The face recognition with expression and occlusion variation becomes the greatest challenge in biometric applications to recognize people. The proposed work concentrates on recognizing occlusion and seven kinds of exp...The face recognition with expression and occlusion variation becomes the greatest challenge in biometric applications to recognize people. The proposed work concentrates on recognizing occlusion and seven kinds of expression variations such as neutral, surprise, happy, sad, fear, disgust and angry. During enrollment process, principle component analysis (PCA) detects facial regions on the input image. The detected facial region is converted into fuzzy domain data to make decision during recognition process. The Haar wavelet transform extracts features from the detected facial regions. The Nested Hidden markov model is employed to train these features and each feature of face image is considered as states in a Markov chain to perform learning among the features. The maximum likelihood for the input image was estimated by using Baum Welch algorithm and these features were kept on database. During recognition process, the expression and occlusion varied face image is taken as the test image and maximum likelihood for test image is found by following same procedure done in enrollment process. The matching score between maximum likelihood of input image and test image is computed and it is utilized by fuzzy rule based method to decide whether the test image belongs to authorized or unauthorized. The proposed work was tested among several expression varied and occluded face images of JAFFE and AR datasets respectively.展开更多
For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergenc...For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE（max1≤k≤n｜Sk｜^1/q-∈bn^1/qp）^＋〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 （log n） ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.展开更多
Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n...Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n|≥εn^1p ),_~n≥1 1nP(|S_n|≥εn^1p ) and _~n≥1 (log n)δnP(|S_n|≥εnlogn) as ε0 are established.展开更多
Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n｜Sk｜,n≥1.Suppose limn→∞ESn^2/n=：σ^2〉0 and ∑n^∞=1 ρ^2/d...Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n｜Sk｜,n≥1.Suppose limn→∞ESn^2/n=：σ^2〉0 and ∑n^∞=1 ρ^2/d（2^n）〈∞,where d=2 if 1≤r〈2 and d〉r if r≥2.We prove that if E｜X｜^r 〈∞,for 1≤p〈2 and r〉p,then limε→0ε^2（r-p）/2-p ∑∞n=1 n^r/p-2 P{Mn≥εn^1/p}=2p/r-p ∑∞k=1（-1）^k/（2k＋1）^2（r-p）/（2-p）E｜Z｜^2（r-p）/2-p,where Z has a normal distribution with mean 0 and variance σ^2.展开更多
文摘The face recognition with expression and occlusion variation becomes the greatest challenge in biometric applications to recognize people. The proposed work concentrates on recognizing occlusion and seven kinds of expression variations such as neutral, surprise, happy, sad, fear, disgust and angry. During enrollment process, principle component analysis (PCA) detects facial regions on the input image. The detected facial region is converted into fuzzy domain data to make decision during recognition process. The Haar wavelet transform extracts features from the detected facial regions. The Nested Hidden markov model is employed to train these features and each feature of face image is considered as states in a Markov chain to perform learning among the features. The maximum likelihood for the input image was estimated by using Baum Welch algorithm and these features were kept on database. During recognition process, the expression and occlusion varied face image is taken as the test image and maximum likelihood for test image is found by following same procedure done in enrollment process. The matching score between maximum likelihood of input image and test image is computed and it is utilized by fuzzy rule based method to decide whether the test image belongs to authorized or unauthorized. The proposed work was tested among several expression varied and occluded face images of JAFFE and AR datasets respectively.
基金supported by National Natural Science Foundation of China (Grant No. 10871146)supported by Natural Sciences and Engineering Research Council of Canada
文摘For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE（max1≤k≤n｜Sk｜^1/q-∈bn^1/qp）^＋〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 （log n） ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.60273054) 高等院校博士学科点专项科研基金(the China Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20050270004)上海市教委科研基金(No.05DZ06) 。
文摘Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n|≥εn^1p ),_~n≥1 1nP(|S_n|≥εn^1p ) and _~n≥1 (log n)δnP(|S_n|≥εnlogn) as ε0 are established.
基金Research supported by Natural Science Foundation of China(No.10071072)
文摘Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n｜Sk｜,n≥1.Suppose limn→∞ESn^2/n=：σ^2〉0 and ∑n^∞=1 ρ^2/d（2^n）〈∞,where d=2 if 1≤r〈2 and d〉r if r≥2.We prove that if E｜X｜^r 〈∞,for 1≤p〈2 and r〉p,then limε→0ε^2（r-p）/2-p ∑∞n=1 n^r/p-2 P{Mn≥εn^1/p}=2p/r-p ∑∞k=1（-1）^k/（2k＋1）^2（r-p）/（2-p）E｜Z｜^2（r-p）/2-p,where Z has a normal distribution with mean 0 and variance σ^2.
