular vector of d maximum eigenwert correspondence, thereby use $W_i=H(I-V_i{V}_i^T)$ The information of cutting of expression local neighborhood.

3. utilize the method for iteration to make up permutation matrix B on the global sense, the present invention utilizes such formula: $B(I_i,I_i)\←B(I_i,I_i)+W_i{W}_i^T$ ，i＝1，Λ，N。Wherein, I _i={ i ₁, Λ, i _kExpression x _iThe index of k nearest neighbor point.

4. final, projection matrix can obtain by finding the solution such generalized eigenvalue problem: XHBHX ^Tα=λ XHX ^Tα.If α ₁, α ₂Λ, α _dBe the proper vector of following formula, it is corresponding to eigenvalue ₁＜λ ₂＜Λ＜λ _dSo, transition matrix A is: A=(α ₁, α ₂Λ, α _d).So just obtained projection matrix.

Described sparse Bayesian regression method is meant: after test sample book is projected to lower dimensional space, and the posture identification method that is adopted.For sparse Bayesian regression, given one group of training set { (x _i, t _i) | i=1, K, N}, wherein, x is the pattern vector of input, t is an export target, can describe with the linear regression problem of such broad sense: t=y (x, w)+ε.(x w) can be expressed as a kernel function K (x to y _i, linear weighted function x) and form: $y(x,w)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{i}K(x_i,x)+w_0$ 。The probability density function of export target is: p (t|x, w, σ ²)=N (y (x, w), σ ²), promptly satisfy a Gaussian distribution.Because all training samples all are considered to independently, so all the likelihood function of training sample can be written as: p (t|{x ₁, L, x _N, w, σ ²)=N (Φ w, σ ²), wherein, Φ is the matrix of a N * (N+1), Φ _Ij=K (x _i, x _J-1), and Φ _I1=l.In likelihood function, the identification of the maximum likelihood of w and σ tends to cause problem concerning study, for fear of this problem, uses a prior probability and adds the constraint to weight w: $p\left(w\right|\mathrm{\α})=\underset{i=0}{\overset{N}{\mathrm{\Π}}}N\left(w_i\right|0,{\mathrm{\α}}_i^{-1})$ , wherein, α is the hypothesis parameter vector.Finally obtain the expression of w: p (w|t, α, σ ²)=N (μ, ∑), wherein ∑ ^-1=σ ^-2Φ ^TΦ+diag (α), μ=σ ^-2∑ Φ ^TT.

The present invention can obtain higher recognition correct rate.The present invention experiment showed, in the enterprising pedestrian's face of CAS-PEAL database gesture recognition, can access the non-of face posture and determine to separate, and accuracy can reach 96.83% (7 postures), is higher than the method based on support vector machine.Secondly, the support vector that the sparse Bayesian regression method is less with compare use based on the method for support vector machine, so the present invention has travelling speed and use storage area still less quickly.

Embodiment

Below embodiments of the invention are elaborated: present embodiment has provided detailed embodiment and process being to implement under the prerequisite with the technical solution of the present invention, but protection scope of the present invention is not limited to following embodiment.

Present embodiment has adopted a public face database: the CAS-PEAL database.The CAS-PEAL database comprises 1040 people.In database, have seven face postures (from left to right rotation), be respectively 0 °, 15 ° ,-15 °, 30 ° ,-30 °, 45 ° ,-45 °.In order to reduce operating cost, get 200 people totally 1400 images, facial image is tapered to 20 * 20.At first, present embodiment utilization Gabor wave filter pursues multi-direction, the multiple dimensioned Gabor transform characteristics that pixel is calculated each pixel, and the people's face that forms the Gabor feature is represented.Present embodiment get 5 yardstick v ∈ 0,1,2,3,4} and 8 direction μ ∈ 0,1,2,3,4,5,6, the last use of 7} Gabor kernel function.Therefore, for each facial image, can obtain the Gabor feature of 40 20 * 20 sizes.

In order further to reduce operating cost, the preliminary dimension that reduces the space, each Gabor feature is carried out down-sampling with decimation factor 1/4, all row that connect the Gabor feature after the sampling then carry out end to endly connecting into a vector, thereby can obtain 40 * 20 * 20 * 1/4 * 1/4=1000 dimension Gabor proper vector of an expansion: $x_i=(O_{\mathrm{0,0}}^T,O_{\mathrm{0,1}}^T,...,O_{\mathrm{4,7}}^T)$ , wherein, T represents the transposition computing.Like this, just obtained vector set X=[x ₁, L, x ₁₄₀₀].

For each posture, choose four samples as training sample, have 800 training samples like this, therefrom use linear tangent space aligning method that facial image is dropped to the d n-dimensional subspace n.Notice that, the size of the transition matrix A that the present invention obtains is 1000 * d here.Utilization sparse Bayesian regression method training parameter w in lower dimensional space, present embodiment utilization gaussian kernel function K (x _i, x)=exp (r ‖ x-x _i‖ ²) as the selection of kernel function.For the formula of the calculating w that describes in the summary of the invention, present embodiment obtains w by the EM alternative manner.

Next, the transition matrix A that each test sample book (totally 600) utilization is obtained projects to low n-dimensional subspace n, use then the parameter that arrives of sparse Bayesian regression method training: t=y (x, w)+ε discerns posture.So far, present embodiment has been finished the overall process of face posture identification.Present embodiment is in the enterprising pedestrian's face of CAS-PEAL database gesture recognition, and accuracy can reach 96.83% (7 postures).

Claims (7)

1. face posture identification method based on sparse Bayesian regression is characterized in that concrete steps are as follows:

(1) adopt Gabor wave filter behaviour face posturography picture to extract the Gabor feature;

(2) the Gabor feature is carried out down-sampling, the feature windrow after will sampling then is stacked as one-dimensional vector, and forms sample set;

(3) the linear tangent space of utilization aligning method on training sample obtains the low n-dimensional subspace n of essence of face posture image, and obtains corresponding projection matrix;

(4) at low n-dimensional subspace n utilization sparse Bayesian regression method training identification parameter;

(5) each test sample book is mapped to low n-dimensional subspace n by the projection matrix that obtains of training, the identification parameter that obtains of utilization training carries out face posture identification.

2. the face posture identification method based on sparse Bayesian regression according to claim 1 is characterized in that, described extraction Gabor feature, be meant: new people's face that the convolution of facial image and one group of Gabor transformation kernel is obtained characterizes, suppose that (x y) is a width of cloth facial image, ψ to I _{μ, v}(x y) is the Gabor transformation kernel, and its Gabor transform definition is as follows: O _{μ v}(x, y)=I (x, y) * ψ _{μ, v}(x, y), wherein, * represents convolution algorithm, (x y) is convolution results to the Gabor transformation kernel on μ direction and the v yardstick to O, and (x y) is facial image I (x, Gabor feature y) to O.

3. the face posture identification method based on sparse Bayesian regression according to claim 2 is characterized in that, described extraction Gabor feature is meant and gets 5 yardstick v ∈ { 0,1,2,3,4} and 8 direction μ ∈ { 0,1,2,3,4,5,6, the last use of 7} Gabor kernel function.

4. the face posture identification method based on sparse Bayesian regression according to claim 1, it is characterized in that, described linear tangent space aligning method is meant: raw data is projected to lower dimensional space obtain corresponding low-dimensional people's face data thereby try to achieve a projection matrix A on training sample.

5. according to claim 1 or 4 described face posture identification methods, it is characterized in that based on sparse Bayesian regression, described linear tangent space aligning method, specific implementation is divided four steps: the supposition lower dimensional space is the d dimension,

1. for each high dimensional data point x _i, search out its k nearest neighbor point, this local neighborhood is designated as X _i

2. to X _iH carries out SVD and decomposes, wherein H _KFor the centralization matrix, make V _iBe the right singular vector of d maximum eigenwert correspondence, thereby use $W_i=H(I-V_i{V}_i^T)$ The information of cutting of expression local neighborhood;

3. utilize the method for iteration to make up permutation matrix B on the global sense, formula is:

$B(I_i,I_i)\←B(I_i,I_i)+W_i{W}_i^T,$ I=1, Λ, N, wherein, I _i={ i ₁, Λ, i _kExpression x _iThe index of k nearest neighbor point;

4. final, obtain projection matrix by finding the solution: XHBHX with next generalized eigenvalue problem ^Tα=λ XHX ^Tα establishes α ₁, α ₂Λ, α _dBe the proper vector of following formula, it is corresponding to eigenvalue ₁＜λ ₂＜Λ＜λ _d, so, transition matrix A is: A=(α ₁, α ₂Λ, α _d), so just obtained projection matrix.

6. the face posture identification method based on sparse Bayesian regression according to claim 1, it is characterized in that described sparse Bayesian regression method is meant: after test sample book is projected to lower dimensional space, for sparse Bayesian regression, given one group of training set { (x _i, t _i) | i=1, K, N}, wherein, x is the pattern vector of input, t is an export target, describes with the linear regression problem of a broad sense: t=y (x, w)+ε, wherein,

$y(x,w)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_{i}K(x_i,x)+w_0;$

The probability density function of export target is: p (t|x, w, σ ²)=N (y (x, w), σ ²), promptly satisfy a Gaussian distribution; All training samples all are considered to independently, and then all the likelihood function of training sample is: p (t|{x ₁, L, x _N, w, σ ²)=N (Φ w, σ ²), wherein, Φ is the matrix of a N * (N+1), Φ _Ij=K (x _i, x _J-1), and Φ _I1=1;

Add a constraint with a prior probability to weight w: $p\left(w\right|\mathrm{\α})=\underset{i=0}{\overset{N}{\mathrm{\Π}}}N\left(w_i\right|0,{\mathrm{\α}}_i^{-1}),$ Wherein, α is the hypothesis parameter vector;

Finally obtain the expression of w: p (w|t, α, σ ²)=N (μ, ∑), wherein ∑ ^-1=σ ^-2Φ ^TΦ+diag (α), μ=σ ^-2∑ Φ ^TT.

7. the face posture identification method based on sparse Bayesian regression according to claim 6 is characterized in that, adopts the EM alternative manner to obtain for weight w.