CN103116742A - Color face identification method based on RGB (red, green and blue) color feature double identification relevance analysis - Google Patents

Abstract

The invention discloses a color face identification method based on RGB (red, green and blue) color feature double identification relevance analysis. Identification analysis is applied in R, G, B (red, green and blue) color components and among the same, feature double identification analysis based on relevance is realized in each color component and among different color components, a large amount of identification information can be acquired, classification accuracy is high, and identification capacity is high. The color face identification method based on RGB (red, green and blue) color feature double identification relevance analysis includes: defining intra-class feature relevance matrix and inter-class feature relevance matrix in each training sample set and intra-class feature relevance matrix and inter-class feature relevance matrix among color component training sample sets; defining target function and solving the same to obtain projected training sample feature sets; and obtaining projected test sample features according to the projected training sample feature sets, calculating relevance from the test sample features to the training sample features and classifying the same to a category in which the training sample with the largest relevance is.

Description

Face identification method based on the dual discriminating correlation analysis of RGB color property

Technical field

The invention belongs to the face recognition technology field, especially relate to a kind of color face recognition method based on the dual discriminating correlation analysis of RGB color property.

Background technology

In recent years, development along with society, various aspects are day by day urgent to auto authentication demand fast and effectively, more and more become a study hotspot of present mode identification and artificial intelligence field in the huge applications prospect of the aspects such as public security criminal identification, safety verification, security authentication systems, credit card validation.Being people's inherent attribute due to biological characteristic, having very strong self stability and individual difference, is therefore the most desirable foundation of authentication.Wherein, utilizing face characteristic to carry out authentication is again the most direct means, than other human body biological characteristics such as fingerprint, retina, iris, genes, it has directly, friendly, characteristics easily, be easier to be accepted by the user, therefore receive much concern, become the popular research direction of current information science forefront.

The research of nearly 40 years is passed through in recognition of face, relates to the knowledge of the subjects such as pattern-recognition, image processing, computer vision, physiology, psychology and cognitive science, has obtained showing great attention to of each area research persons, and has obtained significant progress.In a large amount of recognition of face research, the half-tone information of facial image is widely used in the Classification and Identification of object in the past few decades.Recently, increasing researcher begins to utilize the chromatic information of facial image further to improve the performance of face recognition algorithms.

In existing color face recognition algorithm, although can realize the discriminatory analysis of three chrominance component inside, but when the correlativity of processing between three chrominance components, do not process this correlativity from the angle of identification or discriminating, thereby make the authentication information that obtains relatively less, recognition effect is difficult to guarantee.

Take following two kinds of algorithms as example:

Whole-body quadrature is analyzed (HOA) [1] the quadrature decorrelation between the discriminatory analysis of three groups of R, G, B chrominance component feature inside and three groups of chrominance component features is combined, and successively each chrominance component is calculated a projective transformation according to the order serial of RGB.Specific practice is as follows:

$\max J\left(W_R\right)=\frac{\left|W_R^T{S}_{\mathrm{bR}}{W}_R\right|}{\left|W_R^T{S}_{\mathrm{wR}}{W}_R\right|};$

$\max J\left(W_G\right)=\frac{\left|W_G^T{S}_{\mathrm{bG}}{W}_G\right|}{\left|W_G^T{S}_{\mathrm{wG}}{W}_G\right|};$

$s.t.W_G^T{W}_R=0$

$\max J\left(W_B\right)=\frac{\left|W_B^T{S}_{\mathrm{bB}}{W}_B\right|}{\left|W_B^T{S}_{\mathrm{wB}}{W}_B\right|}.$

$s.t.W_B^T{W}_R=0,$

Wherein, W _R, W _G, W _BRespectively R, G to be asked, the projective transformation of three chrominance components of B, S _bR, S _bG, S _bRRespectively scatter matrix between the class of R, G, three chrominance component sample sets of B, S _wR, S _wG, S _wBRespectively the interior scatter matrix of class of R, G, three chrominance component sample sets of B, || the value of expression matrix determinant.W _R, W _G, W _BSuccessively by matrix

$S_{\mathrm{wG}}^{-1}(I-W_R{\left(W_R^T{S}_{\mathrm{wG}}^{-1}{W}_R\right)}^{-1}{W}_R^T{S}_{\mathrm{wG}}^{-1})S_{\mathrm{bG}},$ $S_{\mathrm{wB}}^{-1}(I-W{\left(W^T{S}_{\mathrm{wB}}^{-1}W\right)}^{-1}{W}^T{S}_{\mathrm{wB}}^{-1})S_{\mathrm{bB}}$ Nonzero eigenvalue characteristic of correspondence vector consist of, W=[W wherein _R, W _G].

The HOA method has realized the discriminatory analysis of three of R, G, B chrominance component inside, and this is favourable for Classification and Identification; But when the correlativity of processing between three chrominance components, just remove three correlativitys between chrominance component by quadrature simply, do not process this correlativity from the angle of differentiating.

Statistics quadrature analysis (SOA) [2] combines the statistics quadrature decorrelation between the discriminatory analysis of three groups of R, G, B chrominance component feature inside and three groups of chrominance component features, successively each chrominance component is calculated a projective transformation according to the order serial of RGB.Specific practice is as follows:

$\max J\left(W_R\right)=\frac{\left|W_R^T{S}_{\mathrm{bR}}{W}_R\right|}{\left|W_R^T{S}_{\mathrm{wR}}{W}_R\right|};$

$\max J\left(W_G\right)=\frac{\left|W_G^T{S}_{\mathrm{bG}}{W}_G\right|}{\left|W_G^T{S}_{\mathrm{wG}}{W}_G\right|};$

$s.t.W_G^T\sqrt{S_{\mathrm{tG}}}{\left(\sqrt{S_{\mathrm{tR}}}\right)}^T{W}_R=0$

$\max J\left(W_B\right)=\frac{\left|W_B^T{S}_{\mathrm{bB}}{W}_B\right|}{\left|W_B^T{S}_{\mathrm{wB}}{W}_B\right|}$

$s.t.W_B^T\sqrt{S_{\mathrm{tB}}}{\left(\sqrt{S_{\mathrm{tR}}}\right)}^T{W}_R=0.$

$W_B^T\sqrt{S_{\mathrm{tB}}}{\left(\sqrt{S_{\mathrm{tG}}}\right)}^T{W}_G=0$

Wherein, S _tR, S _tG, S _tBRespectively the total population scatter matrix of R, G, three chrominance component sample sets of B,

Representing matrix M satisfies $\sqrt{M}{\left(\sqrt{M}\right)}^T=M.$ W _R, W _G, W _BSuccessively by matrix

$S_{\mathrm{wG}}^{-1}(I-W_1{\left(W_1^T{S}_{\mathrm{wG}}^{-1}{W}_1\right)}^{-1}{W}_1^T{S}_{\mathrm{wG}}^{-1})S_{\mathrm{bG}},$ Nonzero eigenvalue characteristic of correspondence vector consist of, wherein

$W_2=[\sqrt{S_{\mathrm{tB}}}{\left(\sqrt{S_{\mathrm{tR}}}\right)}^T{W}_R,\sqrt{S_{\mathrm{tB}}}{\left(\sqrt{S_{\mathrm{tG}}}\right)}^T{W}_G].$

, SOA method similar to HOA just removes three correlativitys between chrominance component by the statistics quadrature, also do not process this correlativity from the angle of identification or discriminating.In addition, the SOA method has also been used relativity measurement in statistics in orthogonality constraint, and what use in the discriminatory analysis of three chrominance component inside is Euclidean distance tolerance.The mode that different metric forms affects recognition effect is different, and inconsistent also the making of this metric form is difficult to guarantee recognition effect.

Summary of the invention

For addressing the above problem, the invention discloses a kind of color face recognition method, to be applied to simultaneously based on the discriminatory analysis technology of relativity measurement between inner and three chrominance components of three chrominance components of R, G, B, realize based on the dual discriminatory analysis of the characteristic layer of relativity measurement between inner and different chrominance components in each chrominance component.

In order to achieve the above object, the invention provides following technical scheme:

A kind of face identification method based on the dual discriminating correlation analysis of RGB color property comprises the steps:

At first obtain training sample set, make X _R, X _G, X _BRepresent respectively R, G, three chrominance component training sample sets of B, w _R, w _G, w _BRepresent respectively X _R, X _G, X _BProjection vector, c represents the classification number of coloured image training sample, n _kThe number that represents k class coloured image training sample, n represents the number of all coloured image training samples,

Expression X _iQ sample of p class in (i=R, G, B),

Expression X _iThe average of all samples in (i=R, G, B),

Represent respectively three the chrominance component training sample sets of R, G, B after centralization,

Expression

In q sample of p class (annotate: centralization refers to $\underset{p=1}{\overset{c}{\mathrm{\Σ}}}\underset{q=1}{\overset{n_p}{\mathrm{\Σ}}}{\hat{x}}_{\mathrm{pq}}^i=0,$ Namely ${\hat{x}}_{\mathrm{pq}}^i=x_{\mathrm{pq}}^i-{\stackrel{\‾}{x}}_i$ ), e _n=[1 ..., 1] ^T∈ R ⁿ,

Represent a n _kThe rank all elements is all 1 square formation, $A=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="E\; n"\; filenames="130201111000.png"\; state="\{\{state\}\}">E</figure-callout>}}_{n_{}}& 0& ...& 0\\ 0& E_{n_2}& ...& 0\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ 0& 0& ...& E_{n_c}\end{array}\right]\&Element;R^{n\&times;n}.$

Define feature correlation matrix in the class of i chrominance component training sample set inside

And feature correlation matrix between class

And feature correlation matrix in the class between i and j chrominance component training sample set

And feature correlation matrix between class

As follows:

$C_w^i=\frac{(1/\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pt}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}{\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pt}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pt}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}}$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{iT}}{w}_i}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}w}_i}\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pt}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{iT}}{w}_i}},---\left(1\right)$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{X}}_i{e}_{n_p}{e}_{n_p}^T{\hat{X}}_i^T{w}_i}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}}$

$=\frac{n{w}_i^T{\hat{X}}_{i}A{\hat{X}}_i^T{w}_i}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}$

$C_b^i=\frac{[1/(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)]\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{\underset{q\&NotEqual;p}{q=1}}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{qt}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}{\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}^i)(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}^i)}^T{w}_i}{\sqrt{\frac{1}{n}\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{qt}}^i-{\stackrel{\&OverBar;}{x}}^i)(x_{\mathrm{qt}}^i-{\stackrel{\&OverBar;}{x}}^i)}^T{w}_i}}_{}}$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{\underset{q\&NotEqual;p}{q=1}}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_q}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{iT}}{w}_i}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}{w}_i}\sqrt{\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{qt}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{iT}}{w}_i}}$

$=\frac{n(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_q}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{iT}}{w}_i-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{iT}}{w}_i)}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}{w}_i}\sqrt{\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{qt}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{iT}}{w}_i}},---\left(2\right)$

$=\frac{n(w_i^T{\hat{X}}_i{e}_n{e}_n^T{\hat{X}}_i^T{w}_i-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{X}}_i{e}_{n_p}{e}_{n_p}^T{\hat{X}}_i^T{w}_i)}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}}$

$=\frac{-n{w}_i^T{\hat{X}}_{i}A{\hat{X}}_i^T{w}_i}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}$

$C_w^{\mathrm{ij}}=\frac{(1/\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pt}}^j-{\stackrel{\&OverBar;}{x}}_j)}^T{w}_j}{\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{(x_{\mathrm{pt}}^j-{\stackrel{\&OverBar;}{x}}_j)(x_{\mathrm{pt}}^j-{\stackrel{\&OverBar;}{x}}_j)}^T{w}_j}}$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{jT}}{w}_j}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}w}_i}\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{\hat{x}}_{\mathrm{pt}}^j{\hat{x}}_{\mathrm{pt}}^{\mathrm{jT}}{w}_j}},---\left(3\right)$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{X}}_i{e}_{n_p}{e}_{n_p}^T{\hat{X}}_i^T{w}_i}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}$

$=\frac{n{w}_i^T{\hat{X}}_i{A\hat{X}}_j^T{w}_j}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}$

$C_b^{\mathrm{ij}}=\frac{[1/(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)]\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{\underset{q\&NotEqual;p}{q=1}}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{qt}}^j-{\stackrel{\&OverBar;}{x}}_j)}^T{w}_j}{\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}{\sqrt{\frac{1}{n}\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{(x_{\mathrm{qt}}^j-{\stackrel{\&OverBar;}{x}}_j)(x_{\mathrm{qt}}^j-{\stackrel{\&OverBar;}{x}}_j)}^T{w}_j}}_{}}$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{\underset{q\&NotEqual;p}{q=1}}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_q}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{jT}}{w}_j}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}{w}_i}\sqrt{\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{\hat{x}}_{\mathrm{qt}}^j{\hat{x}}_{\mathrm{qt}}^{\mathrm{jT}}{w}_j}}$

$=\frac{n(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_q}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{jT}}{w}_j-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{jT}}{w}_j)}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}{w}_i}\sqrt{\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{\hat{x}}_{\mathrm{qt}}^j{\hat{x}}_{\mathrm{qt}}^{\mathrm{jT}}{w}_j}}.---\left(4\right)$

$=\frac{n(w_i^T{\hat{X}}_i{e}_n{e}_n^T{\hat{X}}_j^T{w}_j-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{X}}_i{e}_{n_p}{e}_{n_p}^T{\hat{X}}_j^T{w}_j)}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}$

$=\frac{-n{w}_i^T{\hat{X}}_{i}A{\hat{X}}_j^T{w}_j}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}$

Secondly, the objective definition function is as follows:

$\underset{w_R,w_G,w_B}{\max }\underset{i=R}{\overset{B}{\mathrm{\&Sigma;}}}(C_w^i-\mathrm{\&alpha;}{C}_b^i)+\mathrm{\&gamma;}\underset{i=R}{\overset{B}{\mathrm{\&Sigma;}}}\underset{\underset{j\&NotEqual;i}{j=R}}{\overset{B}{\mathrm{\&Sigma;}}}(C_w^{\mathrm{ij}}-\mathrm{\&beta;}{C}_b^{\mathrm{ij}}).---\left(5\right)$

Wherein, α＞0, β＞0, γ＞0 are three weight coefficients that can adjust according to experimental result, and initial value all is set as 1.The objective function of formula (5) can be rewritten as following form:

$\underset{w_R,w_G,w_B}{\max }\underset{i=R}{\overset{B}{\mathrm{\&Sigma;}}}\frac{w_i^T{\hat{X}}_{i}A{\hat{X}}_i^T{w}_i}{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}+\mathrm{\&eta;}\underset{i=R}{\overset{B}{\mathrm{\&Sigma;}}}\underset{j=R}{\overset{B}{\mathrm{\&Sigma;}}}\frac{w_i^T{\hat{X}}_{i}A{\hat{X}}_j^T{w}_j}{\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}.---\left(6\right)$

Wherein, η＞0 is the weight coefficient that can adjust according to experimental result, and initial value is set as 1.Order $w=\left[\begin{array}{c}{w}_R\\ w_G\\ w_B\end{array}\right],$ $P=\left[\begin{array}{ccc}{\hat{X}}_{R}A{\hat{X}}_R^T& \mathrm{\&eta;}{\hat{X}}_{R}A{\hat{X}}_G^T& \mathrm{\&eta;}{\hat{X}}_{R}A{\hat{X}}_B^T\\ \mathrm{\&eta;}{\hat{X}}_{G}A{\hat{X}}_R^T& {\hat{X}}_{G}A{\hat{X}}_G^T& \mathrm{\&eta;}{\hat{X}}_{G}A{\hat{X}}_B^T\\ \mathrm{\&eta;}{\hat{X}}_{B}A{\hat{X}}_R^T& \mathrm{\&eta;}{\hat{X}}_{B}A{\hat{X}}_G^T& {\hat{X}}_{B}A{\hat{X}}_B^T\end{array}\right],$ Formula (6) can be rewritten as

$\underset{w}{\max }{w}^T\mathrm{Pw}$ (7)

$s.t.w_R^T{\hat{X}}_R{\hat{X}}_R^T{w}_R=1,w_G^T{\hat{X}}_G{\hat{X}}_G^T{w}_G=1,$ $w_B^T{\hat{X}}_B{\hat{X}}_B^T{w}_B=1.$

For the ease of finding the solution, loosen the constraint of formula (7), as follows:

$\underset{w}{\max }{w}^T\mathrm{Pw}$ 。（8)

s.t.w ^TQw＝1

Wherein, $Q=\left[\begin{array}{ccc}{\hat{X}}_R{\hat{X}}_R^T& 0& 0\\ 0& {\hat{X}}_G{\hat{X}}_G^T& 0\\ 0& 0& {\hat{X}}_B{\hat{X}}_B^T\end{array}\right].$

The solution w of formula (8) ^*Can pass through Q ^-1The P matrix carries out feature decomposition and obtains.Obtain Q when ^-1Front d eigenvalue of maximum characteristic of correspondence vector w of P matrix ^k(k=1,2 ..., in the time of d), can be easy to from w ^kIn obtain

Here d is the parameter that can adjust according to experimental result, and the value of d must not surpass Q ^-1The P rank of matrix.Order

The training sample feature set that we can obtain after projection is as follows:

$Z={[{\left(W_R^T{X}_R\right)}^T,{\left(W_G^T{X}_G\right)}^T,{\left(W_B^T{X}_B\right)}^T]}^T.---\left(9\right)$

For test sample book

The test sample book that we can obtain after projection is as follows:

$z_y={[{\left(W_R^T{y}_R\right)}^T,{\left(W_G^T{y}_G\right)}^T,{\left(W_B^T{y}_B\right)}^T]}^T.---\left(10\right)$

The feature that the present invention obtains for dual discriminating correlation analysis is used and is classified and identify based on the nearest neighbor classifier of relativity measurement.Specifically, calculate z _yTo the correlativity of each training sample feature, with the class that y is grouped into that training sample place of correlativity maximum, can complete the classification to test sample book.

Face identification method based on the dual discriminating correlation analysis of RGB color property provided by the invention, to all having carried out the discriminating correlation analysis between R, G, three chrominance components inside of B and three chrominance components, the authentication information that obtains is many, and classification accuracy rate is high, recognition capability is strong; And in chrominance component inner and between all adopted same metric form relativity measurement when carrying out discriminatory analysis, further guaranteed recognition effect, identification result obviously is better than existing face identification method.

Description of drawings

Fig. 1 is the people's face example picture after selecting and process from the colored human face database.

Fig. 2 is for utilizing HOA, SOA and recognition methods provided by the invention (CDDCA) to verify respectively the ROC curve map (experimenter's operating characteristic) of (Verification) experiment.

Embodiment

Below with reference to specific embodiment, technical scheme provided by the invention is elaborated, should understands following embodiment and only be used for explanation the present invention and be not used in and limit the scope of the invention.

Face Recognition Grand Challenge(FRGC is selected in experimental verification of the present invention) version2Experiment4 colored human face database [3].This database is larger, training, target, three word banks of query have been comprised, the training word bank comprises 222 people's 12776 pictures, and the target word bank comprises 466 people's 16028 pictures, and the query word bank comprises 466 people's 8014 pictures.87 public people have been selected in experiment from three word banks, everyone has selected 28 pictures from the training word bank, have selected all pictures from target word bank and query word bank.Experiment has carried out proofreading and correct (making two is horizontal), convergent-divergent and cutting to all original images of choosing, and each picture sample only keeps the human face region of 60 * 60 sizes.People's face sample picture after processing as shown in Figure 1.The picture of selecting from the training word bank is as training sample set, and the picture of selecting in the query word bank is as the test sample book collection, and the picture of selecting from the target word bank is used for the result comparison in checking (Verification) experiment.The picture that uses recognition methods provided by the invention that test sample book is concentrated classify obtain a result after, with the picture of selecting in the target word bank checking of comparing.

As experiment contrast of the present invention, utilize same training sample set, test sample book collection and result comparison data, by HOA, SOA, the test sample book collection is classified and comparison respectively.The result of carrying out confirmatory experiment by HOA, SOA method and the facial image recognition method based on the dual discriminating correlation analysis of RGB color property provided by the invention (CDDCA) as shown in Figure 2.Fig. 2 is Receiver Operating Characteristic(ROC) curve, this curve horizontal ordinate is False Acceptance Rate(FAR), i.e. wrong acceptance rate, ordinate is Verification Rate(VR), i.e. correct verification rate.Compare with the SOA method with HOA, obviously higher based on the recognition effect of the colorized face images recognition methods (i.e. CDDA method in figure) of the dual discriminatory analysis of RGB color property; Particularly when FAR=0.1%, the VR=73.10% of HOA, the VR=73.04% of SOA, and the VR=75.50% of CDDCA.After this explanation was carried out dual discriminating correlation analysis to RGB chrominance component feature, the classification capacity of diagnostic characteristics had obtained enhancing.

The disclosed technological means of the present invention program is not limited only to the disclosed technological means of above-mentioned embodiment, also comprises the technical scheme that is comprised of above technical characterictic combination in any.

The list of references that this instructions needs:

[1]X.Y.Jing,Q.Liu,C.Lan,J.Y.Man,S.Li,and D.Zhang.“Holistic Orthogonal Analysis of Discriminant Transforms for Color Face Recognition”.Int.Conf.Image Processing,pp.3841-3844,2010.

[2]J.Y.Mans,X.Y.Jing,Q.Liu,Y.F.Yao,K.Li,J.Y.Yang.“Color face recognition based on statistically orthogonal analysis of projection transforms”.Lecture Notes in Computer Science,vol.7098,pp.58-65,2011.

[3]P.J.Phillips,P.J.Flynn,T.Scruggs,K.Bowyer,J.Chang,K.Hoffman,J.Marques,J.Min,and W.Worek.Overview of the Face Recognition Grand Challenge.IEEE Conf.Computer Vision and Pattern Recognition,vol.1,pp.947-954,2005.

Claims (6)

1. the face identification method based on the dual discriminating correlation analysis of RGB color property, is characterized in that, comprises the steps:

(1) at first obtain training sample set, feature correlation matrix between feature correlation matrix and class in the class between feature correlation matrix and training sample set between feature correlation matrix and class in the class of definition training sample set inside;

Secondly (2) objective definition function and relaxed constraints are found the solution objective function, obtain the training sample feature set after projection;

(3) obtain test sample book, according to the training sample feature set after above-mentioned projection, draw the test sample book feature after projection, calculate test sample book feature after projection to the correlativity of each training sample feature, test sample book is grouped into the class at that training sample place of correlativity maximum.

2. the face identification method based on the dual discriminating correlation analysis of RGB color property according to claim 1, is characterized in that, described step (1) comprising: define feature correlation matrix in the class of i chrominance component training sample set inside

And feature correlation matrix between class

And feature correlation matrix in the class between i and j chrominance component training sample set

And feature correlation matrix between class

As follows:

$C_w^i=\frac{(1/\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pt}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}{\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pt}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pt}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}}$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{iT}}{w}_i}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}w}_i}\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pt}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{iT}}{w}_i}},$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{X}}_i{e}_{n_p}{e}_{n_p}^T{\hat{X}}_i^T{w}_i}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}}$

$=\frac{n{w}_i^T{\hat{X}}_{i}A{\hat{X}}_i^T{w}_i}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}$

$C_b^i=\frac{[1/(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)]\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{\underset{q\&NotEqual;p}{q=1}}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{qt}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}{\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}^i)(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}^i)}^T{w}_i}{\sqrt{\frac{1}{n}\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{qt}}^i-{\stackrel{\&OverBar;}{x}}^i)(x_{\mathrm{qt}}^i-{\stackrel{\&OverBar;}{x}}^i)}^T{w}_i}}_{}}$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{\underset{q\&NotEqual;p}{q=1}}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_q}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{iT}}{w}_i}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}{w}_i}\sqrt{\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{qt}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{iT}}{w}_i}}$

$=\frac{n(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_q}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{iT}}{w}_i-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{iT}}{w}_i)}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}{w}_i}\sqrt{\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{qt}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{iT}}{w}_i}},$

$=\frac{n(w_i^T{\hat{X}}_i{e}_n{e}_n^T{\hat{X}}_i^T{w}_i-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{X}}_i{e}_{n_p}{e}_{n_p}^T{\hat{X}}_i^T{w}_i)}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}}$

$=\frac{-n{w}_i^T{\hat{X}}_{i}A{\hat{X}}_i^T{w}_i}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}$

$C_w^{\mathrm{ij}}=\frac{(1/\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pt}}^j-{\stackrel{\&OverBar;}{x}}_j)}^T{w}_j}{\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{(x_{\mathrm{pt}}^j-{\stackrel{\&OverBar;}{x}}_j)(x_{\mathrm{pt}}^j-{\stackrel{\&OverBar;}{x}}_j)}^T{w}_j}}$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{jT}}{w}_j}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}w}_i}\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{\hat{x}}_{\mathrm{pt}}^j{\hat{x}}_{\mathrm{pt}}^{\mathrm{jT}}{w}_j}},$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{X}}_i{e}_{n_p}{e}_{n_p}^T{\hat{X}}_i^T{w}_i}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}$

$=\frac{n{w}_i^T{\hat{X}}_i{A\hat{X}}_j^T{w}_j}{\left(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2\right)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}$

$C_b^{\mathrm{ij}}=\frac{[1/(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)]\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{\underset{q\&NotEqual;p}{q=1}}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{qt}}^j-{\stackrel{\&OverBar;}{x}}_j)}^T{w}_j}{\sqrt{\frac{1}{n}\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)(x_{\mathrm{pr}}^i-{\stackrel{\&OverBar;}{x}}_i)}^T{w}_i}{\sqrt{\frac{1}{n}\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{(x_{\mathrm{qt}}^j-{\stackrel{\&OverBar;}{x}}_j)(x_{\mathrm{qt}}^j-{\stackrel{\&OverBar;}{x}}_j)}^T{w}_j}}_{}}$

$=\frac{n\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{\underset{q\&NotEqual;p}{q=1}}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_q}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{jT}}{w}_j}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}{w}_i}\sqrt{\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{\hat{x}}_{\mathrm{qt}}^j{\hat{x}}_{\mathrm{qt}}^{\mathrm{jT}}{w}_j}}$

$=\frac{n(\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_q}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{qt}}^{\mathrm{jT}}{w}_j-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pt}}^{\mathrm{jT}}{w}_j)}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{r=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{x}}_{\mathrm{pr}}^i{\hat{x}}_{\mathrm{pr}}^{\mathrm{iT}}{w}_i}\sqrt{\underset{q=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{w}_j^T{\hat{x}}_{\mathrm{qt}}^j{\hat{x}}_{\mathrm{qt}}^{\mathrm{jT}}{w}_j}};$

$=\frac{n(w_i^T{\hat{X}}_i{e}_n{e}_n^T{\hat{X}}_j^T{w}_j-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{w}_i^T{\hat{X}}_i{e}_{n_p}{e}_{n_p}^T{\hat{X}}_j^T{w}_j)}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}$

$=\frac{-n{w}_i^T{\hat{X}}_{i}A{\hat{X}}_j^T{w}_j}{(n^2-\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}{n}_p^2)\sqrt{w_i^T{\hat{X}}_i{\hat{X}}_i^T{w}_i}\sqrt{w_j^T{\hat{X}}_j{\hat{X}}_j^T{w}_j}}$

Wherein, X _R, X _G, X _BRepresent respectively R, G, three chrominance component training sample sets of B, w _R, w _G, w _BRepresent respectively X _R, X _G, X _BProjection vector, c represents the classification number of coloured image training sample, n _kThe number that represents k class coloured image training sample, n represents the number of all coloured image training samples,

Expression X _iQ sample of p class in (i=R, G, B),

Expression X _iThe average of all samples in (i=R, G, B),

Represent respectively three the chrominance component training sample sets of R, G, B after centralization, Expression

In q sample of p class (annotate: centralization refers to $\underset{p=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{q=1}{\overset{n_p}{\mathrm{\&Sigma;}}}{\hat{x}}_{\mathrm{pq}}^i=0,$ Namely ${\hat{x}}_{\mathrm{pq}}^i=x_{\mathrm{pq}}^i-{\stackrel{\&OverBar;}{x}}_i$ ), e _n=[1 ..., 1] ^T∈ R ⁿ,

Represent a n _kThe rank all elements is all 1 square formation, $A=\left[\begin{array}{cccc}{E}_{n_1}& 0& ...& 0\\ 0& E_{n_2}& ...& 0\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ 0& 0& ...& E_{n_c}\end{array}\right]\&Element;R^{n\&times;n}.$

3. the face identification method based on the dual discriminating correlation analysis of RGB color property according to claim 1 and 2, is characterized in that, in described step (2), objective function is:

$\underset{w_R,w_G,w_B}{\max }\underset{i=R}{\overset{B}{\mathrm{\&Sigma;}}}(C_w^i-\mathrm{\&alpha;}{C}_b^i)+\mathrm{\&gamma;}\underset{i=R}{\overset{B}{\mathrm{\&Sigma;}}}\underset{\underset{j\&NotEqual;i}{j=R}}{\overset{B}{\mathrm{\&Sigma;}}}(C_w^{\mathrm{ij}}-\mathrm{\&beta;}{C}_b^{\mathrm{ij}}),$

Objective function is abbreviated as:

$\underset{w}{\max }{w}^T\mathrm{Pw}$

$s.t.w_R^T{\hat{X}}_R{\hat{X}}_R^T{w}_R=1,w_G^T{\hat{X}}_G{\hat{X}}_G^T{w}_G=1,w_B^T{\hat{X}}_B{\hat{X}}_B^T{w}_B=1,$

After relaxed constraints, objective function is:

$\underset{w}{\max }{w}^T\mathrm{Pw},$

s.t.w ^TQw＝1

By to Q ^-1The P matrix carries out the solution that feature decomposition obtains objective function, thereby the training sample feature set that obtains after projection is:

$Z={[{\left(W_R^T{X}_R\right)}^T,{\left(W_G^T{X}_G\right)}^T,{\left(W_B^T{X}_B\right)}^T]}^T;$

Wherein, $w=\left[\begin{array}{c}{w}_R\\ w_G\\ w_B\end{array}\right],$ $P=\left[\begin{array}{ccc}{\hat{X}}_{R}A{\hat{X}}_R^T& \mathrm{\&eta;}{\hat{X}}_{R}A{\hat{X}}_G^T& \mathrm{\&eta;}{\hat{X}}_{R}A{\hat{X}}_B^T\\ \mathrm{\&eta;}{\hat{X}}_{G}A{\hat{X}}_R^T& {\hat{X}}_{G}A{\hat{X}}_G^T& \mathrm{\&eta;}{\hat{X}}_{G}A{\hat{X}}_B^T\\ \mathrm{\&eta;}{\hat{X}}_{B}A{\hat{X}}_R^T& \mathrm{\&eta;}{\hat{X}}_{B}A{\hat{X}}_G^T& {\hat{X}}_{B}A{\hat{X}}_B^T\end{array}\right],$ $Q=\left[\begin{array}{ccc}{\hat{X}}_R{\hat{X}}_R^T& 0& 0\\ 0& {\hat{X}}_G{\hat{X}}_G^T& 0\\ 0& 0& {\hat{X}}_B{\hat{X}}_B^T\end{array}\right],$ α＞0、β＞0、γ＞0、η＞0、 $W_R=[w_R^1,w_R^2,...,w_R^d],$ $W_G=[w_G^1,w_G^2,...{,w}_G^d],$ $W_B=[w_B^1,w_B^2,...,w_B^d],$ D is that integer and value are not more than Q ^-1The P rank of matrix.

4. the face identification method based on the dual discriminating correlation analysis of RGB color property according to claim 3, is characterized in that, in described step (2), α, β, γ value are 1.

5. the face identification method based on the dual discriminating correlation analysis of RGB color property according to claim 3, is characterized in that, in described step (2), the η value is 1.

6. the face identification method based on the dual discriminating correlation analysis of RGB color property according to claim 1 and 2, is characterized in that, in described step (3), test sample book is:

$y={[y_R^T,y_G^T,y_B^T]}^T,$

Test sample book after projection is characterized as:

$z_y={[{\left(W_R^T{y}_R\right)}^T,{\left(W_G^T{y}_G\right)}^T,{\left(W_B^T{y}_B\right)}^T]}^T.$

Images