CN103020640A - Facial image dimensionality reduction classification method based on two-dimensional principal component analysis - Google Patents
Facial image dimensionality reduction classification method based on two-dimensional principal component analysis Download PDFInfo
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Abstract
The invention discloses a facial image dimensionality reduction classification method based on two-dimensional principal component analysis. The method comprises the steps of: firstly, performing image transformation on training samples; secondly, working out a covariance matrix according to transformed image data by using a 2DPCA (Data Processing Control Area) method, and working out the best projection matrix of a population covariance matrix; thirdly, performing spacial dimensionality reduction on projection of the training samples on the best projection matrix; and finally, classifying the training samples according to a nearest rule in a low-dimensional space. The method disclosed by the invention is quick to calculate a feature vector, accurate in calculation and high in recognition rate.
Description
Technical field
The present invention relates to dimensionality reduction and classification in the facial image identification, refer to particularly a kind of facial image dimension reduction method based on the two-dimensional principal component analysis method.
Background technology
The facial image identification first step is exactly dimensionality reduction, secondly is exactly classification.Can cause that calculated amount increases, the visuality of data is poor owing to classify at higher dimensional space, and in the good Application of Statistic Methods of lower dimensional space robustness behind higher-dimension, its robustness is variation thereupon also.
Because people's face matrix is the matrix of a higher-dimension, it is carried out dimensionality reduction is necessary.Present used recognition of face dimension reduction method normal operation PCA(Principal Component Analysis, principal component analysis (PCA)) and 2DPCA (two-dimensional Principal ComponentAnalysis, two-dimensional principal component analysis method).PCA need to be converted into people's face image array the vector of a higher-dimension, calculate its covariance matrix, because small sample problem (the covariance matrix space is large, and relatively training sample is less), its covariance matrix is difficult to calculate, and it is very consuming time to calculate its proper vector.
In addition, someone has proposed the 2DPCA method, the main thought of the method is that it does not need to transfer the facial image matrix to vector, directly by its covariance matrix of people's face matrix computations, because this covariance matrix space is little, training sample is sufficient relatively, causes small sample problem to alleviate, it is fast to calculate its proper vector, and calculates accurately.
But, covariance matrix from PCA and two kinds of methods calculating of 2DPCA, the covariance matrix that the 2DPCA method is tried to achieve is less than PCA method, and just utilized element on the PCA method covariance matrix diagonal line, many information have been lost obviously, if the 2DPCA method can be utilized more information, the discrimination of the method can be improved.
Summary of the invention
The object of the invention is to overcome above-mentioned the deficiencies in the prior art and a kind of facial image dimensionality reduction and sorting technique based on the two-dimensional principal component analysis method is provided, the method is according to the architectural characteristic of people's face vertical symmetry, the covariance matrix information of utilizing the two-dimensional principal component analysis method to lose, realize rapidly and accurately calculated characteristics vector, and discrimination is high.
Realize that the technical scheme that the object of the invention adopts is: a kind of facial image dimensionality reduction and sorting technique based on the two-dimensional principal component analysis method comprise:
(1) gets the gray level image that resolution is the facial image training sample of h * w;
(2) the left and right half face image array with people's face in the described facial image training sample is listed as respectively conversion, form respectively the column vector of the left and right half face image of people's face, two column vectors that described people's face is left and right are merged into the matrix of one two row in order, namely obtain the facial image matrix after the conversion;
(3) utilize the two-dimensional principal component analysis method to calculate the population covariance matrix of the facial image matrix after the described conversion;
(4) the optimum projection matrix of the described population covariance matrix of calculating;
(5) the space dimensionality reduction is carried out in the projection on described optimum projection matrix with the facial image matrix after the described conversion and facial image test sample book;
(6) according to nearest neighbouring rule test sample book is classified.
The inventive method is based on the realization of two-dimensional principal component analysis method to the dimensionality reduction of facial image, the method does not need to transfer the facial image matrix to vector, directly by its covariance matrix of people's face matrix computations, this covariance matrix space is little, training sample is sufficient relatively, cause small sample problem to alleviate, the calculated characteristics vector is fast, and calculates accurately.
Compare with the employed principal component analysis (PCA) of existing recognition of face dimensionality reduction, the covariance matrix that the present invention uses the two-dimensional principal component analysis method to try to achieve is less than principal component analysis (PCA), has improved the speed of calculating and the accuracy rate of recognition of face.In addition, the covariance matrix information that this method has utilized more two-dimensional principal component analysis method to lose is so that the recognition of face rate is improved.
Description of drawings
Fig. 1 is the process flow diagram that the present invention is based on the facial image dimensionality reduction sorting technique of two-dimensional principal component analysis method;
Fig. 2 is training sample image in the ORL database;
Fig. 3 is the image array of facial image in certain width of cloth training sample among Fig. 1;
Fig. 4 is the image array of left half face of Fig. 3;
Fig. 4-1 is to the image array after the conversion of Fig. 4 procession;
Fig. 5 is the image array of right half face of Fig. 3;
Fig. 5-1 is to the image array after the conversion of Fig. 5 procession;
Fig. 6 is the facial image matrix after Fig. 4-1 and Fig. 5-1 merge.
Embodiment
The present invention is described in further detail below in conjunction with the drawings and specific embodiments.
As shown in Figure 1, the facial image dimension reduction method that the present invention is based on the two-dimensional principal component analysis method may further comprise the steps:
Step S101: getting resolution is the gray level image of the facial image training sample of h * w, and h and w represent respectively line number and the columns of facial image matrix.Present embodiment is got the facial image in the ORL face database, and the ORL face database facial image data that to be univ cambridge uk collect in the laboratory from 1992 to 1994 are by 40 people, everyone 10 width of cloth, totally 400 width of cloth images form.Be that resolution is 112*92 with all image scalings in the ORL face database, gray level 256.In everyone 10 width of cloth facial image samples, choose at random 5 width of cloth people face head portraits as training sample, people's face sample of choosing as shown in Figure 2, remaining 5 width of cloth facial images are test sample book, like this, the sum of test sample book and training sample is respectively 200 width of cloth.
Step S102: all view data among the step S101 are carried out rank transformation.The left and right half face image array of people's face in the getting facial image training sample is listed as respectively conversion.
The image array of facial image training sample is m * n matrix, and then to be as matrix be the matrix of m * (n/2) to left and right half face figure.
The image array of facial image training sample as shown in Figure 3, a left side half face image array of this facial image matrix as shown in Figure 4, left half face image array is as shown in Figure 5.
Ranks conversion method to a left side shown in Figure 4 half face image array is: the back that the secondary series data in the image array is come first row data last column, successively the 3rd row, the 4th row are done same conversion, form the column vector of left half face, shown in Fig. 4-1.
Ranks conversion method to the right side shown in Figure 5 half face image array is: the secondary series data in the image array are come the back of first row data last column, successively the 3rd row, the 4th row are done same conversion, form the column vector of left half face, shown in Fig. 5-1.
The column vector of the left and right half face image of above-mentioned gained is merged into the matrix of one two row in order, namely obtains conversion descendant face image array, as shown in Figure 6.In the present embodiment, the size of everyone face image array is become (56 * 92,2).
Step S103: the facial image matrix to the conversion gained, utilize formula
Calculate the population covariance matrix Gt of training sample, A
jJ sample of random sample matrix of a m * nn of expression,
Be the Mean Matrix of image, M represents number of training.The size of this covariance matrix is (56 * 92,56 * 92) in the present embodiment.
Step S104: the optimum projection matrix that obtains population covariance matrix Gt.This optimum projection matrix is maximum d the corresponding proper vector of eigenwert of covariance matrix Gt, according to formula
J (X) is G
tMark, calculate optimum projection matrix X={X1 ..., Xd}.X
iAnd X
jBe respectively matrix G
tEigenwert d
iAnd d
jProper vector.The numerical value of d is from big to small d, and the numerical value of d is determined to choose the d value according to correct recognition rata and the experience of image.Choose d=10 in the present embodiment, can keep 95% energy, therefore the size of optimum projection matrix is (56 * 92,10).
Step S105: utilize the method for projection to carry out dimensionality reduction to training sample.The training sample original size is 112 * 92, is (56 * 92,2) through the size after step (1) conversion, according to formula Y
k=A
TX
k, k=1,2,, d carries out size (2,10) behind the dimensionality reduction to every class training sample, so original size 112 * 92, through having become 20 dimensions after the method.
Step S106: test sample book is classified according to proximity principle.Sample Y after lower dimensional space is to dimensionality reduction
kClassify two matrix B
i=[Y
1 (i), Y
2 (i)..., Y
d (i)] and B
j=[Y
1 (j), Y
2 (j)..., Y
d (j)] between distance be:
Wherein,
Represent two major component Y
k (i)And Y
k (j)Euclidean distance, suppose whether B of training sample
1, B
2..., B
M, M is the sum of training sample, each training sample distributes a class-mark ω
k, a given test sample book B is if d is (B, B
l)=mind (B, B
j), and B
l∈ ω
k, then the result of classification is B ∈ ω
k
The calculative covariance matrix of the inventive method is larger than 2DPCA, but less than PCA method, as: be 112 * 92 facial image for a resolution, the covariance matrix size of obtaining with the PCA method is (112 * 92) * (112 * 92), the covariance matrix size that calculates with the inventive method is (56 * 92) * (56 * 92), the covariance matrix size that calculates with the 2DPCA method is (92) * (92), therefore, use the dimension of the inventive method gained covariance matrix than PCA method little 4 times ((112 * 92) * (112 * 92)/((56 * 92) * (56 * 92))=4), than large 2116 times of 2DPCA method (((56 * 92) * (56 * 92))/(112 * 112)=2116).The inventive method is with respect to the 2DPCA method, the complicacy of calculating increases, but has utilized drop-out more, and the covariance information of utilization is 2116 times of 2DPCA method, the correct recognition rata of people's face also is improved, and has farthest utilized the covariance information in half face space; Also reduced simultaneously recognition time, because the inventive method represents that the coefficient ratio 2DPCA method that people's face uses is little, such as: be people's face of 112 * 92 for a resolution, the 2DPCA method needs 95 * 5=460 coefficient, and 3 * 2 * 5=30 coefficient of this method needs.So the inventive method improves accuracy rate, the minimizing recognition time of recognition of face and reduces the coefficient of eigenface.
The inventive method is good reliability in actual applications, and efficient is high, uses principal component analysis (PCA) (hereinafter to be referred as PCA) method to compare with tradition, and it has reduced the complicacy of calculating, and has improved the discrimination of facial image; Compare with two-dimensional principal component analysis method (hereinafter to be referred as 2DPCA) method, it can utilize more covariance information, with the face space of leting others have a look at of coefficient table still less, has compressed image energy, has also improved the accuracy rate of recognition of face simultaneously.But owing to used covariance information more, aspect the complicacy of calculating, the time cost of cost is larger than 2DPCA method.Show through a large amount of experimental studies in ORL and YALE storehouse, this algorithm is compared the 2DPCA method, accuracy rate in recognition time and identification improves a lot, and compares with traditional eigenface method, ICA method and nuclear eigenface method, and the accuracy rate of identification also is improved.
The below is take hardware environment as DUO T5850CPU, the 2G internal memory, software environment is used respectively the facial image dimensionality reduction sorting technique (hereinafter to be referred as V2DPCA) that the present invention is based on the two-dimensional principal component analysis method and existing method that present embodiment is got facial image by the concrete experimental enviroment of MATLAB7.0 to carry out the dimensionality reduction sorting technique, with the advantage of explanation this patent method.
Experiment 1
Table 1 is for adopting PCA, 2DPCA and the correct recognition rata of V2DPCA method on the ORL database, and as can be seen from Table 1, the method for V2DPCA is higher than other method aspect the accuracy of identification, is because the V2DPCA method has been used more image local information.
| Method | Correct recognition rata (%) | Dimension |
| The PCA(eigenface) | 83.9 | 34 |
| 2DPCA | 93.4 | 92*10=920 |
| V2DPCA | 96.9 | 2*10=20 |
Table 1
Experiment 2
Table 2 is 2DPCA and the recognition time result of V2DPCA in identical correct recognition rata situation, proper vector dimension and identify relation between alternate.As can be seen from Table 2, the V2DPCA algorithm just can represent a width of cloth head portrait with still less coefficient (such as 2DPCA with 920 coefficients, V2DPCA with 20 coefficients), and the time of identifying also lacks than other method.
| Method | Discrimination (%) | Dimension | Recognition time (S) |
| 2DPCA | 91.5 | 92*10=920 | 1.87 |
| V2DPCA | 91.5 | 2*10=20 | 1.53 |
Table 2
Experiment 3
Test the recognition performance of comparison distinct methods in the situation that sample size changes by one group.In the present embodiment, carry out four groups of test experiments under the training sample number situation of change, when carrying out the k time experiment, each class is chosen a top k sample and is done training sample, all the other samples are made test sample book, use respectively V2DPCA, 2DPCA and PCA method to carry out feature extraction, use at last the arest neighbors method to classify.For V2DPCA and 2DPCA method, calculate the distance between two eigenmatrixes; For the PCA method, use the distance between two vectors of Euclidean distance test.Table 3 is the highest recognition accuracy of three kinds of methods under different training sample sizes.As can be seen from Table 3, the Performance Ratio 2DPCA of V2DPCA method goes with PCA.
| Number of training | 1 | 2 | 3 | 4 |
| PCA | 66.9(39) | 84.7(79) | 88.2(95) | 90.8(60) |
| 2DPCA | 76.7(92*2) | 89.1(92*2) | 91.8(92*6) | 95.0(92*5) |
| V2DPCA | 78.1(10*2) | 90.1(10*2) | 92.3(15*2) | 95.8(13*2) |
Table 3
Experiment 4
Table 4 be three kinds of methods in the used time of feature extraction (second), li can find out that the performance of 2DPCA is best from table 4 because when utilizing the 2DPCA method to carry out feature extraction, the image covariance matrix that obtains is (the dimension of m * m); And V2DPCA, the image covariance matrix that obtains is ((n/2 * m) * (n/2 * m)); And the PCA method, the image covariance matrix that obtains for ((m * n) * ((m * n)), therefore, the dimension that utilizes the covariance matrix of the resulting image of 2DPCA method is minimum, the complicacy of calculating is namely minimum.Along with the number increase of each classification training sample, the calculating relative complexity of V2DPCA, 2DPCA and PCA is also increasing.
| Every class number of training | 1 | 2 | 3 | 4 | 5 |
| PCA | 44.5 | 89.0 | 139.36 | 198.95 | 304.61 |
| 2DPCA | 10.76 | 11.23 | 12.59 | 13.40 | 14.03 |
| V2DPCA | 15.78 | 16.34 | 17.78 | 18.89 | 19.1 |
Table 4
Experiment 5
Use the inventive method and traditional method to compare in the ORL storehouse.V2DPCA method and Fisherfaces, ICA, Kernel Eigenfaces are compared.In relatively, use two experimental programs, scheme one is chosen 5 samples in front for each class of present embodiment and is made training sample, and scheme two is to choose randomly a sample in data centralization to make test sample book, and remaining all is training sample.The result of this experimental program is as shown in table 5.As can be seen from Table 5, the V2DPCA method is higher than the discrimination of other method.
Table 5
Experiment 6
Use the inventive method and classic method to compare in the YALE storehouse.The YALE face database is by Yale University's computation vision and control center, comprises 15 volunteers' 165 pictures, comprises illumination, the variation of expression and attitude, and each has 11 different pictures.In this experiment, the gray scale of every pictures is repositioned onto the 100*80 pixel, the scheme of employing is to choose at random a pictures to make test sample book, and other is training sample.Table 6 is with V2DPCA, PCA(Eigenfaces), the experimental result of ICA, Kernel Eigenfaces method compares.As can be seen from Table 6, V2DPCA method of the present invention is higher than the discrimination of PCA, ICA and kernel Eigenfaces.
| Method | Discrimination (%) |
| PCA（Eigenfaces） | 70.52 |
| ICA | 70.52 |
| Kernel?Eigenfaces | 71.63 |
| V2DPCA | 84.45 |
Table 6.
Claims (6)
1. the facial image dimensionality reduction sorting technique based on the two-dimensional principal component analysis method is characterized in that, comprising:
(1) gets the gray level image that resolution is the facial image training sample of h * w;
(2) the left and right half face image array with people's face in the described facial image training sample is listed as respectively conversion, form respectively the column vector of the left and right half face image of people's face, two column vectors that described people's face is left and right are merged into the matrix of one two row in order, namely obtain the facial image matrix after the conversion;
(3) utilize the two-dimensional principal component analysis method to calculate the population covariance matrix of the facial image matrix after the described conversion;
(4) the optimum projection matrix of the described population covariance matrix of calculating;
(5) the space dimensionality reduction is carried out in the projection on described optimum projection matrix with the facial image matrix after the described conversion and facial image test sample book;
(6) according to nearest neighbouring rule test sample book is classified.
2. described facial image dimensionality reduction sorting technique based on the two-dimensional principal component analysis method according to claim 1 is characterized in that the concrete grammar of described step (3) is:
According to the two-dimensional principal component analysis method, to the facial image matrix after the described conversion, by formula
Calculate the population covariance matrix G of described training sample
t, A
jBe j sample of random sample matrix,
Be the Mean Matrix of image, M represents number of training.
3. described facial image dimensionality reduction sorting technique based on the two-dimensional principal component analysis method according to claim 1 and 2 is characterized in that, the concrete grammar that calculates optimum projection matrix in the described step (4) is:
The optimum projection matrix of described facial image matrix is population covariance matrix G
tMaximum d the corresponding proper vector of eigenwert, namely satisfy formula
J (X) is G
tMark, X={X
1..., X
dBe optimum projection matrix, X
iAnd X
jBe respectively matrix G
tEigenwert d
iAnd d
jProper vector.
4. described facial image dimensionality reduction sorting technique based on the two-dimensional principal component analysis method according to claim 1 is characterized in that the concrete grammar that carries out the space dimensionality reduction in the described step (5) is:
Calculate described facial image training sample within class scatter matrix;
According to formula Y
k=A
TX
k, k=1,2 ..., d. carries out dimensionality reduction to every class training sample, and wherein X is described optimum projection matrix, Y
kBe the sample behind the dimensionality reduction.
5. according to claim 1 or 4 described facial image dimensionality reduction sorting techniques based on the two-dimensional principal component analysis method, it is characterized in that the concrete grammar in the described step (5) is:
According to the nearest neighbor classifier principle, the sample Y after lower dimensional space is to dimensionality reduction
kClassify two matrix B
i=[Y
1 (i), Y
2 (i)..., Y
d (i)] and B
j=[Y
1 (j), Y
2 (j)..., Y
d (j)] between distance be:
Wherein,
Represent two major component Y
k (i)And Y
k (j)Euclidean distance, the setting training sample is B
1, B
2..., B
M, M is the sum of training sample, each training sample distributes a class-mark ω
k, a given test sample book B, if B, B
l)=mind (B, B
j), and B
l∈ ω
k, then the result of classification is B ∈ ω
k
6. described facial image dimensionality reduction sorting technique based on the two-dimensional principal component analysis method according to claim 1, it is characterized in that: the gray level of described gray level image is 256.
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