CN102737237A - Face image dimension reducing method based on local correlation preserving - Google Patents

Abstract

The invention discloses a face image dimension reducing method based on local correlation preserving. The method comprises the following steps of: expressing a face image by using multi-dimensional vectors, acquiring k neighbors of each vector according to the norm of two difference vectors, and calculating normalization weight of the k neighbors of each vector according to a radial basis function; calculating a difference vector of each vector and the sum of the weights of the k neighbors of each vector, acquiring a matrix by multiplying transposition of each difference vector by each difference vector, and adding the matrixes corresponding all the vectors to acquire a local correlation preserving matrix; and calculating characteristic values and characteristic vectors of the local correlation preserving matrix, and selecting the characteristic vectors corresponding to partial large characteristic values as basic vectors to form a projection matrix, and thus realizing dimension reduction. The dimension reduced face image well preserves local data association, the method is beneficial to image identification, and the classification effect after characteristics are extracted by the method is superior to those of primal component analysis (PCA) and locality preserving projection (LPP); and calculation complexity is reduced, and a relation among the new method, the PCA and the LPP is disclosed.

Description

Facial image dimension reduction method based on the local association maintenance

Technical field

The present invention relates to a kind of facial image dimension reduction method, relate in particular to a kind of facial image dimension reduction method that keeps based on local association.

Background technology

Facial image is made up of a large amount of pixel point values, representes through high dimension vector or high level matrix, and facial image identification needs a large amount of calculating and storage cost; Cause dimension disaster, therefore before to the facial image operation, need carry out dimension-reduction treatment facial image; Be about to primitive man's face image mapped to a lower dimensional space; Obtain lower dimensional space and represent the main characteristic of facial image, reduce and calculate and storage cost, realize the automatic identification of facial image.

The classical at present dimension reduction method of not considering the data category mark is that (Primal Component Analysis: principal component analysis (PCA)) simple aspect calculating and theoretical analysis, eigenface is PCA foremost application in facial image identification to PCA.The PCA dimensionality reduction is only considered the overall distribution characteristics of data, has ignored the nonlinear organization characteristic of data.KPCA has expanded the PCA algorithm, through by the nuclear conversion with data map to higher dimensional space more, and in new space data are carried out linear feature and extract, realize extracting based on the nonlinear characteristic of nuclear.The advantage of method is not need clear and definite Nonlinear Mapping function, and feature extraction only need be calculated higher dimensional space inner product of vectors kernel function, and the characteristic of extraction has been described the nonlinear organization of facial image more effectively.The facial image data have stream shape characteristic, and application flow shape learning art is realized the facial image dimensionality reduction, and keep the stream shape characteristic of source images.Main algorithm has LLE (local linear Embedding: local linearity embeds), NPE (Neighborhood Preserving Embedding: the local maintenance embeds), LPP (Locality Preserving Projection: the part keeps projection).In essence on the basis that keeps local relation between data, the nonlinear characteristic that learning data is inherent helps the identification of facial image more based on the feature extraction of manifold learning.The shortcoming of above-mentioned manifold learning method is a calculation of complex, does not provide clear and definite nonlinear transformation matrix, can not directly obtain the transform characteristics of unmarked facial image.

Summary of the invention

The object of the invention is exactly in order to address the above problem, and a kind of facial image dimension reduction method that keeps based on local association is provided, and it has under the prerequisite that keeps the view data local association, realizes face characteristic dimensionality reduction advantage through simple computation.

To achieve these goals, the present invention adopts following technical scheme:

A kind of feature dimension reduction method that keeps based on the facial image local association; At first represent facial image with multi-C vector; Norm according to two vectorial differences vector obtains each vectorial k neighbour, and calculates each vectorial k neighbour's normalized weight according to RBF.Calculate each vector and difference vector of its k neighbour's weighting sum, the transposition through each difference vector obtains matrix with itself multiplying each other, and with the matrix addition of institute's directed quantity correspondence, obtains local association maintenance matrix.Keep the eigenwert and the proper vector of matrix through the calculating local association, and select the big eigenwert characteristic of correspondence vector of part to form projection matrix, realize dimensionality reduction as base vector.Facial image is hinted obliquely at lower dimensional space through projection matrix, realizes facial image identification at lower dimensional space.

Concrete steps of the present invention are:

Step 1: the capable vector x that m width of cloth size is expressed as s * t dimension for the facial image of s * t pixel ₁, x ₂..., x _i..., x _m, wherein m is the facial image number, and s is the image line pixel number, and t is a row image column pixel number, x _iRepresent the row vector of the corresponding s of i width of cloth facial image * t dimension, this m width of cloth facial image comprises p people, everyone

Width of cloth image;

Step 2: for any capable vector x _i(i ∈ 1,2 ..., m}), calculate d _Ij=‖ x _i-x _j‖ (j ∈ 1,2 ..., m} and j ≠ i) therefrom select k (k=9) to make d _IjMinimum row vector is formed set and is designated as Ne (x _i).Wherein ‖ ‖ representes the norm of vector, and d representes x _i-x _jThe norm of gained difference vector;

Step 3: calculate weight matrix W, the capable j row of matrix i member is designated as w _Ij

Step 4: calculate the corresponding difference vector of each row vector, and calculate local association maintenance matrix V;

Step 5: find the solution the eigenwert and the proper vector of matrix V, select d biggest characteristic value characteristic of correspondence vector, and form a matrix as row, be called projection matrix M by this d proper vector; D=min (m, n), wherein n=r (V) is the order of matrix V;

Step 6: any people's face image line vector of p people is mapped to lower dimensional space through the projection matrix M that step 5 obtains.

The capable j row of the i member w of weight matrix W in the said step 3 _IjDefine as follows:

Parameter σ=2 wherein.

The difference vector computing method are in the said step 4: for any capable vector x _i, calculate the difference vector r of the weighting sum of the individual neighbour's row of itself and k (k=9) vector _i

$r_i=x_i-{\mathrm{\Σ}}_{j\∈\mathrm{ne}\left(x_i\right)}\frac{w_{\mathrm{ij}}}{{\mathrm{\Σ}}_{j\∈\mathrm{ne}\left(x_i\right)}{w}_{\mathrm{ij}}}{x}_j---\left(2\right)$

It is following that local association keeps the calculating of matrix V in the said step 4:

$V={\mathrm{\Σ}}_{i=1}^m{r}_i^T{r}_i---\left(3\right)$

In the said step 6, for any capable vector x _i, calculate x _iM obtains a d dimension row vector, and wherein (m, n) s * t tie up thereby facial image is dropped to d d=min, realize the facial image dimensionality reduction.

Beneficial effect of the present invention: the facial image behind the dimensionality reduction has kept the data local association well, helps image recognition, and the error in classification rate on the Yale face database relatively is superior to PCA and LPP through the classifying quality after the inventive method extraction characteristic; The present invention has reduced computational complexity, has disclosed the relation between new method and PCA and LPP simultaneously, works as k=m, and parameter σ is when enough big, and new method deteriorates to PCA; Analysis shows, new method characteristic=LPP characteristic+complex nonlinear recessive character.

Description of drawings

Fig. 1 is a dimension reduction method process flow diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is described further.

Be illustrated in figure 1 as dimension reduction method process flow diagram of the present invention, a kind of facial image dimension reduction method that keeps based on local association,

Concrete steps are:

Step 1: the capable vector x that m width of cloth size is expressed as s * t dimension for the facial image of s * t pixel ₁, x ₂..., x _i..., x _m, wherein m is the facial image number, and s is the image line pixel number, and t is a row image column pixel number, x _iRepresent the row vector of the corresponding s of i width of cloth facial image * t dimension, this m width of cloth facial image comprises p people, everyone

Width of cloth image;

Step 2: for any capable vector x _i(i ∈ 1,2 ..., m}), calculate d _Ij=‖ x _i-x _j‖ (j ∈ 1,2 ..., m} and j ≠ i) therefrom select k (k=9) to make d _IjMinimum row vector is formed set and is designated as Ne (x _i).Wherein ‖ ‖ representes the norm of vector, d _IjExpression x _i-x _jThe norm of gained difference vector;

Step 3: calculate weight matrix W, the capable j row of matrix i member is designated as w _Ij

Step 4: calculate the corresponding difference vector of each row vector, and calculate local association maintenance matrix V;

Step 5: find the solution the eigenwert and the proper vector of matrix V, select d biggest characteristic value characteristic of correspondence vector, and form a matrix as row, be called projection matrix M by this d proper vector; D=min (m, n), wherein n=r (V) is the order of matrix V;

Step 6: any people's face image line vector of p people is mapped to lower dimensional space through the projection matrix M that step 5 obtains.

The capable j row of the i member w of weight matrix W in the said step 3 _IjDefine as follows:

Parameter σ=2 wherein.

The difference vector computing method are in the said step 4: for any capable vector x _i, calculate the difference vector r of the weighting sum of the individual neighbour's row of itself and k (k=9) vector _i

$r_i=x_i-{\mathrm{\Σ}}_{j\∈\mathrm{ne}\left(x_i\right)}\frac{w_{\mathrm{ij}}}{{\mathrm{\Σ}}_{j\∈\mathrm{ne}\left(x_i\right)}{w}_{\mathrm{ij}}}{x}_j---\left(2\right)$

It is following that local association keeps the calculating of matrix V in the said step 4:

$V={\mathrm{\Σ}}_{i=1}^m{r}_i^T{r}_i---\left(3\right)$

In the said step 6, for any capable vector x _i, calculate x _iM obtains a d dimension row vector, wherein

Thereby facial image is dropped to the d dimension, realize the facial image dimensionality reduction.

As embodiment, this database comprises 15 people's total 165 width of cloth facial images with the Yale face database in the present invention, and everyone 11 width of cloth images obtain under different illumination conditions and different expression respectively.Facial image is transformed to the image of 32x32 pixel, gray level 255.Before the dimensionality reduction data being carried out normalization handles.Concrete experimental procedure is following:

(1) selecting everyone preceding 4 width of cloth images, is the row vector of 1024 dimensions with every width of cloth image transformation, amounts to 60 vectors;

(2) norm of the difference vector of compute vector between is in twos selected 9 vectors nearest with it to form its neighbour's vector to each vector and is gathered;

(3) calculate weight matrix according to formula (1), this matrix is the matrix of 60X60, and calculates the corresponding difference vector of each vector according to formula (2), and this difference vector is the row vector of 1024 dimensions;

(4) calculate local association according to formula (3) and keep matrix V, this matrix is a 1024X1024 dimension matrix;

(5) eigenwert and the proper vector of calculating V, this rank of matrix is n=1024, greater than 60, is 60 so select the dimension behind the dimensionality reduction; Get 60 eigenwert characteristic of correspondence vectors of the minimum of V, form the mapping matrix M of 1024X60 dimension by row;

(6) an optional secondary facial image in the Yale face database converts 1024 dimension row vectors into, according to 60 dimensional feature vectors of inventing after step 6 obtains corresponding conversion, realizes dimensionality reduction.

Error in classification rate on the Yale face database relatively (adopts linear band penalty term SVM SVMs sorting algorithm, the parameters C among the SVM=1); Data set Yale, adopt five folding cross validation classification results as shown in table 1 behind 165 width of cloth figure dimensionality reductions:

Dimension reduction method	Nicety of grading and variance
		The inventive method	65.7303±1.0744
The PCA dimensionality reduction	63.6364±0.5051
		The LPP dimensionality reduction	60±1.5335

The error in classification rate of table 1 on the Yale face database relatively

Though the above-mentioned accompanying drawing specific embodiments of the invention that combines is described; But be not restriction to protection domain of the present invention; One of ordinary skill in the art should be understood that; On the basis of technical scheme of the present invention, those skilled in the art need not pay various modifications that creative work can make or distortion still in protection scope of the present invention.

Claims (5)

1. facial image dimension reduction method that keeps based on local association; It is characterized in that; At first represent facial image with multi-C vector, the norm vectorial according to two vectorial differences obtains each vectorial k neighbour, and calculates each vectorial k neighbour's normalized weight according to RBF; Calculate each vector and difference vector of its k neighbour's weighting sum, the transposition through each difference vector obtains matrix with itself multiplying each other, and with the matrix addition of institute's directed quantity correspondence, obtains local association maintenance matrix; Keep the eigenwert and the proper vector of matrix through the calculating local association, and select the big eigenwert characteristic of correspondence vector of part to form projection matrix, realize dimensionality reduction as base vector; Facial image is hinted obliquely at lower dimensional space through projection matrix, realizes facial image identification at lower dimensional space.

2. facial image dimension reduction method that keeps based on local association is characterized in that concrete steps are:

Step 1: the capable vector x that m width of cloth size is expressed as s * t dimension for the facial image of s * t pixel ₁, x ₂..., x _i..., x _m, wherein m is the facial image number, and s is the image line pixel number, and t is a row image column pixel number, x _iRepresent the row vector of the corresponding s of i width of cloth facial image * t dimension, this m width of cloth facial image comprises p people, everyone

Width of cloth image;

Step 2: for any capable vector x _i(i ∈ 1,2 ..., m}), calculate

(j ∈ 1,2 ..., m} and j ≠ i) therefrom select k (k=9) to make d _IjMinimum row vector is formed set and is designated as Ne (x _i); Wherein ‖ ‖ representes the norm of vector, d _IjExpression x _i-x _jThe norm of gained difference vector;

Step 3: calculate weight matrix W, the capable j row of matrix i member is designated as w _Ij

Step 4: calculate the corresponding difference vector of each row vector, and calculate local association maintenance matrix V;

Step 5: find the solution the eigenwert and the proper vector of matrix V, select d biggest characteristic value characteristic of correspondence vector, and form a matrix as row, be called projection matrix M by this d proper vector; D=min (m, n), wherein n=r (V) is the order of matrix V;

Step 6: any people's face image line vector of p people is mapped to lower dimensional space through the projection matrix M that step 5 obtains.

3. like the said a kind of facial image dimension reduction method that keeps based on local association of claim 2, it is characterized in that the capable j row of the i member w of weight matrix W in the said step 3 _IjDefine as follows:

Wherein $\mathrm{\σ}={\mathrm{\Σ}}_{i=1}^m{\mathrm{\Σ}}_{j=1}^m{\left|\right|x_i-x_j\left|\right|}^2/m(m-1).$

4. like the said a kind of facial image dimension reduction method that keeps based on local association of claim 2, it is characterized in that the difference vector computing method are in the said step 4: for any capable vector x _i, calculate the difference vector r of the weighting sum of itself and k neighbour row vector _i, k=9;

$r_i=x_i-{\mathrm{\Σ}}_{j\∈\mathrm{ne}\left(x_i\right)}\frac{w_{\mathrm{ij}}}{{\mathrm{\Σ}}_{j\∈\mathrm{ne}\left(x_i\right)}{w}_{\mathrm{ij}}}{x}_j---\left(2\right)$

Said local association keeps the calculating of matrix V following:

$V={\mathrm{\Σ}}_{i=1}^m{r}_i^T{r}_i---\left(3\right).$

5. like the said a kind of facial image dimension reduction method that keeps based on local association of claim 2, it is characterized in that, in the said step 6, for any capable vector x _i, calculate x _iM obtains a d dimension row vector, and wherein (m, n) s * t tie up thereby facial image is dropped to d d=min, realize the facial image dimensionality reduction.

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