CN111611962A - Face image super-resolution identification method based on fractional order multi-set partial least square - Google Patents

Face image super-resolution identification method based on fractional order multi-set partial least square Download PDF

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CN111611962A
CN111611962A CN202010473054.5A CN202010473054A CN111611962A CN 111611962 A CN111611962 A CN 111611962A CN 202010473054 A CN202010473054 A CN 202010473054A CN 111611962 A CN111611962 A CN 111611962A
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袁运浩
李进
李云
强继朋
朱毅
李斌
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Abstract

The invention discloses a face image super-resolution identification method based on fractional order multi-set partial least square, which comprises the steps of 1, utilizing a training set to learn the correlation among views with different resolutions in a training stage, using PCA to reduce the dimension of an image, utilizing fractional order thinking to re-estimate covariance matrixes in groups and between groups, calculating an FMPLS projection matrix, and projecting principal component characteristics to a consistent coherent subspace of the FMPLS; step 2, in a testing stage, extracting principal component features of multiple input low-resolution images, projecting the principal component features to corresponding FMPLS subspaces, and reconstructing high-resolution features of the input low-resolution images through a neighborhood reconstruction strategy; and 3, finally, carrying out face recognition by using a nearest neighbor classifier. The invention utilizes fractional order multi-set partial least squares, can simultaneously learn the mapping of various specific resolutions between face views with different resolutions, and simultaneously re-estimates the covariance matrix by means of fractional order thinking so as to reduce the influence caused by factors such as insufficient sample quantity, noise and the like.

Description

Face image super-resolution identification method based on fractional order multi-set partial least square
Technical Field
The invention relates to the field of face super-resolution identification, in particular to a face image super-resolution identification method based on fractional order multi-set partial least square.
Background
In real-world applications, especially in the field of video surveillance, due to poor lighting conditions, long imaging distance and posture variation, the face images captured by the device are generally low in resolution, which is a big problem for traditional face recognition algorithms. To solve this problem, many super-resolution facial reconstruction methods have been proposed in recent years, aiming to restore an input low-resolution face image to a high-resolution image.
Multivariate Analysis methods are often used for super-resolution reconstruction for feature extraction, among which Principal Component Analysis (PCA) is popular, and the feature extraction step is usually used to reduce the dimension of data and reduce noise. PCA preserves the appropriate dimensions to extract useful information of a face and filter noise, Wang et al propose a framework for generating high-resolution faces by PCA-deriving image linear combination coefficients.
Super-resolution methods can be roughly divided into three categories: interpolation-based, reconstruction-based, and learning-based methods, wherein the learning-based methods are directed to learning mapping relationships between high and low resolution images from a training set. In recent years, the application of deep learning to face super-resolution technology has been highly successful. However, the deep learning-based method usually requires a large amount of training data to learn the optimal parameters, and although the hardware performance is greatly improved, the learning process of the deep network still requires a large amount of time, so the traditional super-resolution method still has a great research value.
In real life, people often need to face a situation where the same face has multiple views of different resolutions. Previous approaches typically require each resolution view to be trained and processed separately for a number of different low resolution views, which is time consuming and inefficient. In other words, it is difficult for the existing classical method to simultaneously map a plurality of low-resolution views to a high-resolution face space, and thus far, the common learning of the relationship among a plurality of views has not been widely focused; in addition, the covariance matrix may be biased due to insufficient training samples or due to noise.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a face image super-resolution identification method based on fractional order multi-set partial least square, and solves the problems that the correlation among multiple resolution views cannot be learned simultaneously and the covariance matrix possibly has deviation in the prior art.
The purpose of the invention is realized as follows: a face image super-resolution identification method based on fractional order multi-set partial least square comprises the following steps:
step 1, in a training stage, learning a correlation relation between views with different resolutions by using a training set, reducing the dimension of an image by using PCA, re-estimating covariance matrixes in a group and between groups by using fractional order thought, calculating an FMPLS projection matrix, and projecting principal component features to a consistent coherent subspace of FMPLS;
step 2, in a testing stage, extracting principal component features of multiple input low-resolution images, projecting the principal component features to corresponding FMPLS subspaces, and reconstructing high-resolution features of the input low-resolution images through a neighborhood reconstruction strategy;
and 3, finally, predicting the face label by using the nearest neighbor classifier, and outputting a super-resolution face recognition result.
As a further limitation of the present invention, the step 1 specifically comprises the following steps:
(1) for m multidimensional centered random variables
Figure BDA0002514939020000021
Wherein d isiDenotes xiFMPLS aims to solve an optimization problem to find a set of linear transformations
Figure BDA0002514939020000022
Figure BDA0002514939020000031
Where Tr (-) represents the trace of the matrix,
Figure BDA0002514939020000032
for the covariance matrix re-estimated by the fractional order:
Figure BDA0002514939020000033
(2) for re-estimating covariance matrix using fractional order, intra-group covariance matrix is decomposed using eigenvalue decomposition and using fractional order parameters αiRe-estimating for the index:
Figure BDA0002514939020000034
wherein QiAs the covariance S in the groupiiIs used to generate a matrix of feature vectors,
Figure BDA0002514939020000035
is a fractional order parameter αiIs a diagonal matrix of eigenvalues of an exponent, ri＝rank(Sii) And a fractional order parameter αiSatisfy 0 ≦ αiLess than or equal to 1, decomposing the interclass covariance matrix using singular value decomposition and using the fractional order parameters βijAnd (3) re-estimating:
Figure BDA0002514939020000036
wherein U isijAnd VijRespectively, are matrices composed of vectors of left and right singular values,
Figure BDA0002514939020000037
is a fractional order parameter βijIs a diagonal matrix of singular values of an index, rij＝rank(Sij) And a fractional order parameter βijSatisfy 0 ≦ βij≤1；
(3) For the optimization problem, a recursive method is used for solving, and the first k-1 directions are assumed
Figure BDA0002514939020000038
Has been obtained where k ≦ d for the k-th direction
Figure BDA0002514939020000039
Obtained by solving the following optimization problem:
Figure BDA00025149390200000310
Figure BDA00025149390200000311
which can be solved by the characteristic value
Figure BDA00025149390200000312
Is solved to obtain
Figure BDA00025149390200000313
Is a block matrix of which the (i, j) th block is
Figure BDA00025149390200000314
Figure BDA00025149390200000315
Simultaneously:
Figure BDA0002514939020000041
Figure BDA0002514939020000042
Figure BDA0002514939020000043
Figure BDA0002514939020000044
Figure BDA0002514939020000045
Figure BDA0002514939020000046
the characteristic values of the multi-element are shown as,
Figure BDA0002514939020000047
is an identity matrix;
(4) for original high resolution image set in training set
Figure BDA0002514939020000048
Image set of m low resolution views corresponding thereto
Figure BDA0002514939020000049
Wherein d is0The dimension of a column vector of the high-resolution face image is obtained, the number of samples of each view is n, and all low-resolution views are up-sampled to the same size as the high-resolution views by utilizing a bicubic interpolation algorithm;
(5) centralizing individual image block vectors
Figure BDA00025149390200000410
Wherein muiRepresenting the mean value of the face image of the ith resolution view, and extracting the principal component characteristics of each view by PCA
Figure BDA00025149390200000411
Figure BDA00025149390200000412
Wherein P isiIs the principal component coefficient of the ith view;
(6) calculating projection directions using FMPLS
Figure BDA00025149390200000413
Projecting principal component features of the respective views into the potential subspace:
Figure BDA00025149390200000414
as a further limitation of the present invention, the step 2 specifically includes the following steps:
(1) low resolution face for input ith low resolution view
Figure BDA00025149390200000415
By passing
Figure BDA00025149390200000416
Extracting the main component characteristics
Figure BDA00025149390200000417
By
Figure BDA00025149390200000418
Deriving potential FMPLS signatures;
(2) for the
Figure BDA00025149390200000419
From CiThe k neighbor of the medium search is reconstructed to obtain
Figure BDA00025149390200000420
Minimizing the following reconstruction error to obtain weight coefficients
Figure BDA00025149390200000421
Figure BDA00025149390200000422
Will weight
Figure BDA00025149390200000423
To C0Of the corresponding high resolution features
Figure BDA00025149390200000424
Computing high resolution reconstruction features of an input low resolution face image
Figure BDA00025149390200000425
Compared with the prior art, the invention has the beneficial effects that: extracting principal component characteristics of a multi-view face image, re-estimating covariance matrixes in groups and between groups by utilizing fractional order multi-set partial least squares, calculating a projection direction, extracting potential coherent characteristics, recovering high-resolution characteristics of an input image through neighborhood reconstruction, predicting a face label by utilizing a nearest neighbor classifier, outputting a super-resolution face recognition result, and simultaneously learning the mapping of various specific resolutions among different resolution face views by utilizing fractional order multi-set partial least squares; the method solves the problems that low-resolution face images are difficult to recognize due to factors such as insufficient information, posture change and illumination influence, and the traditional face super-resolution algorithm cannot process the input of the face images with various resolutions at the same time.
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FIG. 1 is a flow chart of an implementation of the present invention.
Detailed Description
As shown in fig. 1, a face image super-resolution identification method based on fractional order multi-set partial least squares includes the following steps:
step 1, in a training stage, learning a correlation relation between views with different resolutions by using a training set, reducing the dimension of an image by using PCA, re-estimating covariance matrixes in a group and between groups by using fractional order thought, calculating an FMPLS projection matrix, and projecting principal component features to a consistent coherent subspace of FMPLS;
(1) for m multidimensional centered random variables
Figure BDA0002514939020000051
Wherein d isiDenotes xiFMPLS aims to solve an optimization problem to find a set of linear transformations
Figure BDA0002514939020000052
Figure BDA0002514939020000061
Where Tr (-) represents the trace of the matrix,
Figure BDA0002514939020000062
for the covariance matrix re-estimated by the fractional order:
Figure BDA0002514939020000063
(2) for re-estimating covariance matrix using fractional order, intra-group covariance matrix is decomposed using eigenvalue decomposition and using fractional order parameters αiRe-estimating for the index:
Figure BDA0002514939020000064
wherein QiAs the covariance S in the groupiiIs used to generate a matrix of feature vectors,
Figure BDA0002514939020000065
is a fractional order parameter αiIs a diagonal matrix of eigenvalues of an exponent, ri＝rank(Sii) And a fractional order parameter αiSatisfy 0 ≦ αiLess than or equal to 1, decomposing the interclass covariance matrix using singular value decomposition and using the fractional order parameters βijAnd (3) re-estimating:
Figure BDA0002514939020000066
wherein U isijAnd VijRespectively, are matrices composed of vectors of left and right singular values,
Figure BDA0002514939020000067
is a fractional order parameter βijIs a diagonal matrix of singular values of an index, rij＝rank(Sij) And a fractional order parameter βijSatisfy 0 ≦ βij≤1。
(3) For the optimization problem, a recursive method is used for solving, and the first k-1 directions are assumed
Figure BDA0002514939020000068
Has been obtained where k ≦ d for the k-th direction
Figure BDA0002514939020000069
Obtained by solving the following optimization problem:
Figure BDA00025149390200000610
Figure BDA00025149390200000611
which can be solved by the characteristic value
Figure BDA00025149390200000612
Is solved to obtain
Figure BDA00025149390200000613
Is a block matrix of which the (i, j) th block is
Figure BDA00025149390200000614
Figure BDA00025149390200000615
Simultaneously:
Figure BDA0002514939020000071
Figure BDA0002514939020000072
Figure BDA0002514939020000073
Figure BDA0002514939020000074
Figure BDA0002514939020000075
Figure BDA0002514939020000076
the characteristic values of the multi-element are shown as,
Figure BDA0002514939020000077
is an identity matrix.
(4) For original high resolution image set in training set
Figure BDA0002514939020000078
Image set of m low resolution views corresponding thereto
Figure BDA0002514939020000079
Wherein d is0The dimension of a column vector of the high-resolution face image is obtained, the number of samples of each view is n, and all low-resolution views are up-sampled to the same size as the high-resolution views by utilizing a bicubic interpolation algorithm;
(5) centralizing individual image block vectors
Figure BDA00025149390200000710
Wherein muiRepresents the ithMean value of resolution view face image, and principal component characteristics of each view are extracted by PCA
Figure BDA00025149390200000711
Figure BDA00025149390200000712
Wherein P isiIs the principal component coefficient of the ith view;
(6) calculating projection directions using FMPLS
Figure BDA00025149390200000713
Projecting principal component features of the respective views into the potential subspace:
Figure BDA00025149390200000714
step 2, in a testing stage, extracting principal component features of multiple input low-resolution images, projecting the principal component features to corresponding FMPLS subspaces, and reconstructing high-resolution features of the input low-resolution images through a neighborhood reconstruction strategy;
(1) low resolution face for input ith low resolution view
Figure BDA00025149390200000715
By passing
Figure BDA00025149390200000716
Extracting the main component characteristics
Figure BDA00025149390200000717
By
Figure BDA00025149390200000718
Deriving potential FMPLS signatures;
(2) for the
Figure BDA00025149390200000719
From CiThe k neighbor of the medium search is reconstructed to obtain
Figure BDA00025149390200000720
Minimizing the following reconstruction error to obtain weight coefficients
Figure BDA00025149390200000721
Figure BDA00025149390200000722
Will weight
Figure BDA00025149390200000723
To C0Of the corresponding high resolution features
Figure BDA00025149390200000724
Computing high resolution reconstruction features of an input low resolution face image
Figure BDA0002514939020000081
The reconstructed high-resolution features can be used for face recognition work through a nearest neighbor classifier.
And 3, predicting the face label by using the nearest neighbor classifier, and outputting a super-resolution face recognition result.
In order to test the effectiveness of the invention, the CMU PIE face database and the AT are respectively arranged&CMU PIE database contains 68 different human face images, each of 24 people, including different visual angles, lighting conditions, angles, etc., the even number of human face images of each person are selected as training, the rest are used as test, the size of the high-resolution human face image is 64 × 64, the down-sampling times are 2 times, 4 times and 8 times respectively, the resolutions are 32 × 32, 16 × 16 and 8 ×. AT&The T-face database contains face images of 40 persons, 10 persons each, and the top N of each person is selected respectivelytrainZhang Fang as training set to carry out experiment (N)train7, 5, 3, respectively), the face remaining from each experiment was tested, the original high resolution was 112 × 92, the downsampling multiples were 2, 4, and 8, corresponding to low resolutions 56 × 46, 28 × 23, and 14 × 12.
Experiment 1 super-resolution identification contrast experiment based on CMU PIE face database
In this experiment, the neighborhood size of the present invention was set to 40, preserving the 95-dimensional FMPLS feature, while the fractional order parameters α and β were 0.4 and 0.8, respectively. The obtained face recognition comparison results are shown in table 1, and it can be seen that the present invention achieves the highest face recognition rate under each resolution view.
TABLE 1 face recognition rates (%) -for different scaling factors on CMU PIE face database by seven methods
Multiple of The invention CLLR-SR SRDCCA LINE VDSR TLcR Bic-PCA
2× 95.96 93.63 94.73 95.71 95.71 95.71 87.50
4× 96.20 94.12 94.24 95.59 94.49 95.83 85.42
8× 95.22 93.75 92.52 91.30 86.15 93.26 74.88
Experiment 2 super-resolution identification contrast experiment based on AT & T face database
In this experiment, the neighborhood size of the present invention was set to 50, preserving the 75-dimensional FMPLS feature, and when trained using each of the first 7 pictures, the fractional order parameter α was 0.2 and β was 1; when training is performed using the first 5 pictures of each person, α is 0.4 and β is 1; when training was performed using the first 3 pictures of each person, α was 0.2 and β was 0.8. Table 2 records the face recognition rates of the seven methods under different scaling factors and different numbers of training samples on the AT & T face database. The table shows that the face recognition rate of the invention is superior to that of the comparison method under three different training sample conditions and different scaling factors.
Table 2 face recognition rates (%) -based on different scaling factors and different training sample numbers for the seven methods in the AT & T face database
Figure BDA0002514939020000091
In summary, the invention provides a face image super-resolution recognition method based on fractional order multi-set partial least square, which can simultaneously learn the mapping of various specific resolutions between face views with different resolutions by using the fractional order multi-set partial least square, and simultaneously re-estimate a covariance matrix by means of fractional order thinking so as to reduce the influence caused by factors such as insufficient sample number and noise.
The present invention is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts according to the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.

Claims (3)

1. A face image super-resolution identification method based on fractional order multi-set partial least square is characterized by comprising the following steps:
step 1, in a training stage, learning a correlation relation between views with different resolutions by using a training set, reducing the dimension of an image by using PCA, re-estimating covariance matrixes in a group and between groups by using fractional order thought, calculating an FMPLS projection matrix, and projecting principal component features to a consistent coherent subspace of FMPLS;
step 2, in a testing stage, extracting principal component features of multiple input low-resolution images, projecting the principal component features to corresponding FMPLS subspaces, and reconstructing high-resolution features of the input low-resolution images through a neighborhood reconstruction strategy;
and 3, finally, predicting the face label by using the nearest neighbor classifier, and outputting a super-resolution face recognition result.
2. The method for identifying the super-resolution of the face image based on the fractional order multi-set partial least squares as claimed in claim 1, wherein the step 1 specifically comprises the following steps:
(1) for m multidimensional centered random variables
Figure FDA0002514939010000011
Wherein d isiDenotes xiFMPLS aims to solve an optimization problem to find a set of linear transformations
Figure FDA0002514939010000012
Figure FDA0002514939010000013
Where Tr (-) represents the trace of the matrix,
Figure FDA0002514939010000014
for the covariance matrix re-estimated by the fractional order:
Figure FDA0002514939010000015
(2) for re-estimating covariance matrix using fractional order, intra-group covariance matrix is decomposed using eigenvalue decomposition and using fractional order parameters αiRe-estimating for the index:
Figure FDA0002514939010000016
wherein QiAs the covariance S in the groupiiIs used to generate a matrix of feature vectors,
Figure FDA0002514939010000021
is a fractional order parameter αiIs a diagonal matrix of eigenvalues of an exponent, ri＝rank(Sii) And a fractional order parameter αiSatisfy 0 ≦ αiLess than or equal to 1, decomposing the interclass covariance matrix using singular value decomposition and using the fractional order parameters βijAnd (3) re-estimating:
Figure FDA0002514939010000022
wherein U isijAnd VijRespectively, are matrices composed of vectors of left and right singular values,
Figure FDA0002514939010000023
is a fractional order parameter βijIs a diagonal matrix of singular values of an index, rij＝rank(Sij) And a fractional order parameter βijSatisfy 0 ≦ βij≤1；
(3) For the optimization problem, a recursive method is used for solving, and the first k-1 directions are assumed
Figure FDA0002514939010000024
Has been obtained where k ≦ d for the k-th direction
Figure FDA0002514939010000025
Obtained by solving the following optimization problem:
Figure FDA0002514939010000026
Figure FDA0002514939010000027
which can be solved by the characteristic value
Figure FDA0002514939010000028
Is solved to obtain
Figure FDA0002514939010000029
Is a block matrix of which the (i, j) th block is
Figure FDA00025149390100000210
Figure FDA00025149390100000211
Simultaneously:
Figure FDA00025149390100000212
Figure FDA00025149390100000213
Figure FDA00025149390100000214
Figure FDA00025149390100000215
Figure FDA00025149390100000216
Figure FDA00025149390100000217
the characteristic values of the multi-element are shown as,
Figure FDA00025149390100000218
is an identity matrix;
(4) for original high resolution image set in training set
Figure FDA00025149390100000219
Image set of m low resolution views corresponding thereto
Figure FDA00025149390100000220
Wherein d is0The dimension of a column vector of the high-resolution face image is obtained, the number of samples of each view is n, and all low-resolution views are up-sampled to the same size as the high-resolution views by utilizing a bicubic interpolation algorithm;
(5) centralizing individual image block vectors
Figure FDA0002514939010000031
Wherein muiRepresenting the mean value of the face image of the ith resolution view, and extracting the principal component characteristics of each view by PCA
Figure FDA0002514939010000032
Figure FDA0002514939010000033
Wherein P isiIs the principal component coefficient of the ith view;
(6) calculating projection directions using FMPLS
Figure FDA0002514939010000034
Projecting principal component features of the respective views into the potential subspace:
Figure FDA0002514939010000035
3. the method for identifying the super-resolution of the face image based on the fractional order multi-set partial least squares as claimed in claim 1, wherein the step 2 specifically comprises the following steps:
(1) low resolution face for input ith low resolution view
Figure FDA0002514939010000036
By passing
Figure FDA0002514939010000037
Extracting the main component characteristics
Figure FDA0002514939010000038
By
Figure FDA0002514939010000039
Deriving potential FMPLS signatures;
(2) for the
Figure FDA00025149390100000310
From CiThe k neighbor of the medium search is reconstructed to obtain
Figure FDA00025149390100000311
Minimizing the following reconstruction error to obtain weight coefficients
Figure FDA00025149390100000312
Figure FDA00025149390100000313
Will weight
Figure FDA00025149390100000314
To C0Of the corresponding high resolution features
Figure FDA00025149390100000315
Computing high resolution reconstruction features of an input low resolution face image
Figure FDA00025149390100000316
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CN113887509A (en) * 2021-10-25 2022-01-04 济南大学 Rapid multi-modal video face recognition method based on image set
CN114898423A (en) * 2022-04-01 2022-08-12 东南大学 Face recognition method based on improved recursive least square method
CN115205941A (en) * 2022-07-13 2022-10-18 山西大学 Generic multi-view graph embedding-based relationship verification method

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