CN110991228A - Improved PCA face recognition algorithm resistant to illumination influence - Google Patents

Improved PCA face recognition algorithm resistant to illumination influence Download PDF

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CN110991228A
CN110991228A CN201911015153.2A CN201911015153A CN110991228A CN 110991228 A CN110991228 A CN 110991228A CN 201911015153 A CN201911015153 A CN 201911015153A CN 110991228 A CN110991228 A CN 110991228A
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王海涛
苏南溪
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Qingdao Zhongke Zhibao Technology Co ltd
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Abstract

The invention belongs to the field of image processing, and discloses an improved PCA face recognition algorithm with illumination influence resistance, which comprises the following steps: (1) selecting a training sample set; (2) classifying according to the angle and illumination of the image, and dividing the image data into a plurality of subdata sets; (3) calculating the mean vector, the centralized data matrix and the covariance matrix of all the subdata sets; (4) calculating eigenvalues of the covariance matrix, selecting the largest k eigenvalues from the eigenvalues, and solving the corresponding eigenvectors of the eigenvalues; after weight coefficients are added to the feature vectors respectively, the feature vectors are arranged into a transformation matrix W according to columns; (5) calculating and storing projection matrixes of all images in the training sample set; (6) and calculating a projection matrix of the face to be recognized, traversing the projection matrices of all head portraits in the search sample training set to perform matching calculation, and obtaining a matching result. The invention can reduce the illumination influence and improve the recognition rate.

Description

Improved PCA face recognition algorithm resistant to illumination influence
Technical Field
The invention belongs to the field of image processing, and particularly relates to an improved PCA face recognition algorithm with illumination influence resistance.
Background
Pca (principal Component analysis), also known as principal Component analysis, is a commonly used effective method for processing, compressing, and extracting information based on a variable covariance matrix. The basic principle is that the main components of human face are extracted by K-L transformation to form a characteristic face space, a test image is projected to the space during recognition to obtain a group of projection coefficients, and the projection coefficients are recognized by comparing with each human face image.
The K-L transformation takes an orthogonal matrix formed by normalized orthogonal feature vectors of a covariance matrix of original data as a transformation matrix, and realizes data compression on a transformation domain. The method has the characteristics of decorrelation, energy concentration and the like, is a transformation which has the minimum distortion under the mean square error measure and can remove the correlation between original data, and PCA (principal component analysis) is a K-L transformation matrix formed by selecting eigenvectors formed by the first K maximum eigenvalues of a covariance matrix.
The number of the principal components is selected in such a way that the accumulated variance of the reserved part accounts for the percentage of the sum of the variances, and if one principal component is reserved, the accumulated variance is increased a little and is not reserved any more.
The implementation of conventional PCA theoretically requires many assumptions, which makes it impossible to identify it as effectively as theoretically in many cases. First, the conventional PCA algorithm requires that the standard training matrix conforms to gaussian distribution, and when the probability distribution of the investigated data does not meet the gaussian distribution, it cannot use variance and covariance to properly describe noise and redundancy, and cannot obtain a feature subspace well reflecting the training space, which inevitably makes the recognition rate of PCA relatively low.
1. The probability distribution of the investigated data can not meet the Gaussian distribution and can not resist the noise influence;
2. the image is greatly influenced by illumination change, the illumination influence is not considered in the traditional PCA, and the weight of the feature vector is the same.
Disclosure of Invention
In order to meet the actual requirements in the field of image processing, the invention overcomes the defects in the prior art and solves the technical problem that
In order to solve the technical problems, the invention adopts the technical scheme that: an improved PCA face recognition algorithm resistant to illumination effects, comprising the steps of:
(1) selecting a training sample set, wherein the training sample set comprises a plurality of face targets, each face target selects s images as training samples, and each image is written into a column vector form and arranged into a data matrix:
X＝(X1,X2,...,Xn)；
wherein n represents the number of images and n/s represents the number of human face targets;
(2) classifying according to the angle and illumination of the image, and dividing the image data matrix into j sub-data sets S1,S2...Sj(ii) a j is less than or equal to n, j represents the number of the sub data sets, S represents the collection set with the same attribute in the sample image, wherein, the number of the corresponding data matrix in the ith sub data set is assumed to be niThen n is1+n2+……+niN; subdata set SiThe expression of (a) may be expressed as:
Figure BDA0002245449320000021
wherein i is 1, 2, … … j;
(3) computing all the subdata sets S1,S2...SjMean vector mu of1，μ2……μj(ii) a Then, calculating a centralized data matrix C and a covariance matrix Sigma; the calculation formulas are respectively as follows:
Figure BDA0002245449320000022
C＝(S1-μ1,S2-μ2,...,Sj-μj)；
Figure BDA0002245449320000023
wherein, muiMean vector, S, representing the ith sub-datasetitRepresenting the t-th vector in the i-th sub data set;
(4) calculating the eigenvalues of the covariance matrix, selecting the largest k eigenvalues, and solving the eigenvectors e corresponding to the k eigenvalues from large to small in sequence1，e2……ek(ii) a And after weighting coefficients are added to the feature vectors respectively, the feature vectors are arranged into a transformation matrix according to columnsW；
(5) Calculating and storing projection matrixes of all images X1-Xn in the training sample set;
(6) calculating a projection matrix chZ of the face Z to be recognizediAnd traversing the projection matrixes of all head portraits in the search sample training set to perform matching calculation to obtain a matching result.
In the step (4), the first three principal components e in the k feature vectors are combined1、e2、e3Adding weight coefficient of 0.8 to the fourth and fifth eigenvectors e4、e5Each weight of 1.2 is added, and the transformation matrix W is arranged according to columns, namely:
W＝(0.8e1，0.8e2，0.8e3，1.2e4，1.2e5，e6，...，ek)。
in the step (5), the nth image X in the training sample setnThe calculation formula of the projection matrix is as follows:
Qn＝WT(Xn-μm)；
wherein, WTA transpose matrix that is a transform matrix W; mu.smRepresenting the nth image XnMean vector of the m-th sub-data set.
In the step (6), the projection matrix chZ of the face ZiAnd the formula of the matching calculation is respectively as follows:
chZi＝WT(Z-μi)；
Q＝min||Qi-chZi||k；
wherein, the matching result is that the human face Z is the kth individual.
In the step (4), the value of k is not less than 5.
In the step (1), each face target selects s-4 images as training samples.
Compared with the prior art, the invention has the following beneficial effects:
(1) the invention carries out the block pre-treatment of the sub data sets before the image processing, and the training samples in each sub data set are used to accord with the Gaussian distribution, which is more effective than the traditional PCA algorithm.
(2) The invention carries out the block division of the subdata set and then uses the traditional PCA algorithm to carry out calculation, after the characteristic vector is obtained by calculation, the weighting reduces the proportion of the first three main components, increases the proportion of the fourth component and the fifth component, reduces the influence of illumination on the experimental result and improves the recognition rate;
(3) the algorithm of the invention can better reflect the face attribute and further improve the recognition rate by the characteristic vector obtained by blocking and processing the subdata set.
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FIG. 1 is a schematic flow chart of an improved PCA face recognition algorithm for resisting illumination influence according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of face recognition using an improved PCA face recognition algorithm for resisting illumination effects proposed for the embodiment of the present invention;
FIG. 3 is a schematic diagram of another face recognition process using an improved PCA face recognition algorithm for resisting illumination according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of another face recognition process using an improved PCA face recognition algorithm for resisting illumination according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of another face recognition process using an improved PCA face recognition algorithm for anti-illumination effect proposed for the embodiment of the present invention;
FIG. 6 is a schematic diagram of another face recognition process using an improved PCA face recognition algorithm for resisting illumination according to an embodiment of the present invention;
fig. 7 is a schematic diagram of another face recognition process using an improved PCA face recognition algorithm for resisting illumination according to an embodiment of the present invention.
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to specific embodiments and accompanying drawings, and it is obvious that the described embodiments are some, but not all embodiments of the present invention; all other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, an embodiment of the present invention provides an improved PCA face recognition algorithm with illumination resistance, which includes the following steps:
(1) selecting a training sample set, wherein the training sample set comprises a plurality of face targets, each face target selects s images as training samples, and each image is written into a column vector form and arranged into a data matrix:
X＝(X1,X2,...,Xn)； (1)
where n represents the number of images and n/s represents the number of face objects.
(2) Classifying according to the angle and illumination of the image, and dividing the image data matrix into j sub-data sets S1,S2...Sj(ii) a j is less than or equal to n, j represents the number of the sub data sets, S represents the collection of the same attribute in the sample image, wherein, the number of the corresponding data matrix (image) in the ith sub data set is assumed to be niThen n is1+n2+……+niN; subdata set SiThe expression of (a) may be expressed as:
Figure BDA0002245449320000041
wherein i is 1, 2, … … j; (2)
when the image data matrix is classified, if the angles or illumination of some images tend to be consistent, the images are classified into the same sub data set, the images in each sub data set have similar characteristics, and the data set contains the images with the consistent angles or illumination, so that j is less than or equal to n. The grouping through angles or illumination is a subjective judgment, and finding out image similarity points so that each sub data set better conforms to Gaussian distribution is the prior art, but the grouping is different according to different individuals of images, and is a preprocessing stage of the whole process. By grouping according to the angle and illumination of the image, the image characteristics of each subdata set tend to be consistent, and the internal image of the subdata set is ensured to meet the Gaussian distribution condition.
(3) Computing the mean vector μ for all sub-data sets1，μ2……μj(ii) a Then, calculating a centralized data matrix C and a covariance matrix Sigma; the calculation formulas are respectively as follows:
Figure BDA0002245449320000042
C＝(S1-μ1,S2-μ2,...,Sj-μj)； (4)
Figure BDA0002245449320000043
wherein the covariance matrix is calculated based on the centralized data matrix C after the data set is partitioned. Mu.siMean vector, S, representing the ith sub-datasetitRepresenting the t-th vector in the i-th sub-data set.
(4) By calculating CTC, calculating the eigenvalues of the covariance matrix, selecting the largest k eigenvalues, and solving the eigenvectors e corresponding to the k eigenvalues from large to small in sequence1，e2……ek(ii) a And after weighting coefficients are added to the feature vectors, the feature vectors are arranged into a transformation matrix W by columns.
Specifically, the weight coefficients are added to the first three principal components e in the k feature vectors1、e2、e3Adding weight coefficient of 0.8 to the fourth and fifth eigenvectors e4、e5Each weight of 1.2 is added, and the transformation matrix W is arranged according to columns, namely:
W＝(0.8e1，0.8e2，0.8e3，1.2e4，1.2e5，e6，...，ek)； (6)
specifically, the value of k is a positive integer of 5 or more.
(5) Calculating and storing projection matrixes of all images X1-Xn in the training sample set;
specifically, the calculation formula of the projection matrix of the nth image Xn in the training sample set is as follows:
Qn＝WT(Xn-μm)； (7)
wherein, WTA transpose matrix that is a transform matrix W; mu.smRepresents the mean vector of the mth sub-dataset in which the nth image Xn is located. When the projection of each image is calculated, the weight coefficient in the step (4) is introduced into the used feature vector, namely different coefficients are applied to different feature vectors to resist the influence of illumination change, the key information of the human face can be kept, and the identification accuracy rate is improved.
(6) Calculating a projection matrix chZ of the face Z to be recognizediAnd traversing the projection matrixes of all head portraits in the search sample training set to perform matching calculation to obtain a matching result.
In particular, the projection matrix chZ of the face ZiAnd the formula of the matching calculation is respectively as follows:
chZi＝WT(Z-μi)； (8)
Q＝min||Qi-chZi||k； (9)
wherein, the matching result is that the human face Z is the kth individual.
And selecting 20 persons as face targets, selecting 4 images from each person, using a total of 80 images as training samples to form a sample training set, wherein the number of persons in the testing set is the same as that in the training set, and the facial expression of each person is different from that in the training set, so that the effect of the testing set is verified. As shown in fig. 2 to 7, in the experimental results, the left side is a test set image, which is a real image photographed by a mobile phone, and the right side is a training set image successfully matched. Experimental results show that when people make different expressions and are positioned at different shooting angles, the people can be successfully identified, and the identification rate can reach more than 98%.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (6)

1. An improved PCA face recognition algorithm resistant to illumination effects, comprising the steps of:
(1) selecting a training sample set, wherein the training sample set comprises a plurality of face targets, each face target selects s images as training samples, and each image is written into a column vector form and arranged into a data matrix:
X＝(X1,X2,...,Xn)；
wherein n represents the number of images and n/s represents the number of human face targets;
(2) classifying according to the angle and illumination of the image, and dividing the image data matrix into j sub-data sets S1,S2...Sj(ii) a j is less than or equal to n, j represents the number of the sub data sets, S represents the collection set with the same attribute in the sample image, wherein, the number of the corresponding data matrix in the ith sub data set is assumed to be niThen n is1+n2+……+niN; subdata set SiThe expression of (a) may be expressed as:
Figure FDA0002245449310000011
wherein i is 1, 2, … … j;
(3) computing all the subdata sets S1,S2...SjMean vector mu of1，μ2……μj(ii) a Then, calculating a centralized data matrix C and a covariance matrix Sigma; the calculation formulas are respectively as follows:
Figure FDA0002245449310000012
C＝(S1-μ1,S2-μ2,...,Sj-μj)；
Figure FDA0002245449310000013
wherein, muiMean vector, S, representing the ith sub-datasetitRepresenting the t-th vector in the i-th sub data set;
(4) calculating the eigenvalues of the covariance matrix, selecting the largest k eigenvalues, and solving the eigenvectors e corresponding to the k eigenvalues from large to small in sequence1，e2……ek(ii) a After weight coefficients are added to the feature vectors respectively, the feature vectors are arranged into a transformation matrix W according to columns;
(5) calculating and storing projection matrixes of all images X1-Xn in the training sample set;
(6) calculating a projection matrix chZ of the face Z to be recognizediAnd traversing the projection matrixes of all head portraits in the search sample training set to perform matching calculation to obtain a matching result.
2. An improved PCA face recognition algorithm against illumination as claimed in claim 1 wherein in step (4) the first three principal components e of the k eigenvectors are combined1、e2、e3Adding weight coefficient of 0.8 to the fourth and fifth eigenvectors e4、e5Each weight of 1.2 is added, and the transformation matrix W is arranged according to columns, namely:
W＝(0.8e1，0.8e2，0.8e3，1.2e4，1.2e5，e6，...，ek)。
3. the improved PCA face recognition algorithm against illumination as claimed in claim 1, wherein in step (5), the n image X in the training sample setnThe calculation formula of the projection matrix is as follows:
Qn＝WT(Xn-μm)；
wherein, WTA transpose matrix that is a transform matrix W; mu.smRepresenting the nth image XnMean vector of the m-th sub-data set.
4. An improved PCA face recognition algorithm against illumination as claimed in claim 1 wherein in step (6) the projection matrix chZ of face ZiAnd the formula of the matching calculation is respectively as follows:
chZi＝WT(Z-μi)；
Q＝min||Qi-chZi||k；
wherein, the matching result is that the human face Z is the kth individual.
5. The improved PCA face recognition algorithm against illumination of claim 1 wherein in step (4) k has a value of 5 or more.
6. The improved PCA face recognition algorithm against illumination as claimed in claim 1, wherein in step (1), each face target selects s-4 images as training samples.
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