·462· 智能系统学报 第3卷 the facial expression algorithm is given in Fig 4. Input:Geometric feature sample of facial exp ression x' Training set T=(x,)(x)(x.y),where x,ER,x,is the i-th geometric feature,y=(1,2.3,4.5.6/,y,is the facial expression classifications Number of nearest neighbors k Output:facial expression classifications=1.2.3.4.5.6 1.Find k samples (x.y)with m inmal values ofk(x.x)-2k (x.x,), 2 Train an modified multi-class SVM model on the k selected samples,the modified SVM model incorporates the neighborhood infomation, 3. Classify x,using this model,get the result, 4.retum y Fig 4 The LSVM classifier for facial expression recognition The LSVM makes binary decisions There are a and surprise).Each video sequence starts with a neu- number of methods for making multi-class decisions tral expresson and ends with the peak of the facial ex- with a set of binary classifiers We emp byed pairwise pression This database is annotated with AUs(Action partitioning strategies For pairwise partitioning (1: Units).These combinations ofAUswere translated in- 1),the SVM were trained to discrmn inate all pairs of to facial expressions according Ref [24],in order emotions For six categories that makes 15 SVMs to define the corresponding ground truth for the facial expressions All the subjects were used to fom the da- 4 Exper in en ts and eva lua tions tabase for the experments The database contains 480 In order to validate our proposed app oach for fa- video sequences,containing 84 exp ressons of"fear", cial exp ression recognition,we carried out experments l05of“surprise”,92of“sadness'”,36of“anger'”, on a machine with a Pentium 4/2 0G CPU,IGB 56of“disgust”and107of“happ iness”The upper memory,W indowsXP,and Visual C++60 The row of Fig 5 shows the extraction of facial feature Cohn-Kanade database2s was used to recognize facial points in the initial frames in the video sequences for expression as one of the six basic facial expression the 6 basic exp ression types,while the lower row shows classes anger,disgust,fear,happ iness,sadness, that of the last frames of those video sequences (a)happy (b)disgust (c)fear (d)sad (e)anger (f)surprise Fig 5 ASM based facial feature points extraction examples In our experments,three classification algo-ness Both KNN-SVM and LSVM emply a linear ker rithms,KNN,nonlinear SVM and SVMNN were com- nel The parameters of the classification algorithm,i pared with our LSVM classifier to show its effective- e the k in KNN,c in SVM,bandwidthA in the RBF 1994-2009 China Academic Journal Electronie Publishing House.All rights reserved.http://www.cnki.netthe facial exp ression algorithm is given in Fig. 4. Input: Geometric feature samp le of facial exp ression x′ Training set: T = { ( x1 , y1 ) , ( x2 , y2 ) , …, ( xn , yn ) } , where xi ∈R d , xi is the i2th geometric feature, yi = { 1, 2, 3, 4, 5, 6}, yi is the facial exp ression classifications. Number of nearest neighbors k. Output: facial exp ression classifications yp = { 1, 2, 3, 4, 5, 6} 1. Find k samp les ( xi , yi ) with m inimal values of k ( xi , xi ) - 2k ( x, xi ) , 2. Train an modified multi2class SVM model on the k selected samp les, the modified SVM model incorporates the neighborhood information, 3. Classify xi using this model, get the result yp , 4. return yp . Fig. 4 The LSVM classifier for facial exp ression recognition The LSVM makes binary decisions. There are a number of methods for making multi2class decisions with a set of binary classifiers. W e emp loyed pair2wise partitioning strategies. For pair2wise partitioning ( 1: 1) , the SVM were trained to discrim inate all pairs of emotions. For six categories that makes 15 SVM s. 4 Exper im en ts and eva lua tion s In order to validate our p roposed app roach for fa2 cial exp ression recognition, we carried out experiments on a machine with a Pentium 4 /2. 0G CPU, 1GB memory, W indowsXP, and V isual C + + 6. 0. The Cohn2Kanade database [ 23 ] was used to recognize facial exp ression as one of the six basic facial exp ression classes ( anger, disgust, fear, happ iness, sadness, and surp rise). Each video sequence starts with a neu2 tral exp ression and ends with the peak of the facial ex2 p ression. This database is annotated with AU s (Action Units). These combinations of AU s were translated in2 to facial exp ressions according to Ref. [ 24 ], in order to define the corresponding ground truth for the facial exp ressions. A ll the subjectswere used to form the da2 tabase for the experiments. The database contains 480 video sequences, containing 84 exp ressions of“fear”, 105 of“surp rise”, 92 of“sadness”, 36 of“anger”, 56 of“disgust”and 107 of“happ iness”. The upper row of Fig. 5 shows the extraction of facial feature points in the initial frames in the video sequences for the 6 basic exp ression types, while the lower row shows that of the last frames of those video sequences. Fig. 5 ASM based facial feature points extraction examp les In our experiments, three classification algo2 rithm s, KNN, nonlinear SVM and SVM2NN were com2 pared with our LSVM classifier to show its effective2 ness. Both KNN2SVM and LSVM emp loy a linear ker2 nel. The parameters of the classification algorithm, i. e. the k in KNN, c in SVM, bandwidthλin the RBF ·462· 智 能 系 统 学 报 第 3卷