CN100585617C - Based on sorter integrated face identification system and method thereof - Google Patents

Abstract

The invention discloses a kind ofly, its objective is, to obtain face identification system discrimination preferably by the integrated a plurality of sub-classifiers output of the weighting coefficient of finding the solution a plurality of sub-classifiers based on sorter integrated face identification system and method thereof.Total system comprises training system and categorizing system two parts, wherein training system is finished: facial image is carried out feature extraction, select a plurality of sub-classifiers that posterior probability output is arranged, importing different training samples trains in sub-classifier, obtain the posterior probability of original training sample, adopt linear programming optimization to try to achieve the weighting coefficient of each sub-classifier; Categorizing system is finished: treating after input feature vector extracts obtains treating the posterior probability of classification samples in the sub-classifier of classification samples after the training, and by this posterior probability and sub-classifier weighting coefficient design category rule, output category result.The present invention has advantage of high identification rate, can be used for the recognition of face in machine learning and the pattern-recognition category.

Description

Based on sorter integrated face identification system and method thereof

Technical field

The invention belongs to technical field of image processing, particularly relate to the identification of people's face, can be used for public safety, information security, the supervision of financial security and protection.

Background technology

Recognition of face is than the non-infringement means of identification that is easier to accept for people, thereby becomes the hot issue that fields such as enjoying computer vision and pattern-recognition is paid close attention to.The purpose of face recognition technology is to give computing machine is distinguished personage's identity according to people's face ability.Recognition of face is a typical image model analysis as a problem in science, understands and the computer problem of classifying, and it relates to pattern-recognition, computer vision, intelligent human-machine interaction, graphics, a plurality of subjects such as cognitive science.As the face recognition technology of one of living things feature recognition gordian technique at public safety, information security, fields such as finance have potential application prospect.In face recognition technology, high precision core recognizer is the key of problem, and the final purpose of design Identity System is the discrimination in order to obtain.Traditional method is that the different sorter of design is realized this purpose of recognition of face, the effect of the sorter in recognition system is: come to compose a classification mark to a tested sample according to the proper vector that feature extractor obtains, thereby reach the purpose of classification.Because it is identical that the mistake of different sorters divides sample to differ to establish a capital, thereby can merge sorter, to produce more performance.A large amount of studies show that, integrated a plurality of sub-classifiers are to improve a kind of effective means of discrimination.Can realize identification with this means to people's face.

Existing sorter output integrated approach mainly contains: people such as the J.Kittler of Britain summed up the integrated method of sorter output in the paper in 1998.This method proposes, if the output of single sorter can be expressed as the form of posterior probability, then can adopt product rule and rule, maximum rule, minimum rule and intermediate value rule to come to carry out integrated to the result of a plurality of sub-classifiers, these rules are to belong to nonlinear integration mode, more complicated in application.And the mode of linear Integrated is the most common in actual applications, wherein the simple vote rule is one of linear Integrated mode of using always, people such as gondola G.Fumera compared simple vote and weighting voting method in 2005 for this reason, point out that if single sorter has identical performance and evaluated error is had identical correlativity then the simple average ballot is optimum rule.Otherwise the weighting voting rule can be better than the simple average voting rule.About how seeking weight coefficient, people such as J.A.Benediktsson have proposed in 1993 to find the solution weight coefficient with the mode that returns estimation in people such as 1997 and M.P.Perrone, but these methods are not suitable for classification problem.N.Ueda 2000 at classification problem, designed linear weighted function method based on minimum error in classification principle.The objective function of this method is non-linear, exist Local Extremum theoretically, and find the solution the selection that gradient descending method that objective function adopts depends on initial weight to a great extent, if it is bad that initial weight is selected, will reduce the discrimination of sorter, cause the deterioration of face identification system performance.

The content of invention

The objective of the invention is to overcome the deficiency of above-mentioned prior art, proposed a kind ofly,, improve the performance of face identification system to improve the discrimination of integrated classifier based on sorter integrated face identification system and method thereof.

For achieving the above object, technical scheme of the present invention is:

One. based on the integrated face identification system of sorter, comprising:

Primitive man's face image characteristics extraction module is used for the original facial image that is input to computing machine is carried out feature extraction, obtains the individual original training sample collection that sign is arranged of c class;

The facial image characteristic extracting module of waiting to classify is used for the facial image to be classified that is input to computing machine is carried out feature extraction, obtains and treats classification samples x ∈ R ⁿ

Training module is used to select N sub-classifier of posterior probability output, and it is trained according to the original training sample set pair, and acquisition is about the posterior probability R of original training sample collection _j(ω _k| x _i), x _iRepresent i training sample, ω _kRepresent k classification;

Sub-classifier weighting coefficient computing module is used for according to posterior probability P _j(ω _k| x _i), find the solution the weighting coefficient α of each sub-classifier by linear programming _j, and output to integration module;

The sub-classifier sort module is used for and will treats that classification samples is input in N the sub-classifier that training process trains, and obtains to treat the posterior probability P of classification samples _j(ω _k| x);

Integration module is used for the weighting coefficient α that obtains according to training process _jWith posterior probability P to be classified _j(ω _k| x) design category rule, and obtain classification results according to this classifying rules;

The classification results output module is used for and will treats the form output of the classification results of classification samples with classification logotype, and shows on computer display.

Two, based on the integrated recognition of face training method of sorter, comprise following process:

Extraction is input to the primitive man's face characteristics of image in the computing machine, obtains the individual original training sample collection that sign is arranged of c class: { (x _i, y _i) | x _i∈ R ⁿ, y _i∈ 1,2 ..., c}, i=1 ..., l}, wherein: x _iA sample in the expression n dimension real number space, y _iBe its sign, if value in the positive integer between 1 to c is y _i=k then represents x _i∈ ω _kClass, l is the number of sample;

Selection has N sub-classifier of posterior probability output, and it is trained according to the original training sample set pair, obtains the posterior probability P about the original training sample collection _j(ω _k| x _i), this formula represents that j sub-classifier is about x _iSample belongs to ω _kThe posterior probability of class, j=1 wherein ..., N, k=1 ..., c, i=1 ..., l;

According to posterior probability P _j(ω _k| x _i), find the solution the weighting coefficient α of each sub-classifier by linear programming _j, its solution formula is:

$\underset{\mathrm{\α},\mathrm{\ξ}}{\min }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j+C\underset{q=1}{\overset{l(c-1)}{\mathrm{\Σ}}}{\mathrm{\ξ}}_q$

subject?to $\left[\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j(P_j\left({\mathrm{\ω}}_m\right|x_i)-P_j\left({\mathrm{\ω}}_k\right|x_i))\right]1(x_i\∈{\mathrm{\ω}}_m)\≥-{\mathrm{\ξ}}_q$

ξ _q≥0，α _j≥0，i＝1，…，l，j＝1，…，N，k≠m，k＝1，…，c

q＝1，2，…，l(c-1)

In the formula, j=1 ..., N;

C is the compromise coefficient, ξ _qBe slack variable,

Be the volume controlled item,

It is the empiric risk item;

Weighting coefficient α with each sub-classifier _jOutput to categorizing system.

Three, based on the integrated recognition of face sorting technique of sorter, comprise following process:

Extraction is input to the facial image feature of classifying for the treatment of in the computing machine, obtains and treats classification samples x ∈ R ⁿ

To treat that classification samples is input in N the sub-classifier that trains in the training process, obtain to treat the posterior probability P of classification samples _j(ω _k| x), j=1 ..., N, k=1 ..., c;

The weighting coefficient α that obtains according to training process _jWith posterior probability P to be classified _j(ω _k| x) design category rule, the classifying rules that this module sets is:

If $\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_m\right|x)=\underset{k=\mathrm{1,2},\·\·\·,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_k\right|x),$ X ∈ ω then _mClass, m ∈ 1,2 ..., the classification that the c} representative is different, its classification logotype is y=m.

To treat of the form output of the classification results of classification samples, and on computer display, show with classification logotype.

The present invention is because to obtain the sub-classifier weighting coefficient by sub-classifier weighting coefficient computing module in training system be global optimum, thereby guaranteed that whole categorizing system treats branch facial image high recognition.Simulation result shows that under the condition that 360 width of cloth images is repeated 30 training and classification, average recognition rate of the present invention is higher by 3.54% than the average recognition rate of existing Ueda linear weighted function method.

Description of drawings

Fig. 1 is a virtual system block diagram of the present invention;

Fig. 2 is a training process process flow diagram of the present invention;

Fig. 3 is an assorting process process flow diagram of the present invention.

Embodiment

With reference to Fig. 1, face identification system of the present invention comprises training system and categorizing system two parts, and wherein training system is made up of primitive man's face image characteristics extraction module, training module, sub-classifier weighting coefficient computing module and training result output module.Categorizing system is made up of wait to classify facial image characteristic extracting module, sub-classifier sort module, integration module and classification results output module.Its principle of work is:

Primitive man's face image characteristics extraction module is carried out feature extraction to the original facial image that is input in the computing machine, and obtaining the c class has sign original training sample collection: { (x _i, y _i) | x _i∈ R ⁿ, y _i∈ 1,2 ..., c}, i=1 ..., l}, wherein: x _iA sample in the expression n dimension real number space, y _iBe its sign, if value in the positive integer between 1 to c is y _i=k then represents x _i∈ ω _kClass, l is the number of sample, this original training sample collection flows to training module.Training module, at first selection has N sub-classifier of posterior probability output, trains according to these sub-classifiers of original training sample set pair then, obtains the posterior probability P about the original training sample collection _j(ω _k| x _i), in the formula, x _iRepresent i training sample, ω _kRepresent k classification, j=1 ..., N, k=1 ..., c, i=1 ..., l, the training sample of each sub-classifier generate by the feature of original training sample collection being carried out stochastic sampling, and the characteristic number of each sub-classifier is identical.Sub-classifier weighting coefficient computing module is according to posterior probability P _j(ω _k| x _i), find the solution the weighting coefficient α of each sub-classifier by linear programming _j, its solution formula is:

$\underset{\mathrm{\α},\mathrm{\ξ}}{\min }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j+C\underset{q=1}{\overset{l(c-1)}{\mathrm{\Σ}}}{\mathrm{\ξ}}_q$

subject?to $\left[\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j(P_j\left({\mathrm{\ω}}_m\right|x_i)-P_j\left({\mathrm{\ω}}_k\right|x_i))\right]1(x_i\∈{\mathrm{\ω}}_m)\≥-{\mathrm{\ξ}}_q$

ξ _q≥0，α _j≥0，i＝1，…，l，j＝1，…，N，k≠m，k＝1，…，c

q＝1，2，…，l(c-1)

In the formula, j=1 ..., N; C is the compromise coefficient, ξ _qBe slack variable,

Be the volume controlled item,

It is the empiric risk item.This weighting coefficient α _jConcrete calculating can call existing kit and realize, such as the linear programming function that calls among the Matlab, can try to achieve Optimal Solution of Linear Programming α _jObtain the weighting coefficient α of each sub-classifier _jAfter, output to integration module in the categorizing system as an input parameter of follow-up classification.

Categorizing system wait the facial image characteristic extracting module of classifying, the facial image to be classified that is input in the computing machine is carried out feature extraction, obtain and treat classification samples x ∈ R ⁿ, and export to the sub-classifier sort module, treat that wherein classification samples can not appear at training sample and concentrate.The sub-classifier sort module treats that with this classification samples is input in N the sub-classifier that has trained in the training module again, obtains to treat the posterior probability P of classification samples _j(ω _k| x), and export to integration module.Integration module, the weight coefficient α that obtains according to training system _jWith posterior probability P to be classified _j(ω _k| x) design category rule and obtain classification results, the classifying rules that this module sets is: if $\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_m\right|x)=\underset{k=\mathrm{1,2},\·\·\·,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_k\right|x),$ X ∈ ω then _mClass, m ∈ 1,2 ..., the classification that the c} representative is different, its classification results available categories sign y=m represents, and shows on computer display by the classification results output module.

Each module in the above-mentioned whole face identification system all realizes its function by computer program, finishes the identification to facial image.

With reference to Fig. 2, the present invention is realized the training implementation process of recognition of face is carried out following detailed description:

This embodiment is being to implement under the prerequisite with the technical solution of the present invention, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Embodiment has adopted a public face database---UMIST database.In this database, have 574 20 different facial images.This image library is various visual angles, has the database that arrives positive different attitude people's faces from the side, and its training process is:

Step 1 is carried out feature extraction to original facial image, obtains the original training sample collection that the c class has sign: { (x _i, y _i) | x _i∈ R ⁿ, yi ∈ 1,2 ..., c}, i=1 ..., l}, wherein: x _iA sample in the expression n dimension real number space, y _iBe its sign, if value in the positive integer between 1 to c is y _i=k then represents x _i∈ ω _kClass, l is the number of sample; Feature extraction is meant carries out principal component analysis or down-sampling or various conversion to image.

The size of original facial image is 112 * 92, and feature extracting method has adopted time four method of samplings here, and the size of the every width of cloth image in sampling back is n=28 * 23.

Lack because the number of samples that each classification has has to have more, minimum is 19 width of cloth.Each classification is randomly drawed 18 samples, and then whole data set size is 360 width of cloth images.5 samples of picked at random are as training sample from 18 to every class people's face during emulation, and remaining 13 as test sample book.Formed one group of training-test sample book collection like this.Here the value of the parameter n of training sample, c and l is respectively n=644, c=20 and l=100.

Step 2 selects to have the sorter of posterior probability output, and sets the number N of sub-classifier, the design sub-classifier; The selection of sorter can have neural network or support vector machine or k nearest neighbor or method of discrimination or decision tree or Bayesian decision sorter.The design sub-classifier is to show the sub-classifier design different training set, and its method adopts carries out stochastic sampling to the direct stochastic sampling of original training set or to the feature of original training set, makes sub-classifier have diversity.

In implementation process, selected the k nearest neighbor sorter, this is a kind of nonparametric learning model, and because k nearest neighbor sorter itself does not have probability output, so to handle its output, to obtain the form of probability output.Concrete processing procedure is: to certain training or treat that classification samples x ' finds its K neighbour in training sample, if belong to ω in this K neighbour _kThe training sample of class is K _k, then $K={\mathrm{\Σ}}_{k=1}^c{K}_k.$ With P (ω _k| x ')=K _k/ K represents the posterior probability of k nearest neighbor sorter about x '.Here set sorter number N=100, and neighbour's number K is as a variable parameter.In experiment the variation range of K be 3,4,5}.To its training sample of each sub-classifier is to adopt the feature of original training set is carried out stochastic sampling, and the characteristic number of each sub-classifier is identical.Here characteristic number also being treated as is a variable parameter, and variation range is { 2 ³, 2 ⁴, 2 ⁵, 2 ⁶.

Step 3 is trained N sub-classifier, and obtains the posterior probability P of each sub-classifier about original training sample _j(ω _k| x _i), in the formula, x _iRepresent i sample, ω _kRepresent k classification, j=1 ..., N, k=1 ..., c, i=1 ..., l;

Step 4 is tried to achieve each sub-classifier weighting coefficient α by linear programming _j, j=1 ..., N.

The form of linear programming is:

$\underset{\mathrm{\α},\mathrm{\ξ}}{\min }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j+C\underset{q=1}{\overset{l(c-1)}{\mathrm{\Σ}}}{\mathrm{\ξ}}_q$

subject?to $\left[\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j(P_j\left({\mathrm{\ω}}_m\right|x_i)-P_j\left({\mathrm{\ω}}_k\right|x_i))\right]1(x_i\∈{\mathrm{\ω}}_m)\≥-{\mathrm{\ξ}}_q$

ξ _q≥0，α _j≥0，i＝1，…，l，j＝1，…，N，k≠m，k＝1，…，c

q＝1，2，…，l(c-1)

Wherein C is the compromise coefficient, ξ _qBe slack variable and α _jIt is the weighting coefficient of j sorter.

At objective function

In, first is the volume controlled item, and second is the empiric risk item, and minimizing of this objective function embodied structural risk minimization.The finding the solution of linear programming can be called existing kit and be realized, such as the linear programming function that calls among the Matlab, can try to achieve Optimal Solution of Linear Programming α _j

With reference to Fig. 3, the present invention is realized the classification implementation process of recognition of face is carried out following detailed description:

Steps A, the facial image for the treatment of classification carries out feature extraction, obtains and treats classification samples x ∈ R ⁿ, and be entered in N the sub-classifier that trains in the training process; The feature extraction here is consistent with feature extraction mode in the training process;

Treat that in the present embodiment it is test sample book that classification samples is also referred to as, can not appear at training sample and concentrate.

Step B adopts the method identical with training process to obtain to treat the posterior probability P of classification samples _j(ω _k| x), j=1 ..., N, k=1 ..., c;

Step C, the classification results of classification samples is treated in output; Classifying rules is:

If $\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_m\right|x)=\underset{k=\mathrm{1,2},\·\·\·,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_k\right|x),$ X ∈ ω then _kClass, promptly it is designated y=m.

Effect of the present invention can further specify by following emulated data:

1, simulated conditions and content

The UMIST data set is all carried out emulation according to the mode that above-mentioned specific implementation process is obtained training-classified sample set, generate 30 groups of training-classified sample sets at random, repeat above-mentioned training and assorting process 30 times, and calculate its average recognition rate.The emulation of several method is to carry out under identical experimental situation.

2, simulation result

In repeating above-mentioned training and assorting process 30 times, note the discrimination that each emulation obtains, and calculate its average recognition rate, as shown in table 1." k nearest neighbor method " in the table 1 is not adopt integrated sorter; In the integrated approach, all adopted 100 sub-classifiers, " simple vote " refers to weights and all is taken as 1/100, and " Ueda linear weighted function " employing is the emulation that N.Ueda carried out at the optimum linearity method of weighting of classification problem design in 2000.

Table 1. recognition performance relatively

From the simulation result of table 1 as can be seen, the discrimination of integrated approach is higher than does not have integrated method, and in these integrated approaches, the average recognition rate of the inventive method will be higher than the optimum linearity method of weighting that people such as simple vote and Ueda propose.

Claims (2)

1, a kind of based on the integrated face identification system of sorter, comprising:

Primitive man's face image characteristics extraction module is used for the original facial image that is input to computing machine is carried out feature extraction, obtains c the original training sample collection that sign is arranged;

The facial image characteristic extracting module of waiting to classify is used for the facial image to be classified that is input to computing machine is carried out feature extraction, obtains to treat classification samples x in the n dimension real number space;

Training module is used to select N sub-classifier of posterior probability output, and it is trained according to the original training sample set pair, and the expression formula of this original training sample collection is: { (x _i, y _i) | x _i∈ R ⁿ, y _i∈ 1,2 ..., c}, i=1 ..., l}, wherein: x _iI sample in the expression n dimension real number space, y _iBe its sign, if value in the positive integer between 1 to c is y _i=k then represents x _i∈ ω _kClass, ω _kRepresent k classification, l is the number of sample; By the posterior probability P of training acquisition about the original training sample collection _j(ω _k| x _i), this formula represents that j sub-classifier is about x _iSample belongs to ω _kThe posterior probability of class, j=1 wherein ..., N, k=1 ..., c, i=1 ..., l;

Sub-classifier weighting coefficient computing module is used for according to posterior probability P _j(ω _k| x _i), find the solution the weighting coefficient α of each sub-classifier by linear programming _j, and output to integration module, the solution formula of this weighting coefficient is:

$\underset{\mathrm{\α},\mathrm{\ξ}}{\min }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j+C\underset{q=1}{\overset{l(c-1)}{\mathrm{\Σ}}}{\mathrm{\ξ}}_q$

$\mathrm{subject\; to}\left[\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j(P_j\left({\mathrm{\ω}}_m\right|x_i)-P_j\left({\mathrm{\ω}}_k\right|x_i))\right]1(x_i\∈{\mathrm{\ω}}_m)\≥-{\mathrm{\ξ}}_q$

ξ _q≥0，α _j≥0，i＝1，…，l，j＝1，…，N，k≠m，k＝1，…，c，

q＝1，2，…，l(c-1)

In the formula,

C is the compromise coefficient, ξ _qBe slack variable and α _jBe the weighting coefficient of j sorter,

Be the volume controlled item,

It is the empiric risk item;

The sub-classifier sort module is used for and will treats that classification samples is input in N the sub-classifier that training process trains, and obtains to treat the posterior probability P of classification samples _j(ω _k| x);

Integration module is used for the weight coefficient α that obtains according to training process _jWith posterior probability P to be classified _j(ω _k| x) design category rule, and obtain classification results according to this classifying rules, this classifying rules is:

If $\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_m\right|x)=\underset{k=\mathrm{1,2},\·\·\·,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_k\right|x),$ X ∈ ω then _mClass, m ∈ 1,2 ..., the classification that the c} representative is different, its classification results available categories sign y=m represents;

The classification results output module is used for and will treats the form output of the classification results of classification samples with classification logotype, and shows on computer display.

2, a kind of based on the integrated face identification method of sorter, comprising:

(1) recognition of face training process:

Extraction is input to the primitive man's face characteristics of image in the computing machine, and obtaining c has sign original training sample collection: { (x _i, y _i) | x _i∈ R ⁿ, y _i∈ 1,2 ..., c}, i=1 ..., l}, wherein: x _iI sample in the expression n dimension real number space, y _iBe its sign, if value in the positive integer between 1 to c is y _i=k then represents x _i∈ ω _kClass, ω _kRepresent k classification, l is the number of sample;

Selection has N sub-classifier of posterior probability output, and it is trained according to the original training sample set pair, obtains the posterior probability P about the original training sample collection _j(ω _k| x _i), this formula represents that j sub-classifier is about x _iSample belongs to ω _kThe posterior probability of class, j=1 wherein ..., N, k=1 ..., c, i=1 ..., l;

According to posterior probability P _j(ω _k| x _i), find the solution the weighting coefficient α of each sub-classifier by linear programming _j, its solution formula is:

$\underset{\mathrm{\α},\mathrm{\ξ}}{\min }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j+C\underset{q=1}{\overset{l(c-1)}{\mathrm{\Σ}}}{\mathrm{\ξ}}_q$

$\mathrm{subject\; to}\left[\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j(P_j\left({\mathrm{\ω}}_m\right|x_i)-P_j\left({\mathrm{\ω}}_k\right|x_i))\right]1(x_i\∈{\mathrm{\ω}}_m)\≥-{\mathrm{\ξ}}_q$

ξ _q≥0，α _j≥0，i＝1，…，l，j＝1，…，N，k≠m，k＝1，…，c，

q＝1，2，…，l(c-1)

In the formula, j=1 ..., N;

C is the compromise coefficient, ξ _qBe slack variable,

Be the volume controlled item,

It is the empiric risk item;

Weighting coefficient α with each sub-classifier _jOutput to categorizing system;

(2) recognition of face assorting process:

Extraction is input to the facial image feature of classifying for the treatment of in the computing machine, obtains and treats classification samples x ∈ R ⁿ

To treat that classification samples is input in N the sub-classifier that trains in the training process, obtain to treat the posterior probability P of classification samples _j(ω _k| x), j=1 ..., N, k=1 ..., c;

The weight coefficient α that obtains according to training process _jWith the posterior probability P that treats classification samples _j(ω _k| x) the design category rule is:

If $\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_m\right|x)=\underset{k=\mathrm{1,2},\·\·\·,c}{\max }\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j{P}_j\left({\mathrm{\ω}}_k\right|x),$ X ∈ ω then _mClass, m ∈ 1,2 ..., the classification that the c} representative is different, its classification logotype is y=m;

To treat of the form output of the classification results of classification samples, and on computer display, show with classification logotype.

Images