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Facial Feature Extraction and Image Warping Using PCA Based Statistic Model

Facial Feature Extraction and Image Warping Using PCA Based Statistic Model
Facial Feature Extraction and Image Warping Using PCA Based Statistic Model

FACIAL FEATURE EXTRACTION AND IMAGE W ARPING USING PCA

BASED STATISTIC MODEL

Zhong Xue,Stan Z.Li,Eam Khwang Teoh

School of Electrical&Electronic Engineering Microsoft Research China Nanyang Technological University Zhi Chun Road,Haidian District Nanyang Avenue,Singapore,639798Beijing,100080,P.R.China Emails:zhong xue@https://www.doczj.com/doc/5e3558626.html,,eekteoh@https://www.doczj.com/doc/5e3558626.html,.sg,szli@https://www.doczj.com/doc/5e3558626.html,

ABSTRACT

A new algorithm is proposed to extract the facial features and estimate the control points for facial image warping us-ing the Principle Component Analysis(PCA)based statistic face model.In this algorithm,?rst a full-face model con-sisting the contour points and the control points is built. Based on a number of manually marked training samples, the prior distribution of the full-face model can be obtained by using the PCA.Given an input face image,?rst the con-tour points are obtained by using the recently developed Bayesian Shape Model(BSM),and then the control points are estimated from the contour points.Finally,the extracted face path is normalized using the piece-wise af?ne triangle warping algorithm.Experimental results illustrate the effec-tiveness of the proposed algorithm.

1.INTRODUCTION

In face recognition,one of the main procedures is?rst match-ing and extracting the face patch,and then warping it to the standard view and the normal expression.In this process, the accuracy in extraction and modeling the face is crucial, e.g.in[1],the normalized frontal view face is not visually satis?ed since there is no face extraction performed.

The Active Shape/Appearance Models(ASM&AAM) have been demonstrated to be successful in facial feature matching[2,3].However,in the ASM,the reconstructed prototype or its geometrical transformed version is regarded as the?nal matching result,and hence the accuracy of match-ing is largely depended on the training samples selected. Provided there were enough samples,ASM can globally match the object shapes very well,but with lower local ac-curacy,i.e.the performance deteriorates under local shape variations.To overcome this disadvantage,the Bayesian Shape Model(BSM)is developed[4],where both the global and local shape deformations are considered:the global shape variations are modeled by the prior distribution of the marked samples and the local deformations are constrained by the measures between the deformable model and the pro-totype.In this way,object shapes can be extracted with im-proved accuracy.

Generally,the feature points used by the ASM or BSM are the outline contours of the facial features,i.e.the out-lines of the face,eyebrows,eyes,nose and mouth(see Fig.1). Although these points are enough to describe the shape of a face,they are insuf?cient in dealing with face image warp-ing/normalization.To solve the problem,in[3],the De-launey triangulation is utilized to partition the area that is surrounded by the contour points into a set of triangles. However,this algorithm does not consider the characteris-tics of the expression/action of the face,and the triangles ob-tained differ greatly when the position of the contour points changes.

In this paper,a2-D full-face model is built based on the CANDIDE model,which consists of the contour points and the control points.The contour points include the out-line of face,eyebrows,eyes,nose and mouse;the control points are the feature points used for facial image warping. Based on a number of manually marked training samples, the prior distribution of the full-face model is obtained by using PCA.Given an input face image,?rst the contour points of the face can be matched accurately by using the recently developed Bayesian Shape Model(BSM),and the control points are determined by the matching results ac-cording to the prior distribution of the full-face model.As a result,the facial image warping can be performed very eas-ily using the piece-wise af?ne algorithm based on the full face model.

Experimental results for normalizing the BSM matching results are presented to demonstrate the effectiveness of the proposed algorithm.

2.MODELING THE FULL FACE USING PCA The full-face model consists of two point sets:1.Contour points:the outline contours of the face,the eyebrows,eyes,

contour points,‘*’:control

points.

nose and mouse;2.Control points:the points that are useful for face image warping,but lack image features.

Denoting the full shape model of the face as ,refers to the number of the points,

(1)

represents the contour points and indicates the control

points.Fig.1shows two examples of the marked face,where ‘o’is the contour point representing the outlines of the face,eyebrows,eyes,nose and mouth respectively and ‘*’stands for the control point.

The PCA is utilized to build the shape model of the face.First,all the sample face images are manually marked and normalized/aligned to a standard view by using least square errors method.Then,we use the following steps to

model

the shape variations.

i).Compute the mean of the data,,

where is the number of samples.

ii).Computer the covariance of the data,

(2)

iii).Compute the eigenvectors,,and corresponding eigenvalues of (sorted so that ).

Therefore,the shape of a face can be reconstructed from the mean and the shape parameter,:

(3)

where

is the matrix containing the eigenvectors cor-responding to the largest eigenvalues,.

When is known,the shape parameter

is given by

(4)

Normalizing input face image removes the effect of po-sition/expressions and gives more reliable recognition re-sults.It can be performed by extracting the facial features and determining the control points of the face model,and then applying image warping.

3.MATCHING FACIAL FEATURES USING BSM The BSM formulates the matching of a deformable model to the object in a given image as maximizing a posteriori (MAP)estimation problem [5].According to the Bayesian estimation,the joint posterior distribution of and ,,

is

(5)

where

is the likelihood distribution of

input image data .

(6)

is the joint prior distribution of and .

For a given image ,the MAP estimates,and

,are de?ned as,

(7)

where is the distribution of the prototype ,describes the variations between and ,and indi-cates the matching between and the salient features of the object in image .Provided the densities in Eq.(7)can be

modeled as Gibb’s distribution,maximizing the posterior distribution is equivalent to minimizing the corresponding energy function of the contour:

(8) where.

The constraint energy term of the prototype con-tour is caused by the prior distribution,,which can be approximated by and modeled by a single Gaussian distribution[6].

(9)

where is given in Eq.(4).Since is unknown,it is set to.Experiments show that this approximation is accept-able because generally the variations of can represent the variations of the full-face model.Therefore,the constraint energy is denoted as

(10)

The variations of the prototypes contour is limited by the plausible area of the corresponding shape parameters,

(11)

The threshold,,is chosen using the distribution[2].

On the other hand,BSM uses a transformational invari-ant internal energy term,which describes degree of match-ing between the deformable model in the image domain and the prototype in the shape domain.Mathematically, and are related by, where is the transformational matrix,T is a translation vector.The invariant internal energy term is de?ned as(see [7]about the detail of Eq.(14):

(12)

(13)

(14)

The external energy term can be calculated as follows [8].

First,the image is smoothed using Gaus-sian function,,.Sec-ond,the normalized gradient of the smoothed image at each pixel location,is computed:

,and?nally,the external energy is de?ned as:

(15)

is the direction(unit vector)of the gradient, and indicates the normal vector of the contour at point,with and

is the tan-gent vector of contour at point.

4.DETERMINING THE CONTROL POINTS FOR

FACIAL IMAGE W ARPING

Using the BSM facial feature extraction algorithm,the match-ing results of the contour points and,and the pose rela-tionship and(between and)can be obtained.Then, the contour points in the shape domain is calculated by

(16) The algorithm to determine the control points correspond-ing to is to estimate the shape parameter,so that the contour points of the reconstructed model

match closely,and hence the corresponding reconstructed control points can be regarded as the estimate of the con-trol points.The detail algorithm is follows,

i).The estimation problem is to?nd out,so that the re-sult matches in the sense of least square errors.From Eq.(3),can be calculated by

(17) where is a unity matrix and is a zero matrix.Denoting

,,and noting that,,and

are known,the shape parameter can be estimated using

(18) ii).The control points can be calculated through,

(19)

Fig.4.The original (upper row)and the warped (lower row)face images.

iii).The ?nal full-face contour in the shape domain is rep-resented by

and hence its transformed counter-part in the image domain,is

.

Fig.4shows several examples of the warping results us-ing the proposed face model.The upper row is the orig-inal faces,while the bottom row is the warped images of

the upper row correspondingly.For example,the ?rst col-umn of the images illustrates changing the expression to smile,and the second column stops the smile.It can be seen from the ?gure that the face model describes the face well and by image warping,the expressions of face can be removed/changed,which is very useful for face recognition.

5.EXPERIMENTAL RESULTS

The experiments are carried out using the BSM toolkit de-veloped in the Matlab 5.3Environment.Given an input face image,the BSM is utilized to match the contour points of the face model.The matching results are then utilized to estimate the control points of the face model to obtain the extracted full face in the image domain.Finally,an im-age warping algorithm is performed to transfer the extracted face into the mean of the face model in the shape domain.Fig.5presents examples of the experiment results using the proposed algorithm.The left column is the input face im-age,the middle column shows the extracted contour points,and the normalized faces are plotted in the right column.

6.CONCLUSION

In this paper,a full-face model consisting the contour points and the control points is built based on PCA,and an algo-rithm is proposed to estimate the control points from the contour points that are matched by the BSM facial feature extraction algorithm.Then the warping and normalization of the extracted face patch can be performed by using piece-wise af?ne algorithm.Experimental results demonstrate

good

tion/warping results.

performance of the proposed algorithm.

7.REFERENCES

[1]W.Zhao and R.Chellappa,“Sfs based view synthesis for ro-bust face recognition,”in 4th IEEE Conference on Automatic Face and Gesture Recognition,Grenoble,France ,2000,pp.285–292.[2]T.F.Cootes,C.J.Taylor,D.H.Cooper,and J.Graham,“Ac-tive shape models -their training and application,”Computer Vision and Image Understanding ,vol.61,no.1,pp.38–59,1995.[3]T.Cootes,G.J.Edwards,and C.J.Taylor,“Active appearance

models,”in Proceeding of 5th European Conference on Com-puter Vision ,1998,vol.2,pp.484–498.[4]Z.Xue,Stan Z.Li,J.W.Lu,and E.K.Teoh,“Bayesian model

for extracting facial features,”in Sixth International Con-ference on Control,Automation,Robotics &Vision,ICARCV 2000,Dec.,Singapore ,2000.[5]Stan.Z.Li and J.Lu,“Modeling Bayesian estimation for de-formable contours,”in Proceedings of 7th IEEE International Conference on Computer Vision,Kerkyra,Greece.,1999,pp.991–996.[6] B.Moghaddam and A.Pentland,“Probabilistic visual

learninig for object representation,”IEEE Transactions on Pattern Analysis and Machine Intelligence ,vol.19,no.7,pp.696–710,1997.[7]H.H.S.Ip and D.Shen,“An af?ne-invariant active contour

model (AI-Snake)for model-based segmentation,”Image and Vision Computing ,vol.16,no.2,pp.125–146,1998.[8] A.L.Yuille,P.W.Hallinan,and D.S.Cohen,“Feature extrac-tion from faces using deformable templates,”International Journal of Computer Vision ,vol.8,no.2,pp.99–111,1992.

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4.对图像text.png中的字母a完成特征识别操作。

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图1.3-1图像窗口连接 图1.3-2图像连接后显示 1.4.图像格式转换(自行定义转入转出格式) 点击Display #1窗口上的file中的Save Image As,然后选择Image File弹出图1.4-1所示窗口,在Output File Type中即可选择图像要转换成的格式。

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