CN108520210A - Based on wavelet transformation and the face identification method being locally linear embedding into - Google Patents
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Abstract
The invention discloses a kind of based on wavelet transformation and the face identification method being locally linear embedding into, facial image is pre-processed, face is decomposed by wavelet transformation, obtain four group component amount of facial image, the feature of four components is extracted using Local Liner Prediction, and Weighted Fusion is selected to obtain facial information feature, utilize least square method supporting vector machine training feature vector, and it is combined to form facial image grader with DAG, recognition of face is carried out by facial image grader, and exports recognition result；Face identification rate and calculating speed are accelerated, recognition of face efficiency is improved.
Description
Technical field：
The present invention relates to a kind of field of face identification, based on wavelet transformation and it is locally linear embedding into more particularly to a kind of
Face identification method.
Background technology：
Compared with biometrics identification technology, face characteristic has many advantages, such as uniqueness, easily access property, low cost.In order to
The needs for meeting practical application need to explore face identification method.In the prior art, under certain constraints,
Recognition of face achieves higher discrimination.But in actual operation, face is easy by illumination, imaging device and blocks etc. outer
The combined effect of boundary's factor, cause it is unrestricted under the conditions of recognition of face performance drastically decline.Therefore, recognition of face is still one
Challenging task.
Invention content：
The technical problem to be solved by the present invention is to：Overcome the deficiencies of the prior art and provide a kind of utilization wavelet transformation point
Solution obtains four components of facial image, later, executes LLE algorithms and distinguishes extraction feature from four components, and utilize weighting
It merges to obtain face recognition features' vector, finally, using least square method supporting vector machine learning training sample, to establish people
Face recognition classifier, realize recognition of face based on wavelet transformation and the face identification method that is locally linear embedding into.
The technical scheme is that：It is a kind of based on wavelet transformation and the face identification method that is locally linear embedding into, it is A, right
Facial image is pre-processed, and is decomposed to face by wavelet transformation, and four group component amount of facial image are obtained；
B, the feature of four components is extracted using Local Liner Prediction, and Weighted Fusion is selected to obtain facial information spy
Sign；
C, it using least square method supporting vector machine training feature vector, and is combined to form facial image grader with DAG；
D, recognition of face is carried out by facial image grader by the facial image of step A and step B operations, and exported
Recognition result.
Four group component amount are respectively depicted as LL, LH, HL and HH in the step A；Wherein, LL defines low frequency component, protects
The bulk information in original image is stayed, the feature of original image is substantially represented；LH indicates horizontal component, includes mainly related
The internal information of facial expression between eyes and face；HL is vertical component, including the hair of people, nose, ear and edge wheel
Wide information；HH represents diagonal line information, and reflection original contents are less；Its four group component amount are obtained by following steps：
DefinitionTwo dimensional scaling function is decomposed, can be used for calculating the product of two unidimensional scale functions later：
ψ (x) is phase wavelet function, and it is as follows to define three two-dimensional orthogonal wavelets functions：
F (x, y) is enabled to indicate that facial image, the approximate image of two-dimensional discrete signal f (m, n) are：
In above-mentioned formula, first item is the low-frequency approximation of facial image, and rest part is detail signal.
Size is the facial image A (x, y), wavelet transform (DWT, Discrete Wavelet of m*n
Transform) it is：
The step of component characterization, is in step B：It is locally linear embedding into (LLE) by establishing following mathematical model minimum
The error of linear expression：
The committed step of linearly embedding algorithm is：
Input：Sample cloth x={ x1,x2,…xn∈RD, the feature of D representative sample cloth amounts, ε represents neighbours space；
Output：Y={ y1,y2,…yn∈RD}；
(1) neighborhood search calculates the arest neighbors of each sample point Xi in higher dimensional space using k- near neighbor methods；
(2) the Partial Reconstruction weight matrix of sample point is calculated, and defines a cost function and is missed to minimize overall reconstruct
Difference；
Herein, xiRepresentative sample vector；WijRepresent weights；Weight is solved using smallest error function；
xiLinear combination be：
Wherein, NiRepresent the matrix of a D × K, Ni=[xi1,xi2,...,xik], WiRepresent the matrix of k × 1, wi
=[wi1,wi2,...,wik]T；
In each point and its neighbour by an anticlockwise or Scale Matrixes R, obtained weight matrix rebuilds expression, is：
(3) a local covariance matrix C is constructed, it is desirable that reconstruct minimal error is minimized, to obtain：
Cjk=(xi-xi,j)T(xi-xi,k) (10)
(4) local optimum W is obtained using method of Lagrange multipliers：
(5) mapping function y is foundI,All sample points are mapped in lower dimensional space, to obtain minimum object function：
The step of Weighted Fusion, is in step B：Select the corresponding minimum d non-zero of the facial characteristics of each component of vector
Characteristic value；Later, certain weight is selected to be merged, to obtain facial information feature；
X=ω1×LL'1+ω2×LH'1+ω3×HL'1+ω4×HH'1 (16)
The training step of feature vector is in step C：
Setting training sample cloth collection, such as (xi,yi), i=1,2 ..., n, the LSSVM linear classifications function in high-dimensional feature space
It is：
Wherein, b and w indicates two parameters；
In view of the complexity of error of fitting and function, according to structural risk minimization, formula (12) is：
Wherein, γ is regularization parameter；
In order to improve the efficiency of solution, it converts formula (13) to the optimization problem of Lagrange multiplier：
Wherein, αiIt is Lagrange multiplier；
According to KKT conditions, we can obtain：
And
Herein, I represents recognition matrix,
Least square method supporting vector machine of the radial basis function as kernel function is chosen, it is defined as follows：
Wherein, σ is bandwidth parameter.
The beneficial effects of the invention are as follows：
1, the present invention decomposes to obtain four components of facial image using wavelet transformation, later, executes LLE algorithms from four
Extraction feature is distinguished in component, and obtains face recognition features' vector using Weighted Fusion, finally, is supported using least square
Vector machine learning training sample realizes effective identification of face, accelerates face identification rate to establish recognition of face grader
And calculating speed, improve recognition of face efficiency.
2, facial image can be resolved into different components by wavelet transformation of the present invention.Its high frequency components includes face
Detailed information, low frequency component focus the more details of original facial image, to effectively reduce redundancy feature.
3, the present invention carries out feature extraction by being locally linear embedding into face component, each in nested space is adopted
Sampling point can carry out linear expression by its neighbour, keep the weight of each neighborhood constant in lower dimensional space, rebuild original
Data reduce reconstruction error.
4, the present invention by strategy combination builds a multiclass face classification device, by by all Multiple Classifier Fusions to k
(k-1)/2 in the DAG of node and k leaf, the multiclass face classification device for combining DAG to be combined with two class LSSVM is proposed.
Description of the drawings：
Fig. 1 is the flow chart based on wavelet transformation and the face identification method being locally linear embedding into.
Fig. 2 is wavelet decomposition component schematic diagram.
Fig. 3 is the relational graph of four components.
Fig. 4 is the structural schematic diagram of facial image grader.
Specific implementation mode：
Embodiment：Referring to Fig. 1, and the application is described in detail in conjunction with the embodiments.
Facial image is pre-processed, is definedTwo dimensional scaling function is decomposed, can be used for calculating two later
The product of unidimensional scale function.
ψ (x) is phase wavelet function, and it is as follows to define three two-dimensional orthogonal wavelets functions：
F (x, y) is enabled to indicate that facial image, the approximate image of two-dimensional discrete signal f (m, n) are：
In above-mentioned formula, first item is the low-frequency approximation of facial image, and rest part is detail signal.
Size is the facial image A (x, y), wavelet transform (DWT, Discrete Wavelet of m*n
Transform) it is：
Four components can be calculated after wavelet transformation, as shown in Figure 2.As seen from the figure, compared with original image, after transformation
Image maintain face and the more detailed frame of essential information, although losing the interior details feature of part, resolution
Or it is higher than in the past.
Above-mentioned four component based on wavelet transformation is respectively depicted as LL, LH, HL and HH.Wherein, LL defines low frequency component,
Retain the bulk information in original image, substantially represents the feature of original image；LH indicates horizontal component, includes mainly
Close the internal information of facial expression between eyes and face.HL is vertical component, including the hair of people, nose, ear and edge
Profile information.HH represents diagonal line information, and reflection original contents are less.Shown in Fig. 3.
It is a kind of Method of Nonlinear Dimensionality Reduction to be locally linear embedding into (LLE), is mainly assumed that on local sense, data knot
Structure be linear or local sense on point be hyperplane.Therefore, the linear combination of the consecutive points of any point is used for table
Show this point.The data set that there is nested manifold for one group, between nested space and the local neighborhood of internal lower dimensional space
Relationship should remain unchanged.Each sampled point in i.e. nested space can carry out linear expression by its neighbour, low
It keeps the weight of each neighborhood constant in dimension space, initial data is rebuild, to reduce reconstruction error.
By minimizing the error of this linear expression, following mathematical model can be established：
The committed step of linearly embedding algorithm is：
Input：Sample cloth x={ x1,x2,…xn∈RD, the feature of D representative sample cloth amounts, ε represents neighbours space.
Output：Y={ y1,y2,…yn∈RD}。
Set the number of sample：X={ xi|xi∈RD, i=1,2 ..., N }, the method based on LLE finds a low-dimensional mapping,
That is Y={ yi|yi∈Rd, i=1,2 ..., N }, d<<D, this is to be based on several standards, is target to improve recognition result.
(1) neighborhood search calculates the arest neighbors of each sample point Xi in higher dimensional space using k- near neighbor methods.
(2) the Partial Reconstruction weight matrix of sample point is calculated, and defines a cost function to minimize overall reconstruct
Error.
Herein, xiRepresentative sample vector；WijRepresent weights.Weight is solved using smallest error function.xij(i=1 ...
K) (j=1 ... k) represent point xiArest neighbors, be constrained to accordingly：
Weights are smaller, then weight matrix is about ideal, xiLinear combination be：
Wherein, NiRepresent the matrix of a D × K, Ni=[xi1,xi2,...,xik], WiRepresent the matrix of k × 1, wi
=[wi1,wi2,...,wik]T。
The main purpose of the algorithm is to reduce dimension, i.e., the data in higher dimensional space is mapped to lower dimensional space.For weight
Weight matrix is built, the coefficient of matrix needs three invariance for meeting Linear Mapping：Translation, scaling and rotation.It is shown below
The rotation of weight matrix coefficient and scaling invariance.In each point and its neighbour by an anticlockwise or Scale Matrixes R, obtain
Weight matrix, which is rebuild, to be indicated, is：
Formula (4) can portray for：
(3) a local covariance matrix C is constructed, it is desirable that reconstruct minimal error is minimized, to obtain：
Cjk=(xi-xi,j)T(xi-xi,k) (10)
(4) local optimum W is obtained using method of Lagrange multipliers：
(5) it in order to which all sample points are mapped in lower dimensional space, to obtain minimum object function, needs to find and reflect
Penetrate function yi：
Wherein, yiIt is xiLow-dimensional map vector, meet condition：
Formula (8) can be substituted by equation (10).
ε (y)=tr (yMyT) (14)
Using lagrange multiplier approach, then have：
In order to obtain the minimum loss function, Y is enabled to indicate the characteristic value for corresponding to b non-zero characteristics in matrix M, the spy of M
Value indicative arranges from small to large, and first characteristic value is almost nil, is generally discarded, be typically chosen characteristic value between 2 and d+1 to
Amount is output result.Matrix M is equal to (I-W)T(I-W)。
Select the corresponding minimum d nonzero eigenvalue of the facial characteristics of each component of vector.
Facial characteristics, i.e. LL'1、LH'1、HL'1、HH'1, extracted from four components LL1, LH1, HL1, HH1
's.Later, certain weight is selected to be merged, to obtain facial information feature.
X=ω1×LL'1+ω2×LH'1+ω3×HL'1+ω4×HH'1 (16)
During actual modeling and recognition of face, LL1 contains the main information of facial image, therefore its power
Weight is relatively large.LH1, HL1 include the facial characteristics of people, and weights are subsequent.HH1 includes then less information and minimum weight.Institute
The summation of weighted value is 1.Since low frequency component contains most of information of original image, for the weight of LL1 distribution
It is maximum；LH1 contains horizontal information, such as the eyes of face, mouth；HL1 contains more vertical informations, such as nose, ear and
Face contour etc., therefore HL1 is assigned with slightly smaller weighted value.
Setting training sample cloth collection, such as (xi,yi), i=1,2 ..., n, the LSSVM linear classifications function in high-dimensional feature space
It is：
Wherein, b and w indicates two parameters.
In view of the complexity of error of fitting and function, according to structural risk minimization, formula (12) is：
Wherein, γ is regularization parameter.
In order to improve the efficiency of solution, it converts formula (13) to the optimization problem of Lagrange multiplier：
Wherein, αiIt is Lagrange multiplier.
According to KKT conditions, we can obtain：
And
Herein, I represents recognition matrix,
Least square method supporting vector machine of the radial basis function as kernel function is chosen, it is defined as follows：
Wherein, σ is bandwidth parameter.
Herein, the facial image feature extracted is input to LSSVM to be trained, runs face classification device later.
Since the identification of facial image is a multicategory classification problem, least square method supporting vector machine can only solve the problems, such as two classification.
Therefore, it is necessary to build a multiclass face classification device by strategy combination, proposition combines DAG to be combined with two class LSSVM
Method, facial image grader is as shown in Figure 4, by by all Multiple Classifier Fusions to k (k-1)/2 node and k leaf
DAG in, it is therein to contain k unknown sample.
The above described is only a preferred embodiment of the present invention, be not intended to limit the present invention in any form, it is all
It is that any simple modification, equivalent change and modification made by above example are still fallen within according to the technical essence of the invention
In the range of technical solution of the present invention.
Claims (5)
1. a kind of based on wavelet transformation and the face identification method being locally linear embedding into, step is：A, facial image is carried out
Pretreatment, decomposes face by wavelet transformation, obtains four group component amount of facial image；
B, the feature of four components is extracted using Local Liner Prediction, and Weighted Fusion is selected to obtain facial information feature；
C, it using least square method supporting vector machine training feature vector, and is combined to form facial image grader with DAG；
D, recognition of face is carried out by facial image grader by the facial image of step A and step B operations, and exports identification
As a result.
2. it is according to claim 1 based on wavelet transformation and the face identification method being locally linear embedding into, it is characterized in that：Institute
It states four group component amount in step A and is respectively depicted as LL, LH, HL and HH；Wherein, LL defines low frequency component, retains original image
In bulk information, substantially represent the feature of original image；LH indicates horizontal component, includes mainly related eyes and face
Between facial expression internal information；HL is vertical component, including the hair of people, nose, ear and edge contour information；HH generations
Table diagonal line information, reflection original contents are less；Its four group component amount are obtained by following steps：
DefinitionTwo dimensional scaling function is decomposed, can be used for calculating the product of two unidimensional scale functions later：
ψ (x) is phase wavelet function, and it is as follows to define three two-dimensional orthogonal wavelets functions：
F (x, y) is enabled to indicate that facial image, the approximate image of two-dimensional discrete signal f (m, n) are：
In above-mentioned formula, first item is the low-frequency approximation of facial image, and rest part is detail signal.
Size is the facial image A (x, y) of m*n, wavelet transform (DWT, Discrete Wavelet Transform)
For：
。
3. it is according to claim 1 based on wavelet transformation and the face identification method being locally linear embedding into, it is characterized in that：Step
The step of component characterization, is in rapid B：It is locally linear embedding into linear expression in (LLE) by establishing following mathematical model minimum
Error：
The committed step of linearly embedding algorithm is：
Input：Sample cloth x={ x1,x2,…xn∈RD, the feature of D representative sample cloth amounts, ε represents neighbours space；
Output：Y={ y1,y2,…yn∈RD}；
(1) neighborhood search calculates the arest neighbors of each sample point Xi in higher dimensional space using k- near neighbor methods；
(2) the Partial Reconstruction weight matrix of sample point is calculated, and defines a cost function to minimize overall reconstructed error；
Herein, xiRepresentative sample vector；WijRepresent weights；Weight is solved using smallest error function；
xiLinear combination be：
Wherein, NiRepresent the matrix of a D × K, Ni=[xi1,xi2,...,xik], WiRepresent the matrix of k × 1, wi=
[wi1,wi2,...,wik]T；
In each point and its neighbour by an anticlockwise or Scale Matrixes R, obtained weight matrix rebuilds expression, is：
(3) a local covariance matrix C is constructed, it is desirable that reconstruct minimal error is minimized, to obtain：
Cjk=(xi-xi,j)T(xi-xi,k) (10)
(4) local optimum W is obtained using method of Lagrange multipliers：
(5) mapping function y is foundi, all sample points are mapped in lower dimensional space, to obtain minimum object function：
。
4. it is according to claim 1 based on wavelet transformation and the face identification method being locally linear embedding into, it is characterized in that：Step
The step of Weighted Fusion, is in rapid B：Select the corresponding minimum d nonzero eigenvalue of the facial characteristics of each component of vector；It
Afterwards, certain weight is selected to be merged, to obtain facial information feature；
X=ω1×LL′1+ω2×LH′1+ω3×HL′1+ω4×HH′1 (16) 。
5. it is according to claim 1 based on wavelet transformation and the face identification method being locally linear embedding into, it is characterized in that：Step
The training step of feature vector is in rapid C：
Setting training sample cloth collection, such as (xi,yi), i=1,2 ..., n, LSSVM linear classifications function is in high-dimensional feature space：
Wherein, b and w indicates two parameters；
In view of the complexity of error of fitting and function, according to structural risk minimization, formula (12) is：
Wherein, γ is regularization parameter；
In order to improve the efficiency of solution, it converts formula (13) to the optimization problem of Lagrange multiplier：
Wherein, αiIt is Lagrange multiplier；
According to KKT conditions, we can obtain：
And
Herein, I represents recognition matrix,
Least square method supporting vector machine of the radial basis function as kernel function is chosen, it is defined as follows：
Wherein, σ is bandwidth parameter.
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