CN102622616A - Human face recognition method based on two-dimensional kernel principal component analysis and fuzzy maximum scatter difference - Google Patents

Human face recognition method based on two-dimensional kernel principal component analysis and fuzzy maximum scatter difference Download PDF

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CN102622616A
CN102622616A CN2012100321291A CN201210032129A CN102622616A CN 102622616 A CN102622616 A CN 102622616A CN 2012100321291 A CN2012100321291 A CN 2012100321291A CN 201210032129 A CN201210032129 A CN 201210032129A CN 102622616 A CN102622616 A CN 102622616A
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face
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曾接贤
田金权
符祥
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Nanchang Hangkong University
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Abstract

A human face recognition method based on two-dimensional kernel principal component analysis and fuzzy maximum scatter difference includes steps of firstly, effectively extracting a non-linear structural feature of a human face by a K2DPCA (two-dimensional kernel principal component analysis) method; secondly, selecting a feature vector with between-class scatter larger than in-class scatter after projection as an optimal projection axis, and accordingly leading feature vectors corresponding to small feature values to be choices of the optimal projection axis so as to fuse subtle expression change information of the human face; and thirdly, redefining a scatter matrix of samples according to a membership degree function by the aid of advantages of FMSD (fuzzy maximum scatter difference), and sufficiently integrating original distribution information of the samples into feature extraction of the human face via corresponding membership degree information. Effective improvement is made according to hard classification problems in human face recognition, and the problem that a judgment and analysis method based on bidirectional maximum scatter difference cannot effectively extract non-linear discriminant features of the human face in terms of human face recognition, and has edge classes and hard classification.

Description

Based on the face identification method of two-dimensional nucleus principal component analysis (PCA) with fuzzy maximum divergence difference
Technical field
The present invention relates to a kind of face identification method; Relate in particular to a kind of face identification method based on two-dimensional nucleus principal component analysis (PCA) and fuzzy maximum divergence difference and belong to pattern-recognition and computer vision research category, the major technique field relates to extracts effective people's face diagnostic characteristics and sorter reasonable in design.
Background technology
Recognition of face has become important research direction in the living things feature recognition, mainly carries out through the sorter that extracts effective people's face diagnostic characteristics and complex design.Wherein principal component analysis (PCA) (Principle Components Analysis is called for short PCA) method and linear discriminant analysis (Linear Discriminant Analysis is called for short LDA) method all are effective linear characteristic extracting methods.
The PCA method is redeveloped into purpose with optimum, through maximizing the optimum projector space that the total volume divergence of training sample obtains sample, is not suitable for classification problem.LDA is a purpose with the diagnostic characteristics that extracts the Different Individual facial image; A between class scatter and type ratio of interior divergence through the maximization training sample; Can extract the authentication information between all kinds of effectively; But in computation process, need to guarantee that scatter matrix is reversible in the class, and recognition of face is typical higher-dimension, small sample problem that the divergence matrix is unusual often in type.In order to address this problem; People such as Belhumeur have proposed Fisherface method (Fisherlinear Discriminant Analysis; Be called for short FLDA) [Belhumeur P N; Hespanha Joao P; Kriegman David J. Eigenfaces vs. Fisherfaces:Recognition using class specific linear projection [J]. IEEE Trans. Pattern Analysis and Machine Intelligence, 1997,19 (7): 711-720.].This method at first utilizes PCA that sample is carried out dimensionality reduction, makes the interior divergence matrix of class of sample nonsingular, utilizes LDA to obtain to differentiate projector space then.Yet selectivity PCA dimensionality reduction can not guarantee the nonsingularity of between class scatter matrix.Can't directly find the solution the problem of optimum axis of projection in order fundamentally to eliminate traditional F isher discriminating criterion because of the divergence matrix is unusual in the class that small sample problem caused; People such as Song Fengxi have proposed the face identification method [Song Fengxi of maximum divergence poor (MSD) and big spacing linear projection and SVMs; Cheng Ke, Yang Jingyu, etc. maximum divergence difference and big spacing linear projection and SVMs [J]. the robotization journal; 2004,30 (6): 890-896.].MSD utilizes the difference of between class scatter and type interior divergence as the sorter criterion, need not construct inverse matrix, has not only solved the small sample problem in the recognition of face effectively, has also improved the speed of algorithm.But MSD is a kind of two types of sorters in essence, and in order to solve the multiclass pattern recognition problem, Song Fengxi etc. have proposed the people's face method for expressing based on the maximum divergence difference of multiclass, extracts effective people's face diagnostic characteristics through setting up the maximum divergence difference discriminating of multiclass criterion.In order to obtain
Figure 886061DEST_PATH_IMAGE001
value suitable among the MSD; Song Fengxi etc. have proposed to differentiate based on maximum divergence difference adaptive classification algorithm (the AMSD) [Song Fengxi of criterion; Magnify roc; Yang Jingyu; Gao Xiumei. differentiate the adaptive classification algorithm [J] of criterion based on maximum divergence difference. robotization journal, 2006,32 (4): 541-549.].Yet there is the deficiency of two aspects in AMSD: the one, parameter
Figure 147278DEST_PATH_IMAGE001
value to choose scope bigger; The 2nd, there is the suboptimality problem in the MSD method.Value as
Figure 425944DEST_PATH_IMAGE001
hour; The relative between class scatter of divergence is enough little in can not type of assurance, makes between foreign peoples's sample and enough separates; When the value as
Figure 373303DEST_PATH_IMAGE001
is enough big; Divergence goes to zero in type; Be equivalent to the class average of the distribution or accumulation of all kinds of samples, so the recognition of face performance depends on the order of accuarcy that sample average is calculated in such sample.But in face recognition process, people's face number of training is generally less on the one hand, can not accurately calculate sample average; The opposing party's dough figurine face sample puts a certain type hard classification problem because of influenced by extraneous factors such as illumination, expression to produce under away from the caused edge of the sample class problem at actual type center with edge class sample simply, all can cause recognition performance to descend.Poplar ten thousand buttons wait face identification method [poplar ten thousand buttons that proposed fuzzy maximum divergence difference differentiation (FMSD) and analyzed; Wang Jianguo; Ren Mingwu, Yang Jingyu. fuzzy contrary Fisher discriminatory analysis and the application in recognition of face [J] thereof. Chinese image graphics journal, 2009; 14 (1): 88-93.]; Through introducing fuzzy set theory each training sample is belonged to all kinds of samples with different extent, utilize the degree of membership information of sample to define the class average and the divergence matrix of sample again, the classification information that makes full use of known sample helps the feature extraction of classifying.Though FMSD has done effective improvement to edge class in the recognition of face and hard classification problem, can not extract the nonlinear organization characteristic of people's face effectively and realize linear separability.KMSD [the Wang JG that Wang etc. propose; Lin YS; Yang WK, et al. Kernel maximum scatter difference based feature extraction and its application to face recognition [J]. Pattern Recognition Letters, 2008; 29 (13): 1832-1835.] utilize the advantage of kernel method and maximum divergence difference sorter to realize the identification of people's face; Can extract the nonlinear organization characteristic of people's face effectively and reduce calculated amount, however said method all need to convert image array into image vector, can not effectively extract the structural information in the facial image.In order to obtain the structural information in the image; Hui Kong etc. has proposed two-dimensional nucleus principal component analysis (PCA) (K2DPCA) method [Hui Kong; Lei Wang, Eam Khwang Teoh, et al.Generalized 2D principal component analysis for face image representation and recognition [J]. Neural Networks; 2005; 18:585-594.], though can extract the structural information of people's face effectively, but can not effectively solve extraneous factors such as receiving illumination because of people's face sample and change edge class problem and the hard classification problem that produces; And Wang Jianguo etc. have proposed face identification method (2DPCA+2DMSD) [the Wang Jianguo based on two-way maximum divergence difference discriminatory analysis (Two-directional maximum scatter difference discriminant analysis); Yang Wankou; Lin Yusheng; Yang Jingyu. Two-directional maximum scatter difference discriminant analysis for face recognition [J]. Neurocomputing; 2008,72 (1-3): 352-358.], it at first utilizes the 2DPCA method that original image is projected in the lower dimensional space; Removed the correlativity between the image line effectively; Utilize maximum divergence difference method to extract effective diagnostic characteristics that facial image lists then, reduced the dimension of people's face diagnostic characteristics, realize the Classification and Identification fast and effeciently of people's face.Though the face identification method based on the discriminatory analysis of two-way maximum divergence difference has obtained recognition of face effect preferably, can not extract the nonlinear organization characteristic and solution edge class problem and hard classification problem of people's face effectively.
Summary of the invention
In recognition of face, can not extract the non-linear diagnostic characteristics and the problem that has edge class and hard classification of people's face effectively to two-way maximum divergence difference discriminant analysis method, the present invention has provided based on the method for two-dimensional nucleus principal component analysis (PCA) with the recognition of face of fuzzy maximum divergence difference.At first utilize the K2DPCA method to extract the nonlinear organization characteristic of people's face; Next is chosen, and to meet between class scatter after the projection be optimum axis of projection greater than the proper vector of divergence in the class; Use the FMSD method of discrimination then, the original distribution information of sample is dissolved in the feature extraction of people's face fully according to membership function; Adopt nearest neighbor classifier to carry out Classification and Identification at last.Specifically comprise:
The image collection of 1, be provided with
Figure 189949DEST_PATH_IMAGE002
type
Figure 740010DEST_PATH_IMAGE003
individual face training sample; And
Figure 568606DEST_PATH_IMAGE005
; be
Figure 960721DEST_PATH_IMAGE007
type
Figure 666509DEST_PATH_IMAGE008
individual sample image wherein; The number of
Figure 814725DEST_PATH_IMAGE009
type training sample
Figure 497827DEST_PATH_IMAGE010
that is
Figure 605963DEST_PATH_IMAGE007
;
Figure 58121DEST_PATH_IMAGE011
is the sum of training sample;
Figure 564189DEST_PATH_IMAGE012
is mapped to the nuclear sample matrix in the high-dimensional feature space
Figure 692093DEST_PATH_IMAGE014
for sample
Figure 581737DEST_PATH_IMAGE006
through non-linear transform function
Figure 526559DEST_PATH_IMAGE013
;
Figure 634641DEST_PATH_IMAGE015
is the corresponding average of
Figure 134892DEST_PATH_IMAGE016
last type sample;
Figure 841128DEST_PATH_IMAGE017
is
Figure 751315DEST_PATH_IMAGE016
goes up the corresponding average of all training samples,
Figure 489595DEST_PATH_IMAGE018
prior probability of type sample that is
Figure 776220DEST_PATH_IMAGE007
.
2, the divergence matrix does in the sample class of definition sample in high-dimensional feature space
Figure 200697DEST_PATH_IMAGE020
（1）
3, the sample between class scatter matrix of definition sample in high-dimensional feature space
Figure 675540DEST_PATH_IMAGE019
does
Figure 437960DEST_PATH_IMAGE021
（2）
4, the sample total volume divergence matrix of definition sample in high-dimensional feature space
Figure 432592DEST_PATH_IMAGE019
does
Figure 950161DEST_PATH_IMAGE022
（3）
5, the two-dimentional principal component analysis (PCA) criterion function on the high-dimensional feature space
Figure 849984DEST_PATH_IMAGE016
does
, and
Figure 327550DEST_PATH_IMAGE024
(4)
6, optimum axis of projection and optimum projector space
Separate the optimum projector space
Figure 757842DEST_PATH_IMAGE029
on the pairing mutually orthogonal proper vector of preceding
Figure 153871DEST_PATH_IMAGE026
individual relatively large eigenwert
Figure 320410DEST_PATH_IMAGE027
Figure 289635DEST_PATH_IMAGE028
formation
Figure 149006DEST_PATH_IMAGE016
that formula (4) can obtain , and
Figure 744384DEST_PATH_IMAGE029
unties
Figure 817382DEST_PATH_IMAGE030
.Because the concrete form of function
Figure 785338DEST_PATH_IMAGE013
is unknown, can't directly obtain the solution space of formula (4).Can know according to theory of reproducing kernel space; In
Figure 202861DEST_PATH_IMAGE016
; The solution space
Figure 333628DEST_PATH_IMAGE029
of all nuclear learning methods can be expressed as
Figure 285535DEST_PATH_IMAGE031
inner product sum in feature space, that is:
Figure 931280DEST_PATH_IMAGE032
（5）
Wherein
Figure 994045DEST_PATH_IMAGE033
;
Figure 979318DEST_PATH_IMAGE034
is optimum projector space, and .
Therefore; In order to obtain projector space
Figure 235167DEST_PATH_IMAGE029
, a demand goes out
Figure 288574DEST_PATH_IMAGE034
.For the major component of test sample book
Figure 484380DEST_PATH_IMAGE006
in extracting , a demand goes out that
Figure 509285DEST_PATH_IMAGE012
gets final product at upslide movie queen's sample characteristics matrix
Figure 917450DEST_PATH_IMAGE036
in
Figure 839138DEST_PATH_IMAGE016
.
Figure 600034DEST_PATH_IMAGE037
（6）
Wherein
Figure 995243DEST_PATH_IMAGE038
.Project on
Figure 836794DEST_PATH_IMAGE029
if go up corresponding population mean
Figure 507444DEST_PATH_IMAGE039
to
Figure 606353DEST_PATH_IMAGE016
, then have
Figure 770115DEST_PATH_IMAGE040
（7）
Wherein
Figure 252043DEST_PATH_IMAGE041
; Then according to formula (4); Formula (6), formula (7) can get:
（8）
Figure 62054DEST_PATH_IMAGE043
（9）
Therefore with formula (4) high-dimensional feature space
Figure 877694DEST_PATH_IMAGE016
of equal value in two-dimentional principal component analysis (PCA) criterion function following:
Figure 463396DEST_PATH_IMAGE044
（10）
Preceding
Figure 682336DEST_PATH_IMAGE026
individual relatively large nonzero eigenvalue that will be obtained
Figure 627661DEST_PATH_IMAGE045
by separating of formula (10) and corresponding proper vector
Figure 285356DEST_PATH_IMAGE046
are as optimum axis of projection; Constitute optimum projector space
Figure 476297DEST_PATH_IMAGE047
by optimum axis of projection, and
Figure 77042DEST_PATH_IMAGE048
.From equation (5) to obtain
Figure 602701DEST_PATH_IMAGE016
human face samples optimal projection space
Figure 760144DEST_PATH_IMAGE029
.
7, the image
Figure 258122DEST_PATH_IMAGE006
with arbitrary sample projects to optimum projector space
Figure 826506DEST_PATH_IMAGE049
; Obtain respective sample eigenmatrix
Figure 855774DEST_PATH_IMAGE050
, constitute new sample space thus for :
Figure 966129DEST_PATH_IMAGE052
（11）
8, obtain corresponding membership function according to fuzzy
Figure 705415DEST_PATH_IMAGE053
neighbour's criterion
Utilize the FMSD method directly
Figure 143349DEST_PATH_IMAGE036
to be carried out feature extraction.As training sample set, it is following to obtain corresponding membership function through fuzzy
Figure 911902DEST_PATH_IMAGE053
neighbour's criterion with
Figure 642595DEST_PATH_IMAGE051
:
Figure 838401DEST_PATH_IMAGE054
（12）
Where indicates sample of
Figure 252699DEST_PATH_IMAGE053
nearest neighbors of the sample belongs to the first
Figure 537050DEST_PATH_IMAGE056
class number of samples.
9, calculate sample average
Fuzzy
Figure 497047DEST_PATH_IMAGE001
formula to calculate the mean first
Figure 587363DEST_PATH_IMAGE056
class sample sample mean is:
Figure 581994DEST_PATH_IMAGE057
（13）
10, calculate the dimensionality reduction samples
Figure 99563DEST_PATH_IMAGE051
corresponding class scatter matrix
Figure 999386DEST_PATH_IMAGE058
and within-class scatter matrix
Figure 378546DEST_PATH_IMAGE059
According to membership function and sample average; Can obtain a corresponding between class scatter matrix
Figure 916155DEST_PATH_IMAGE058
of sample
Figure 476952DEST_PATH_IMAGE051
and a type interior divergence matrix
Figure 100012DEST_PATH_IMAGE060
behind the dimensionality reduction, they are respectively:
Figure 271144DEST_PATH_IMAGE061
（14）
Figure 427319DEST_PATH_IMAGE062
（15）
Where
Figure 286690DEST_PATH_IMAGE063
for the overall sample
Figure 708575DEST_PATH_IMAGE051
is the mean vector.
11, it is following to obtain corresponding maximum divergence difference criterion by a between class scatter matrix (formula 14) and a type interior divergence matrix (formula 15):
Figure 616488DEST_PATH_IMAGE064
（16）
12, can obtain the optimum projector space
Figure 628941DEST_PATH_IMAGE067
of characteristic value collection and characteristic of correspondence vector
Figure 470492DEST_PATH_IMAGE066
formation by separating of maximum divergence difference criterion (formula 16), then
Figure 340545DEST_PATH_IMAGE068
（17）
13, all samples are projected onto the optimal projection space
Figure 284361DEST_PATH_IMAGE029
and
Figure 485536DEST_PATH_IMAGE067
in the characteristics of the sample matrix is obtained:
Figure 616434DEST_PATH_IMAGE069
（18）
14, people's face training sample
Figure 131729DEST_PATH_IMAGE006
is projected to the optimum diagnostic characteristics matrix that optimum projector space
Figure 179319DEST_PATH_IMAGE070
and
Figure 302127DEST_PATH_IMAGE071
obtain respective sample, that is:
Figure 222996DEST_PATH_IMAGE073
（19）
Then any samples are projected onto the optimal projection space
Figure 875825DEST_PATH_IMAGE029
and get samples to identify the optimal feature matrix are
Figure 976822DEST_PATH_IMAGE074
-dimensional matrix;
15, so that
Figure 381390DEST_PATH_IMAGE075
means
Figure 403572DEST_PATH_IMAGE003
Personal Facial training set first
Figure 868183DEST_PATH_IMAGE076
The first characteristic matrix samples
Figure 647920DEST_PATH_IMAGE077
column
Figure 105446DEST_PATH_IMAGE026
-dimensional column vector.Therefore the optimum diagnostic characteristics matrix of any two samples can be expressed as
Figure 732868DEST_PATH_IMAGE078
and
Figure 555330DEST_PATH_IMAGE079
, and the distance between the sample is:
Figure 884680DEST_PATH_IMAGE080
（20）
16, will any one test sample
Figure 896630DEST_PATH_IMAGE081
projected onto the optimal projection space
Figure 565509DEST_PATH_IMAGE029
and
Figure 621189DEST_PATH_IMAGE067
get the corresponding optimal identification of the characteristic matrix .
17, according to nearest neighbor classifier people's face is carried out Classification and Identification.When satisfied and
Figure 589910DEST_PATH_IMAGE084
belong to type sample, test sample book is
Figure 474187DEST_PATH_IMAGE085
type facial image.
Technique effect of the present invention: at first utilize the K2DPCA method to extract the nonlinear organization characteristic of people's face; Next is chosen the between class scatter that can make after the projection and constitutes optimum projector space
Figure 665128DEST_PATH_IMAGE029
greater than the axis of projection of divergence in the class; So that the identification of people's face; And, remove the correlativity between the image line with the sample that obtains after original sample projects to
Figure 666899DEST_PATH_IMAGE029
behind the dimensionality reduction; Then in space
Figure 68459DEST_PATH_IMAGE051
; Utilize fuzzy maximum divergence difference method of discrimination directly to extract the diagnostic characteristics of facial image, remove the correlativity between the image column; Adopt nearest neighbor classifier to carry out Classification and Identification at last.This method has been concentrated the superiority of two-dimensional nucleus principal component analysis (PCA) with fuzzy maximum divergence difference sorter; Through introducing fuzzy theory; Again define the divergence matrix of sample; The degree of membership information of sample is dissolved in the feature extraction of people's face fully, has been carried out effective improvement to non-linear diagnostic characteristics that in recognition of face, can not extract people's face based on two-way maximum divergence difference discriminant analysis method effectively and the problem that has edge class and hard classification.
Description of drawings
Fig. 1 is one type of people's face sample image in the ORL face database.
Fig. 2 is one type of sample image in the YALE face database.
Fig. 3 sample distribution figure, wherein a is that the interval of two types of samples exists and to comprise and involved relation, b be the common factor of two types of sample intervals for empty, c be the common factor of two types of sample intervals for empty, d is the distribution plan of three types of samples.
Embodiment
Through concrete enforcement technical scheme of the present invention and effect are done further to describe below.
1,, will on facial image database ORL and YALE, carry out the contrast experiment respectively based on the face identification method of the face identification method (2DKFMSD) of two-dimensional nucleus principal component analysis (PCA) and fuzzy maximum divergence difference and 2DMSD, 2DFLD, 2DPCA+2DFLD, 2DPCA+2DMSD, KMSD in order to verify validity of the present invention.
2, (http://www.uk.research.att. com/facedatabase.html) has 40 people to the ORL facial image database; Everyone 10; By resolution be 112
Figure 902423DEST_PATH_IMAGE086
people's face gray level image of 92 forms, comprising: different times (1992-1994), different expression and facial detail (open eyes/close one's eyes, laugh at/do not laugh at, the wear a pair of spectacles of wear a pair of spectacles/not), degree of depth rotation image with plane rotation (can reach 20 degree), dimensional variation (rate of change is 10%).
3, YALE facial image database (http://cvc.yale.edu/projects/ yalefaces/yalefaces.html) has 15 people; Everyone have 11 resolution be 243 320 image, comprising: different expressions and different facial detail (surprised/sleepiness/nictation/happiness/grief), lighting angle (left/in/right side) and the gray level image of wearing glasses/not wearing glasses.
4, in order to let experimental result have objectivity and comparability; This paper chooses
Figure DEST_PATH_IMAGE087
individual facial image at random as training sample from every type of sample storehouse, the residue sample is tested.
5, in order to reduce calculated amount, with the picture size in ORL and the YALE facial image database be normalized to respectively 56
Figure 610933DEST_PATH_IMAGE086
46 and 40 50.
6, getting kernel function is gaussian kernel function:
Figure 719014DEST_PATH_IMAGE088
; Wherein
Figure 219266DEST_PATH_IMAGE089
adopts nearest neighbor classifier to classify.
7, in order under the situation of different characteristic dimension and identical number of training, to obtain average correct recognition rata, the value of parameter in the maximum divergence difference criterion function
Figure 718511DEST_PATH_IMAGE001
all is taken as 1.
8, shown in accompanying drawing 1 and the accompanying drawing 2 be someone image in ORL and the YALE face database respectively.
9, be respectively the average recognition rate of distinct methods different training number of samples on ORL, YALE face database shown in subordinate list 1 and the subordinate list 3, therefrom be not difficult to find out, the 2DKFMSD method on the overall performance of recognition of face than KMSD and 2DPCA+2DMSD ]Stable more more efficient etc. method.Main cause is: 2DKFMSD utilizes the K2DPCA method that sample is mapped in the high-dimensional feature space; Is optimum axis of projection through choosing the between class scatter that meets after the projection greater than the proper vector of divergence in the class; Not only avoided coming a balance between class scatter and a type interior divergence through asking for suitable
Figure 925502DEST_PATH_IMAGE001
value; Thereby realize the problem of the linear separation between people's face foreign peoples sample; And can also extract the nonlinear characteristic of people's face effectively, reduce the dimension of sample characteristics matrix.
10, accompanying drawing 3 is depicted as sample distribution figure; The distribution of sample in the space in the blue round dot representation class 1; The distribution of sample in the space in the red square representation class 2, the distribution of sample in the space of purple dot representation class 3, the class center of blue hollow ring representation class 1 sample; The class center of red hollow rectangle representation class 2 samples, the class center of purple hollow ring representation class 3 samples.
11, the existence of the interval of 1: two type of sample of situation comprises and involved relation, shown in accompanying drawing 3 (a), works as test sample book C(sample CSample in actual type of belonging to 2) when the distance of two types of center of a sample equates; If utilize nearest neighbor classifier to discern; Because from the sample of nearest sample point type of belonging to 1 of this test sample book, so mistake identification this moment appearred in this test sample book type of belonging to 1 sample.
12, the common factor of 2: two types of sample intervals of situation is empty, shown in accompanying drawing 3 (b), works as test sample book CThe distance that is positioned at two types of sample class centers equates, and when divergence was unequal in the class of two types of samples, if utilize nearest neighbor classifier to discern, the probability of the sample that then divergence is bigger in this test sample book type of belonging to was big, the same identification problem by mistake that exists,
13, the common factor of 3: two types of sample intervals of situation is not empty, and shown in accompanying drawing 3 (c), the midpoint when class 1 center and type 2 centers has the test sample book of existence C(test sample book CThe sample of actual type of belonging to 1), like divergence in the class of fruit 1 sample during greater than the between class scatter of class 1 sample and type 2 samples, if utilize nearest neighbor classifier to classify, because test sample book CLittler than it and the distance of sample 2 in type 1 with the distance of sample 1 in the class 2, then the sample in this test sample book type of belonging to 2 mistake also occurred and discerned this moment.
14, in order to address this problem; Visual recognition according to the people; Difference between the similar sample (divergence is represented in type) is inevitable less than the difference between foreign peoples's sample (between class scatter is represented), therefore chooses between class scatter greater than divergence in the class, meets human visual recognition rule.
15, shown in accompanying drawing 3 (a); When choose between class scatter after meeting projection greater than class in the proper vector of divergence when being optimum axis of projection; Lose the main information of the ability presentation video that utilizes the extraction of KPCA method rather than the axis of projection of authentication information, reduced the dimension of sample characteristics matrix effectively.
16, being directed against the mistake identification problem that exists in the accompanying drawing 3 (a), is to cause owing to part in the class 1 receives extraneous factor to influence bigger edge class sample on the one hand; Be because traditional MSD method utilizes
Figure 101268DEST_PATH_IMAGE001
value to carry out the deficiency that concerns between balance between class scatter and type interior divergence on the other hand; MSD is enough little with respect between class scatter through divergence in adjustment
Figure 839548DEST_PATH_IMAGE001
value type of making, so that classification.When in type of dwindling during divergence, be equivalent to all sample points and draw close, and utilize the inaccuracy at the class center that small sample calculates to cause the decline of discrimination to the class center of sample.
17, be worth so that the deficiency of classification to the edge class problem in the recognition of face of small sample with through adjustment
Figure 63856DEST_PATH_IMAGE001
; The present invention is through the FMSD method;
Figure 453249DEST_PATH_IMAGE001
value is made as 1; The space distribution information of sample is dissolved in the diagnostic characteristics extraction of facial image, has been improved the discrimination of people's face effectively.
18, shown in accompanying drawing 3 (d); Calculate the degree of membership information of sample 1; During the space distribution information of type of the belonging to 2 samples diagnostic characteristics of being dissolved into facial image does not extract with sample 3 grades; Avoided the hard classification problem that exists in the recognition of face effectively, the class center of type of calculating 2 samples is more accurate like this.
19, shown in accompanying drawing 3 (a); In four nearest samples of test specimen C, there are 3 to be type of belonging to 2 and 1 class 1 composition of sample; Leave five nearest samples of sample C by 4 classes 2 and 1 class 1 composition of sample; Utilize FMSD can extract the space distribution information of this sample effectively, the degree of membership of sample C type of belonging to 2 is respectively (
Figure 285070DEST_PATH_IMAGE090
;
Figure 697597DEST_PATH_IMAGE091
).
20, shown in accompanying drawing 3 (c), the degree of membership of test specimen C type of belonging to 1 is ( ;
Figure 782545DEST_PATH_IMAGE092
), therefore utilize optimum axis of projection that the FMSD method obtains to classify effectively less than the test sample book under the divergence situation in the class to the accompanying drawing 3 (a) and (c) between class scatter of middle sample.
21, the 2DKFMSD method at first utilizes KPCA to extract the capable authentication information of facial image; Extract the row authentication information of facial image then with the FMSD method; Take into account the authentication information of image row and column effectively; Not only reduce the optimum diagnostic characteristics space dimensionality of sample, and improved edge class and the hard classification problem that exists in the recognition of face effectively.
22, shown in subordinate list 2 and the subordinate list 4 be optimal identification rate, feature axis number and the recognition time table of comparisons of distinct methods distinct methods on ORL, YALE face database respectively.
23, the experimental data from subordinate list 2 and subordinate list 4 can be explained well: when people's face number of training is 5; The 2DKFMSD method has certain minimizing on recognition efficiency, recognition time (being the sample classification time), identification T.T. (comprising feature extraction time and sample classification time) and feature axis number (i.e. the minimum dimension of the sample characteristics matrix that obtains after the process feature extraction); Be fit to large-scale people's face sample identification more, as shown in Figure 1.
The average recognition rate of subordinate list 1 different training number of samples on the ORL face database
Table 1 The average recognition rate with different number of training sample On the ORL face image database
Figure 237797DEST_PATH_IMAGE093
Like Fig. 2 is one type of sample image in the YALE face database.
Figure 2 A class of sample images in the YALE face image database
The average recognition rate of subordinate list 3 different training number of samples on YALE
Table 3 The average recognition rate with different number of training sample On the YALE face image database
Figure 934357DEST_PATH_IMAGE094
Optimal identification rate, feature axis number and the recognition time table of comparisons of subordinate list 4 distinct methods on YALE
Table 4 The control table of different methods for optimal recognition rate, the number of characteristic shaft and recognition time on the YALE face image database
Figure 313517DEST_PATH_IMAGE095

Claims (6)

1. one kind based on the face identification method of two-dimensional nucleus principal component analysis (PCA) with fuzzy maximum divergence difference, it is characterized in that method step is:
1.1, based on the optimum projector space model construction method of two-dimensional nucleus principal component analysis (PCA) and the fuzzy maximum divergence difference of two dimension;
1.2, based on people's face sample dimension reduction method of optimum projector space model;
1.3, based on people's face sample characteristics method for distilling of optimum projector space model;
1.4, based on kernel method the sample image matrix is mapped in the higher dimensional space, the demand not set up is separated the fuzzy maximum divergence difference sorter of the parameter model
Figure 388806DEST_PATH_IMAGE001
in the maximum divergence difference sorter;
1.5, carry out the step of people's face Classification and Identification based on the face identification method (2DKFMSD) of two-dimensional nucleus principal component analysis (PCA) (K2DPCA) and fuzzy maximum divergence poor (FMSD).
2. according to claim 1 based on the face identification method of two-dimensional nucleus principal component analysis (PCA) with fuzzy maximum divergence difference; It is characterized in that described optimum projector space model construction method, comprise the steps: based on two-dimensional nucleus principal component analysis (PCA) and the fuzzy maximum divergence difference of two dimension
2.1, the image collection
Figure 194716DEST_PATH_IMAGE004
of be provided with
Figure 828009DEST_PATH_IMAGE002
type
Figure 11865DEST_PATH_IMAGE003
individual face training sample; And
Figure 350891DEST_PATH_IMAGE005
;
Figure 210263DEST_PATH_IMAGE006
be
Figure 632148DEST_PATH_IMAGE007
type
Figure 540061DEST_PATH_IMAGE008
individual sample image wherein; The number of
Figure 613059DEST_PATH_IMAGE009
type training sample
Figure 552513DEST_PATH_IMAGE010
that is
Figure 394065DEST_PATH_IMAGE007
; is the sum of training sample;
Figure 4672DEST_PATH_IMAGE012
is mapped to the nuclear sample matrix in the high-dimensional feature space for sample
Figure 956578DEST_PATH_IMAGE006
through non-linear transform function
Figure 540006DEST_PATH_IMAGE013
; is the corresponding average of
Figure 960120DEST_PATH_IMAGE016
last
Figure 93161DEST_PATH_IMAGE007
type sample;
Figure 947899DEST_PATH_IMAGE017
is
Figure 849996DEST_PATH_IMAGE016
goes up the corresponding average of all training samples,
Figure 330655DEST_PATH_IMAGE018
prior probability of type sample that is
Figure 701725DEST_PATH_IMAGE007
;
2.2, the divergence matrix does in the definition sample class of sample in high-dimensional feature space
Figure 355560DEST_PATH_IMAGE019
（1）
2.3, the definition sample between class scatter matrix of sample in high-dimensional feature space
Figure 780037DEST_PATH_IMAGE019
do
Figure 622091DEST_PATH_IMAGE021
（2）
2.4, the definition sample total volume divergence matrix of sample in high-dimensional feature space
Figure 830349DEST_PATH_IMAGE019
do
Figure 644721DEST_PATH_IMAGE022
（3）
2.5, the two-dimentional principal component analysis (PCA) criterion function on the high-dimensional feature space
Figure 529501DEST_PATH_IMAGE016
does
Figure 609583DEST_PATH_IMAGE023
, and (4)
2.6, optimum axis of projection and optimum projector space
Separate the optimum projector space
Figure 541396DEST_PATH_IMAGE029
on the pairing mutually orthogonal proper vector of preceding
Figure 346092DEST_PATH_IMAGE026
individual relatively large eigenwert
Figure 975788DEST_PATH_IMAGE027
formation
Figure 298502DEST_PATH_IMAGE016
that formula (4) can obtain
Figure 539679DEST_PATH_IMAGE025
; And
Figure 845338DEST_PATH_IMAGE029
satisfies
Figure 933511DEST_PATH_IMAGE030
; Because the concrete form of function
Figure 639299DEST_PATH_IMAGE013
is unknown; Can't directly obtain the solution space
Figure 787514DEST_PATH_IMAGE029
of formula (4); Can know according to theory of reproducing kernel space; In
Figure 578753DEST_PATH_IMAGE016
; The solution space of all nuclear learning methods can be expressed as
Figure 30911DEST_PATH_IMAGE031
inner product sum in feature space, that is:
（5）
Wherein
Figure 628563DEST_PATH_IMAGE033
;
Figure 324117DEST_PATH_IMAGE034
is optimum projector space, and
Figure 738918DEST_PATH_IMAGE035
;
Therefore; In order to obtain projector space
Figure 681466DEST_PATH_IMAGE029
; Demand goes out
Figure 932450DEST_PATH_IMAGE034
; For the major component of test sample book
Figure 887954DEST_PATH_IMAGE006
in extracting
Figure 415384DEST_PATH_IMAGE016
, a demand goes out in
Figure 814453DEST_PATH_IMAGE016
Figure 802000DEST_PATH_IMAGE012
and Ji Kes at
Figure 26308DEST_PATH_IMAGE029
upslide movie queen's sample characteristics matrix
Figure 900854DEST_PATH_IMAGE036
;
Figure 247522DEST_PATH_IMAGE037
（6）
Wherein
Figure 660049DEST_PATH_IMAGE038
; Project on
Figure 946388DEST_PATH_IMAGE029
if go up corresponding population mean
Figure 756715DEST_PATH_IMAGE039
to
Figure 512816DEST_PATH_IMAGE016
, then have
Figure 659260DEST_PATH_IMAGE040
（7）
Wherein
Figure 287688DEST_PATH_IMAGE041
; Then according to formula (4); Formula (6), formula (7) can get:
Figure 589356DEST_PATH_IMAGE042
（8）
Figure 762980DEST_PATH_IMAGE043
（9）
Therefore with formula (4) high-dimensional feature space
Figure 212416DEST_PATH_IMAGE016
of equal value in two-dimentional principal component analysis (PCA) criterion function following:
（10）
Preceding
Figure 145234DEST_PATH_IMAGE026
individual relatively large nonzero eigenvalue that will be obtained
Figure 285862DEST_PATH_IMAGE045
by separating of formula (10) and corresponding proper vector are as optimum axis of projection; Constitute optimum projector space by optimum axis of projection; And
Figure 813609DEST_PATH_IMAGE048
is then by the optimum projector space
Figure 690747DEST_PATH_IMAGE029
of people's face sample during formula (5) obtains .
3. according to claim 1 based on the face identification method of two-dimensional nucleus principal component analysis (PCA) with fuzzy maximum divergence difference; It is characterized in that described people's face sample dimension reduction method based on optimum projector space model; The building method of its new samples space for
Figure 464668DEST_PATH_IMAGE049
is following: the image
Figure 329855DEST_PATH_IMAGE006
of arbitrary sample is projected to optimum projector space ; Obtain respective sample eigenmatrix , constitute new sample space thus for :
Figure 37862DEST_PATH_IMAGE052
（11）。
4. the face identification method based on two-dimensional nucleus principal component analysis (PCA) and fuzzy maximum divergence difference according to claim 1 is characterized in that said people's face sample characteristics method for distilling based on optimum projector space model, comprises the steps:
4.1, obtain corresponding membership function according to fuzzy
Figure 160670DEST_PATH_IMAGE053
neighbour's criterion
Utilize the FMSD method directly
Figure 231395DEST_PATH_IMAGE036
to be carried out feature extraction; As training sample set, it is following to obtain corresponding membership function through fuzzy neighbour's criterion with :
Figure 480607DEST_PATH_IMAGE054
（12）
Where
Figure 835365DEST_PATH_IMAGE055
indicates sample
Figure 505512DEST_PATH_IMAGE036
of
Figure 199799DEST_PATH_IMAGE053
nearest neighbors of the sample belongs to the first
Figure 913677DEST_PATH_IMAGE056
class number of samples;
4.2, calculate sample average
Fuzzy
Figure 772043DEST_PATH_IMAGE057
formula to calculate the mean first class sample sample mean is:
Figure 778362DEST_PATH_IMAGE058
（13）
4.3, calculate the dimensionality reduction samples
Figure 679453DEST_PATH_IMAGE049
corresponding between-class scatter matrix
Figure 8803DEST_PATH_IMAGE059
and within-class scatter matrix
Figure 207703DEST_PATH_IMAGE060
According to membership function and sample average; Can obtain a corresponding between class scatter matrix
Figure 745312DEST_PATH_IMAGE059
of sample
Figure 424052DEST_PATH_IMAGE049
and a type interior divergence matrix
Figure 499641DEST_PATH_IMAGE061
behind the dimensionality reduction, they are respectively:
（14）
（15）
Where
Figure 65249DEST_PATH_IMAGE064
for the overall sample
Figure 854344DEST_PATH_IMAGE049
The mean vector.
5. according to claim 1 based on the face identification method of two-dimensional nucleus principal component analysis (PCA) with fuzzy maximum divergence difference; It is characterized in that saidly the sample image matrix being mapped in the higher dimensional space based on kernel method; The demand not set up is separated the fuzzy maximum divergence difference sorter of the parameter model
Figure 457364DEST_PATH_IMAGE065
in the maximum divergence difference sorter, comprises the steps:
5.1, by between class scatter matrix (formula 14) and type in a divergence matrix (formula 15) to obtain corresponding maximum divergence difference criterion following:
Figure 100835DEST_PATH_IMAGE066
（16）
5.2, can obtain the optimum projector space
Figure 920434DEST_PATH_IMAGE069
that characteristic value collection
Figure 237332DEST_PATH_IMAGE067
and characteristic of correspondence vector
Figure 28570DEST_PATH_IMAGE068
constitutes by separating of maximum divergence difference criterion (formula 16), then
Figure 418412DEST_PATH_IMAGE070
（17）
5.3, all samples are projected onto the optimal projection space
Figure 986796DEST_PATH_IMAGE029
and
Figure 16063DEST_PATH_IMAGE069
in the characteristics of the sample matrix is obtained:
（18）。
6. according to claim 1 based on the face identification method of two-dimensional nucleus principal component analysis (PCA) with fuzzy maximum divergence difference, it is characterized in that based on two-dimensional nucleus principal component analysis (PCA) (K2DPCA) following with the step that the face identification method (2DKFMSD) that blurs maximum divergence poor (FMSD) carries out people's face Classification and Identification:
6.1, people's face training sample is projected to the optimum diagnostic characteristics matrix
Figure 802885DEST_PATH_IMAGE074
that optimum projector space
Figure 131284DEST_PATH_IMAGE072
and obtain respective sample, that is:
Figure 337771DEST_PATH_IMAGE075
（19）
Then any samples are projected onto the optimal projection space
Figure 998691DEST_PATH_IMAGE029
and
Figure 923922DEST_PATH_IMAGE069
get samples to identify the optimal feature matrix are
Figure 210546DEST_PATH_IMAGE076
-dimensional matrix;
6.2, expression
Figure 697340DEST_PATH_IMAGE003
the individual face training sample that makes concentrates
Figure 747652DEST_PATH_IMAGE079
row
Figure 742284DEST_PATH_IMAGE026
dimensional vector of
Figure 985233DEST_PATH_IMAGE078
individual sample characteristics matrix; Therefore the optimum diagnostic characteristics matrix of any two samples can be expressed as
Figure 259853DEST_PATH_IMAGE080
and
Figure 972725DEST_PATH_IMAGE081
, and the distance between the sample is:
Figure 538836DEST_PATH_IMAGE082
（20）
6.3, will any one test sample
Figure 637242DEST_PATH_IMAGE083
projected onto the optimal projection space
Figure 76445DEST_PATH_IMAGE029
and get the corresponding optimal identification of the characteristic matrix
Figure 630103DEST_PATH_IMAGE084
;
6.4, according to nearest neighbor classifier people's face is carried out Classification and Identification; When satisfied and
Figure 458699DEST_PATH_IMAGE086
belong to type sample, test sample book
Figure 54076DEST_PATH_IMAGE083
is
Figure 127074DEST_PATH_IMAGE087
type facial image.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105975965A (en) * 2016-07-18 2016-09-28 江苏大学 Bidirectional identification feature extraction method for facial image recognition
CN106503750A (en) * 2016-11-02 2017-03-15 广州大学 A kind of fusion difference subspace and the image set sorting technique of orthogonal subspaces
CN109872190A (en) * 2019-02-20 2019-06-11 北京亿百分科技有限公司 Based on LDA model extraction consumer to the method for advertising campaign interest-degree
CN110363063A (en) * 2019-05-17 2019-10-22 深圳市趣创科技有限公司 Face identification method and system and its storage medium based on Fisherface and Nearest Neighbor Classifier

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101093539A (en) * 2007-07-27 2007-12-26 哈尔滨工程大学 Matching identification method by extracting characters of vein from finger
CN101221612A (en) * 2007-01-11 2008-07-16 上海银晨智能识别科技有限公司 Method for enciphering and deciphering electric document file by face recognition
CN101329724A (en) * 2008-07-29 2008-12-24 上海天冠卫视技术研究所 Optimized human face recognition method and apparatus

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101221612A (en) * 2007-01-11 2008-07-16 上海银晨智能识别科技有限公司 Method for enciphering and deciphering electric document file by face recognition
CN101093539A (en) * 2007-07-27 2007-12-26 哈尔滨工程大学 Matching identification method by extracting characters of vein from finger
CN101329724A (en) * 2008-07-29 2008-12-24 上海天冠卫视技术研究所 Optimized human face recognition method and apparatus

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
曾接贤等: "基于KPCA和FMSD的人脸识别", 《计算机工程》, vol. 37, no. 17, 30 September 2011 (2011-09-30) *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105975965A (en) * 2016-07-18 2016-09-28 江苏大学 Bidirectional identification feature extraction method for facial image recognition
CN106503750A (en) * 2016-11-02 2017-03-15 广州大学 A kind of fusion difference subspace and the image set sorting technique of orthogonal subspaces
CN106503750B (en) * 2016-11-02 2019-07-23 广州大学 A kind of image set classification method merging difference subspace and orthogonal subspaces
CN109872190A (en) * 2019-02-20 2019-06-11 北京亿百分科技有限公司 Based on LDA model extraction consumer to the method for advertising campaign interest-degree
CN110363063A (en) * 2019-05-17 2019-10-22 深圳市趣创科技有限公司 Face identification method and system and its storage medium based on Fisherface and Nearest Neighbor Classifier

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