CN107977630A

CN107977630A - A kind of smile's kind judging method based on character face's Expression Recognition

Info

Publication number: CN107977630A
Application number: CN201711261098.6A
Authority: CN
Inventors: 杨世鹏
Original assignee: Individual
Current assignee: Individual
Priority date: 2017-12-04
Filing date: 2017-12-04
Publication date: 2018-05-01

Abstract

The invention belongs to smile's kind judging method field, is in particular a kind of smile's kind judging method based on character face's Expression Recognition, it is possible to increase to the accuracy of face face smile identification, comprises the following steps：The notable feature standard parameter of a few class smiles is established, determines the comparison relation of standard parameter and identified parameter；Portrait face smile's picture is pre-processed；To the picture structure point distribution shape model pre-processed, the feature extraction based on uniformLGBP is done, establishes the picture feature of conspicuousness；Feature Selection is carried out to picture feature using genetic algorithm, obtains outstanding population；Using obtained outstanding population as the fiducial value per class smile's feature, two new object functions in class and between class are established, target is exactly the value for minimizing class inner function and the value for maximizing function between class；The classification of face feature is carried out, after optimal characteristics have been chosen, the method for random forest is taken to classify to feature, completes the identification of smile's classification and judgement.

Description

A kind of smile's kind judging method based on character face's Expression Recognition

Technical field

The present invention relates to smile's kind judging method, is in particular a kind of smile based on character face's Expression Recognition Kind judging method.

Background technology

It is that character face's smile's information is handled using software technology that facial smile, which knows, extracts its feature and is known The process of classification is not judged.The facial smile identification of face is typically used to human-computer interaction and artificial intelligence field.For example, pass through Facial smile's identification can strengthen intelligent robot and the direct interaction of the mankind, what intelligent robot can be arrived by image recognition Information performs their action to plan arrangement.Facial smile's identification is the further intelligence on the basis of human facial expression recognition Smile in analysis detection facial image, to determine smile's classification of identified object, such as professional formula smile, passive type are laughed at Appearance, active smile, Di Xieenshi smiles etc..Currently to facial smile identification several method mainly have, by such as happily, The various moods such as sad, and model or topological structure are established in corresponding characteristic area, such as face, eyes, eyebrow, afterwards Required characteristic point, such as the eyes and pixel on periphery, the pixel on eyebrow and periphery are extracted in figure after imaging Deng, or it is finally again that these are special using geometric properties region, the geometric properties region in geometric properties region, eyes such as face Sign point either determines in geometric properties region after being contrasted with the model or topological structure accordingly having had built up, at this During one, primitive decision is made just for the general expression of the face such as happy, sad.As " local Gabor binary patterns (LGBP) " after, mainly being converted with Gabor wavelet to image characteristic region, by LBP extraction feature pixels and surrounding picture Relation between vegetarian refreshments, and this relation is shown as into histogram.This method does not have in traditional face characteristic extraction model Have and consider the otherness of different classes of expression in Feature Selection, can not accomplish to distinguish facial smile's level, it is right Smile's classification of identified object is tested and assessed.

The content of the invention

The invention mainly solves the technical problem of providing a kind of smile's kind judging based on character face's Expression Recognition Method, it is possible to increase to the accuracy of face face smile identification.

In order to solve the above technical problems, the present invention relates to a kind of smile kind judging side based on character face's Expression Recognition Method, comprises the following steps：

(1) professional formula smile, passive type smile, active smile, the notable feature standard parameter of Di Xieenshi smiles are established, really Determine the comparison relation of standard parameter and identified parameter.Professional formula smile feature shows as smile shape, mouth week contraction of muscle.Passively Formula smile's feature shows as cheekbone and periocular muscle is shunk at the same time, and eyes are in " narrowing eye " shape.Active smile's feature shows as cheekbone Bone is shunk, periocular muscle Outer shrink.Di Xieenshi smile's features show as cheekbone contraction, periocular muscle Outer shrink, canthus It is obvious to locate crow's feet；

(2) portrait face smile's picture is pre-processed；

(3) to the portrait face smile picture structure point distribution shape model pre-processed, the feature based on uniformLGBP is done Extraction, establishes the picture feature of conspicuousness；

(4) first time Feature Selection is carried out to picture feature using genetic algorithm, obtains outstanding population；

(5) it is new to establish two in class and between class using obtained outstanding population as the fiducial value per class smile's feature Object function, target be exactly minimize class inner function value and maximize class between function value, and using Pareto optimization calculate Method optimizes it；

(6) classification of face feature is carried out, after optimal characteristics have been chosen, takes the method for random forest to carry out feature Classification, completes the identification of smile's classification and judges.

Preferably, professional formula smile's feature shows as smile shape, mouth week contraction of muscle；The passive type smile feature Show as cheekbone and periocular muscle is shunk at the same time, eyes are in " narrowing eye " shape；Active smile's feature shows as cheekbone contraction, Periocular muscle Outer shrink；The Di Xieenshi smiles feature shows as cheekbone and shrinks, periocular muscle Outer shrink, fish at canthus Tail line is obvious.

Preferably, the pretreatment in the step (2) includes recognition of face, noise processed and face alignment.

Preferably, the method for the feature extraction based on uniformLGBP is as follows in the step (3)：First to picture into Row Gabor filtering transformations, secondly use all pixels in picture feature of the LBP operator extractions histogram as face, i.e., Using center pixel value as threshold value, pixel value in adjacent domains is then 1 if greater than the threshold value, is otherwise 0, by using this After method binaryzation, 2Q binary pattern can be obtained, a uniform pattern is defined again, that is, is formed after the binaryzation obtained Description；It is otherwise non-uniform pattern if there is no more than twice from 0 to 1 or 1 to 0 saltus step is then uniform pattern；Finally Justice in this way, Q2-Q+2 is reduced to by 2Q original binary pattern.

Preferably, the method for the picture feature for establishing conspicuousness based on uniformLGBP is as follows in the step (3)： For the picture of a given n × n-pixel, m × m face feature block is divided it into first.Each face feature block is actual Upper is also the picture of l × l pixel, and then the picture of this l × l is done based on uniformLGBP feature extractions, in order to Significant face feature is enough picked out, it is necessary to it is the maximum intensity value in uniformLGBP to set a threshold value 0.2q, wherein q, Then, the maximum intensity value of each pixel in l × l pictures and this threshold value are compared, if this pixel Intensity level is greater than or equal to this threshold value, then corresponding pixel is regarded as significantly, for each face feature Block, if there is there is four or more to be considered as significant point, then this face feature block is defined as 1, otherwise It is defined as 0.

Preferably, the step (4) is specially：Random initializtion population first, then calculates the accuracy of each population, Four classes are divided into according to accuracy, provide every a kind of fitness function for calculating population；Finally optimized using genetic algorithm Obtain outstanding population.

Preferably, the fitness function is that wherein α is the ratio for being correctly categorized into its classification, and ε, ρ 1, ρ 2 is parameter, Arc is the state of face feature block, and m is the quantity of face feature block.

Preferably, the object function in the step (5) in class is：F1(Sk)=1NwΣr=1mΣc=1m(Sk-mw)2]] >；Object function in the step (5) between class is：F2(Sk)=1lΣi=1l(1NbΣr=1mΣc=1m(Si-mb)2),]]>.

Preferably, mw=1Nw Σ i=1NwMi, mb=1Nb Σ j=1NbMj, described]]>Mi is calculated by heredity The solution that method is obtained from a kind of smile, the Nw are the numbers of solution, and the Mj is to be obtained by genetic algorithm from different classes of Solution, the Nb is the number of its homographic solution, and the l then represents the number of variety classes smile, and the Sk is population.

Advantageous effects：

A kind of smile's kind judging method based on character face's Expression Recognition of the present invention, based on traditional LGBP and UniformLGBP expression recognitions, have used the fitness function of GA and the target letter of new Pareto optimization algorithms Number, can more accurately judge smile's classification.The present invention is made that energetically tentative in face face smile's identification decision field Explore.

Brief description of the drawings

Fig. 1 is the flow diagram of the present invention.

Embodiment

With reference to specific embodiment, the present invention is further explained.It is to be understood that these embodiments are merely to illustrate the present invention Rather than limit the scope of the invention.In addition, it should also be understood that, after reading the content taught by the present invention, people in the art Member can make various changes or modifications the present invention, and such equivalent forms equally fall within the application the appended claims and limited Scope.

Embodiments of the present invention are related to smile's kind judging method based on character face's Expression Recognition, as shown in Figure 1, Comprise the following steps：Face picture is pre-processed；Feature based on uniformLGBP is done to the face picture pre-processed Extraction, and establish the conspicuousness of picture feature；First time Feature Selection is carried out to picture feature using genetic algorithm, is obtained outstanding Population；According to fiducial value of the obtained outstanding population as the outstanding population per class smile's feature, to establish in class and class Between two new object functions, target is exactly the value for minimizing class inner function and the value for maximizing function between class, and is used Pareto optimizes algorithm to be optimized to it；The classification of face feature is carried out, after optimal characteristics have been chosen, is taken random The method of forest classifies feature.It is specific as follows：

The picture of step 1, given lineup's face, is pre-processed first, wherein mainly identified comprising people's face, noise processed and Face face alignment.Comprise the following steps that：

Step 1.1.1, in recognition of face step, Haar-like recognitions of face have been used.Haar-like features pass through four kinds Mode represents face：Edge feature, linear character, central feature, to corner characteristics.The feature of every kind of form all contains white With the square of black, characteristic value is sums that the are all pixels in white square and subtracting all pixels in black square.So The template that the feature of four kinds of forms forms a standard is ultimately used to detection face.

Step 1.1.2, noise processed is done using two-sided filter.Talk about publicly known, Gaussian filter is in each sampling time Only consider pixel between space length and without considering the similarity degree between pixel.Therefore, Gaussian filter method is often Picture to be dealt with is made blur.Unlike, two-sided filter possesses two parameters, respectively by the geometry of pixel The difference of distance and pixel determines.Therefore, two-sided filter can be effectively protected the marginality of picture and can also eliminate at the same time The noise of picture.

Step 1.1.3, because CK+ databases (this database used in an experiment) contain the mark point of face, Mark point need not be followed the trail of again to describe facial contours.It is pointed out that in CK+ databases, the number of mark point is 68, But the present invention only needs the point that those can describe face border.Only retain the pixel value within face border, remove background The unwanted information of those in picture, can so improve the precision of picture extraction.

Step 2, in this step, Gabor filtering methods are used on picture to represent face's picture first.Then, In the selection of picture texture expression, consider to replace traditional LGBP using uniformLGBP.What last basis obtained UniformLGBP, generation face notable feature.Provide uniformLGBP methods by detailed below and be based on The process of uniformLGBP generations face notable feature.

It is identical with LBP, a label is set to each pixel in picture by following formula

Η (xp, yp)=I (f (xp, yp) >=f (xc, yc)) (1)

Wherein f (xc, yc) is the pixel value in central point (xc, yc), and f (xp, yp) (p=0,1 ..., Q-1) is central point The pixel value of the peripheral point of (xc, yc) position, for I (A) for 1 when the value in A is true, I (A) is that 0 value worked as in A is non- Very.The shape considered now is no longer traditional square but changes circle into consider.The realization for the step of passing through the above, obtains 2Q binary pattern.It is no more than twice from 0 to 1 or 1 to 0 binary pattern of saltus step is uniform next, defining those and existing Pattern, is otherwise non-uniform pattern.The number of original binary pattern is reduced to by Q2-Q+2 according to the method for proposition.

Step 3, establish face's notable feature based on uniformLGBP.It is first for the picture of a given n × n-pixel First divide it into m × m face feature block.Each face feature block is actually also the picture of l × l pixel then to this The picture of a l × l does uniformLGBP feature extracting methods.In order to pick out significant face feature, it is necessary to set one A threshold value 0.2q, wherein q are the maximum intensity values in uniformLGBP.Then, each pixel in l × l pictures is most Big intensity level and this threshold value are compared.If the intensity level of this pixel is greater than or equal to this threshold value, then corresponding Pixel be regarded as significantly.For each face feature block, if there is there is four or more to be considered It is significant point, then this face feature block is defined as 1, is otherwise defined as 0.

Step 4, define initial population：Make the state that aij is face feature block.Set when face feature block is notable Aij is 1, is otherwise 0.All face feature aij blocks are formed matrix Sk, matrix is as follows：

Wherein Sk, which is that the optimal characteristics in a specific smile population are one of, to be solved, and N is then the number of population.

Step 5, calculating parameter α：It is D to make similar smile's training sample concentrate a trained picture, then obtains this instruction Practice the face feature matrix of picture D, it is ID to be set to the matrix.When meeting following rule, this training picture D, which belongs to this, to be laughed at Hold class：

|ID∩Sk|≥ΩΣr=1mΣc=1marc---(3)]]>

Wherein Ω is that a threshold value is set to 0.8, and the similarity that this feature for demonstrating the need for and choosing has 80% just can be shown that it is Belong to this smile's class.

The required parameter that is over is defined in step 6, above-mentioned steps, the solution of optimal characteristics is next searched for using GA. Because having had been removed from unwanted external context in face's alignment step, in initial matrix Sk, boundary element a1j The then random selection of=amj=0 (j=1,2 ..., m), ai1=aim=0 (i=1,2 ..., m) other elements.Replaced for non- Generation solution NR, its initial solution are also randomly selected from these candidate solutions.After initialization terminates, Sk is according to following for solution Fitness function is evolved：

Wherein α be correctly be categorized into its classification ratio and ε, ρ 1, ρ 2 be parameter.Fitness value F (Sk) depends primarily upon parameter alpha And Characteristic Number, usually smaller fitness value correspond to better solution.As α=0, usual solution be it is very infeasible, in order to It is this as a result, setting ε=0.0001 to make F (Sk) as big as possible to avoid occurring again α=0.As α=100, this solution very may be used OK, therefore in order to prevent unrelated feature enters solution, is arranged to 0.005.Therefore, it is selected to the quantity of feature can both protect The advantage of card population can reduce intrinsic dimensionality again.As 90≤α ＜ 100, more features meetings are because of this high α value and often Number enters disaggregation.In order not to make value F (Sk) small in α=100 in 90≤α ＜ 100 when ratios, plus a threshold constant ρ 1 and set It is 1.As 0≤α ＜ 90, the value needs of F (Sk) are smaller than in 90≤α ＜ 100, make ρ 2=2.

Fitness function is defined by above formula, the Feature Selection algorithm based on GA is summarized as shown in algorithm 1.

Algorithm 1：Feature Selection algorithm based on GA

Input：

Fitness function, F ()

Maximum iteration, G

Assuming that population number, n

By intersecting the ratio of substitution group member, r in each step

Aberration rate, m%

New population, NR

Output：

Population P

Start

Step 1：Generate random population P (S1, S2 ..., Sk) (k=1,2 ..., n)；

Step 2：Assess each population, calculate F (Sk) (k=1,2 ..., n)；

Step 3：Selection：(1-r) n member is selected to be added to NR from population P with probabilistic method；

Step 4：Intersect：Assume from population P by probability selection pair.For each pair it is assumed that producing two offsprings with crossover operator. All the progeny is added NR；

Step 5：Variation：M% (1-r) n member is selected from NR using uniform probability.For select it is each into Member, in its expression randomly choose one negate；

Step 6：Renewal：Value in NR is copied in P；

Step 7：If iterationses≤G

Continue step 2；

else

Stop；

Terminate

Step 7, according to from the obtained solution of improved GA algorithms (step 6) optimization, next, using Pareto optimization algorithms do into The Feature Selection optimization of one step.

Sk is solved in order to obtain, considers this following multi-objective optimization question：

Min/maxF (Sk)=(F1 (Sk), F1 (Sk) ..., F1 (Sk))

In the feature selecting based on Pareto optimization algorithms, consider to have used Fisher linear decision rules establish two it is new Optimization object function：

F1(Sk)=1NwΣr=1mΣc=1m(Sk-mw)2]]>With F2 (Sk)=1l Σ i=1l (1Nb Σ r=1m Σ c=1m (Si-mb) 2)---(6)]]>

And

mw=1NwΣi=1NwMi,mb=1NbΣj=1NbMj---(7)]]>

Wherein Mi is the number that the solution and Nw obtained by GA from a kind of smile is solution, Mj be by GA from different classes of To solution and Nb be its homographic solution number, l then represents the number of variety classes smile.

Pass through the object function provided, it can be seen that F1 (Sk) and F2 (Sk) is to have corresponded to gap and expansion between diminution class respectively Gap between major class.

By using SPEA, the two the objective function optimization problems provided by above formula can be resolved.And it is based on The flow of Pareto optimization algorithms is provided by algorithm 2.

Algorithm 2：Feature selecting algorithm based on Pareto optimization algorithms

Input：

Size be k population, P (S1, S2 ..., Sk)

Each solve based on formula (6), the object function F1, F2 of (7)

Maximum iterations, H

Output：

Population P and P '

Start

Step 1：Generation initial population P and establish one it is empty extra non-by dominant set P '；

Step 2：Non- copied to by domination solution in P is additionally collected in P '；

Step 3：The solution dominated in P ' by P ' other members is deleted；

Step 4：The quantity of ifP '>N'

P ' is trimmed using the method for cluster；

end

Step 5：Calculate the fitness each solved in P and P '；

Step 6：Sm member is selected from P+P ' from the statistical method of uniform sampling；

Step 7：Sm member is done and is intersected；

Step 8：Make a variation to Sm member；

Step 9：If iterationses≤H

Continue step 2；

else

Stop；

Terminate

After step 8, optimal characteristics are elected, to be classified into four class smiles, these four smiles are respectively：Professional formula is laughed at Appearance, passive type smile, active smile, Di Xieenshi smiles.Next random forest grader method is provided, it can be effective Improve the precision of face face smile classification in ground.

Random forest is a kind of assembled classifier, its essence is the set of a tree classificator, base grader therein It is the categorised decision tree without beta pruning built with post-class processing algorithm, output result is then true using simple majority ballot method It is fixed.

Gini coefficient indexs are the fragmentation criterions of post-class processing in random forest, its calculating process is as follows：

Gini(S)=1-Σi=1mtryPi2---(8)]]>

Wherein Pi represents the probability that class Yi occurs in sample set S.

Face feature sorting algorithm based on random forest provides in algorithm 3.

Algorithm 3：Face feature sorting algorithm based on random forest

Input：

One training set (X, Y), X is characterized, and Y is classification

Classification number has, c

Original training set size, N

Intrinsic dimensionality in each training sample, M

The number of post-class processing, T

The intrinsic dimensionality that each node uses, mtry (mtry≤M)

Minimum sample number on node, s (end condition)

Output：

The feature of each node split institute foundation

Start

Step 1：Establish i post-class processing；

Step 2：I=1；

Step 3：Have from original training set (X, Y) and put back to repetition extraction one new training set S of N number of sample composition, as i-th The root node of tree, and is trained since root node；

Step 4：When if present nodes meet end condition s

If present node is leaf node；

else

Mtry feature is randomly selected from M dimensional features as candidate feature.Present node is calculated according to mtry candidate feature Gini coefficients.The feature of selection Gini coefficient minimums is come into line splitting, is divided into left child node and right child node；

endif

Calculate other nodes on i-th tree；

Step 5：ifi≠T

I=i+1；Continue to do step 3；

else

Stop；

Terminate

Finally provide the Feature Selection based on uniformLGBP feature extractions, GA and Pareto optimization algorithms, face face smile Algorithm：

Algorithm 4：Face's face smile's recognizer

Input：

Training picture in all smile's classifications

Significant face feature block

Other specification is set

Output：

Represent the optimal solution per class smile

Start

Step 1：Initialization population P (S1, S2 ..., Sk) (k=1,2 ..., n)；

Step 2：GA (algorithm 1) is to initial population P；

Step 3：Optimal solution Si is picked out from GA；

Step 4：Two parts will be divided into solution Si：Ui and Li；

Step 5：Fixed Ui, is Li GA (algorithm 1)；Fixed Li, is Ui GA (algorithm 1)；

Step 6：New Ui and Li is formed new Si and is copied into P；

Step 7：Optimal characteristic results P is chosen from GA；

Step 8：Each solution in 6,7 couples of P of formula is evaluated, and obtains F1 and F2；

Step 9：Pareto optimization algorithms (algorithm 2) are done to the solution in P；

Step 10：Return to Pareto optimal solutions；

Step 11：Selected feature is classified using random forest grader (algorithm 3)；

Terminate

Step 9, finally select database to train inventive algorithm until algorithmic statement, has many open platforms to provide at present The database of face face smile, such as CK+, eNTERFACE and MMI.A database is selected to carry out inventive algorithm Training and test, a preferable disaggregated model is obtained according to last test result.

It is not difficult to find that the present invention is effectively by expression recognition technology successful implantation to facial smile's identification technology, Have the following advantages that and good effect：The present invention is used based on traditional LGBP and uniformLGBP expression recognitions The object function of the fitness function of GA and new Pareto optimization algorithms, can more accurately judge smile's classification.This hair Bright be made that in face face smile's identification decision field energetically attempts sex exploration.

Certainly, described above is not limitation of the present invention, and the present invention is also not limited to the example above, the art The variations, modifications, additions or substitutions that those of ordinary skill is made in the essential scope of the present invention, fall within the guarantor of the present invention Protect scope.

Claims

1. a kind of smile's kind judging method based on character face's Expression Recognition, comprises the following steps：

(1) professional formula smile, passive type smile, active smile, the notable feature standard parameter of Di Xieenshi smiles are established, really Determine the comparison relation of standard parameter and identified parameter；

(2) portrait face smile's picture is pre-processed；

2. a kind of smile's kind judging method based on character face's Expression Recognition according to claim 1, its feature exist In：Occupation formula smile's feature shows as smile shape, mouth week contraction of muscle；The passive type smile feature show as cheekbone and Periocular muscle is shunk at the same time, and eyes are in " narrowing eye " shape；Active smile's feature shows as cheekbone and shrinks, outside periocular muscle Shrink；The Di Xieenshi smiles feature shows as cheekbone and shrinks, periocular muscle Outer shrink, and crow's feet is obvious at canthus.

3. a kind of smile's kind judging method based on character face's Expression Recognition according to claim 1, its feature exist In：Pretreatment in the step (2) includes recognition of face, noise processed and face alignment.

4. a kind of smile's kind judging method based on character face's Expression Recognition according to claim 1, its feature exist In：The method of the feature extraction based on uniformLGBP is as follows in the step (3)：Gabor filtering is carried out to picture first to become Change, all pixels in picture secondly are used with feature of the LBP operator extractions histogram as face, i.e., is made center pixel value For threshold value, pixel value in adjacent domains is then 1 if greater than the threshold value, is otherwise 0, by using this method binaryzation with Afterwards, 2Q binary pattern can be obtained, define a uniform pattern again, that is, description formed after the binaryzation obtained；If It is otherwise non-uniform pattern in the presence of no more than twice from 0 to 1 or 1 to 0 saltus step is then uniform pattern；Finally by such Justice, Q2-Q+2 is reduced to by 2Q original binary pattern.

5. a kind of smile's kind judging method based on character face's Expression Recognition according to claim 1, its feature exist In：The method of the picture feature for establishing conspicuousness based on uniformLGBP is as follows in the step (3)：It is given for one N × n-pixel picture, divide it into m × m face feature block first；Each face feature block be actually also a l × The picture of l pixels, then makees based on uniformLGBP feature extractions the picture of this l × l, in order to pick out significantly Face feature, it is necessary to which it is the maximum intensity value in uniformLGBP to set a threshold value 0.2q, wherein q, then, in l × l The maximum intensity value of each pixel in picture and this threshold value are compared, if the intensity level of this pixel be more than or Equal to this threshold value, then corresponding pixel is regarded as significantly, for each face feature block, if there is having Four or more is considered as significant point, then this face feature block is defined as 1, is otherwise defined as 0.

6. a kind of smile's kind judging method based on character face's Expression Recognition according to claim 1, its feature exist In：The step (4) is specially：Random initializtion population first, then calculates the accuracy of each population, according to accuracy point For four classes, every a kind of fitness function for calculating population is provided；Finally optimize to obtain outstanding kind using genetic algorithm Group.

7. a kind of smile's kind judging method based on character face's Expression Recognition according to claim 6, its feature exist In：The fitness function is wherein, α is the ratio for being correctly categorized into its classification, and ε, ρ 1, ρ 2 is parameter, and arc is face feature The state of block, m are the quantity of face feature block.

8. a kind of smile's kind judging method based on character face's Expression Recognition according to claim 1, its feature exist In：Object function in the step (5) in class is：F1(Sk)=1NwΣr=1mΣc=1m(Sk-mw)2]]>；The step (5) object function between class is：F2(Sk)=1lΣi=1l(1NbΣr=1mΣc=1m(Si-mb)2),]]>.

9. a kind of smile's kind judging method based on character face's Expression Recognition according to claim 8, its feature exist In：Mw=1Nw Σ i=1NwMi, mb=1Nb Σ j=1NbMj, described]]>Mi is from a kind of smile by genetic algorithm In obtained solution, the Nw is the number of solution, and the Mj is the solution obtained by genetic algorithm from different classes of, and the Nb is The number of its homographic solution, the l then represent the number of variety classes smile, and the Sk is population.