画像の認識 理解シンポジウム (MIRU2006) 2006 年 7 月 y y y y 153-8505 4-6-1 E-mail: yfonoy,takahiro,ysatog@iisu-tokyoacjp N SVD Gaze Estimation from Low Resolution Images Consideration of Appearance Variations due to Identity by Using Kernel-based Multilinear Models Yasuhiro ONO y, Takahiro OKABE y, and Yoichi SATO y y Institute ofindustrial Science, The University oftokyo 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8505 JAPAN E-mail: yfonoy,takahiro,ysatog@iisu-tokyoacjp Abstract We propose an appearance-based method for estimating gaze directions from low resolution images Positioning errors of eye regions and appearance variations due to changes in identity may seriously degrade the accuracy of gaze estimation To improve the accuracy, we consider a nonlinear relationship between eye images and the feature vectors for each mode, for example, gaze direction and identity Thus, we introduce the use of kernel-based multilinear models We prepare a set of training images with various gaze directions and positioning errors from a few people The training images are mapped into a high dimensional space via a nonlinear mapping In the space, feature vectors for gaze direction are extracted We describe our method and report experimental results demonstrating the merit of our method Key words gaze estimation,low resolution,appearance-based method,identity,nonlinear N-mode SVD 1 595
[2], [3], [8], [20] [4] [6], [18] [1], [11], [19] [13] [10] N SVD PCA N SVD Vasilescu Vasilescu N SVD [14] [17] Y Li [7] Y Li N SVD [12] 2,,,,, 596
2 1 N SVD N SVD [14] N SVD N,, 4 SVD i(1< = i< = I) j(1< = j< = J) k(1< = k< = K) l(1< = l< = L) 4 Z2< I J K L (Z) ijkl N SVD Z Z = ^D 1 ^UG 2 ^UPOS 3 ^UP ^D ^UG, ^UPOS, ^UP 2 2 N SVD N SVD Y Li N SVD [7] N SVD Z F Φ Φ(Z):= W2< I J K M (M > L) W W = D 1 UG 2 UPOS 3 UP F UG, UPOS, UP D2< I J K M D = W 1 U T G 2 U T POS 3 U T P (1) 4 W 2 6 4 W (G) = Φ(z 111 ) T ::: Φ(z 11K ) T ::: Φ(z 1J1 ) T ::: Φ(z 1JK ) T Φ(z 211 ) T ::: Φ(z 21K ) T ::: Φ(z 2J1 ) T ::: Φ(z 2JK ) T Φ(z I11 ) T ::: Φ(z I1K ) T ::: Φ(z IJ1 ) T ::: Φ(z IJK ) T z ijk 2< L i j k 3 7 5 Φ(z ijk )2< M Φ z ijk F BG2< I I BG : = (W (G) )(W (G) ) T T T = (UG± GVG )(UG± GVG ) T = UG± 2 G U G T 2< I I (2) Φ BG JX (B G)m;n = KX Φ(z mjk ) Φ(z njk )= JX KX k(z mjk ; z njk ) j=1 k=1 j=1 k=1 (2) (3) UG N SVD UG i(1< = i< = I) u i G UG T =[u 1 G; u 2 G; :::; u I G] UPOS UP 2 3 (1) (2) (1) PC (2) (2) (3) UG k(z mjk ; z npq )=exp kz mjk z npq k =c 2 2< 2 4 (1), (2), (3), (1), (2) [12] Z test 2< 1 1 1 L F Φ(Z test )2< 1 1 1 M N SVD Φ(Z test ) P (G) m = I P J P K i=1 j=1 k=1 D ijkm(u G)i(uPOS)j(uP )k Φ(Z test ) (G) 2< 1 M 4 Φ(Z test )2< 1 1 1 M A (n) 2< In (I 1I 2 :::I n1i n+1 :::I N ) N (3) 597
A2< I 1 I 2 ::: I N n ug2< I, upos2< J, up 2< K F f(ug; upos; up ) f(ug; upos; up ):= ψ Φ(Z test ) (G) m MX m=1 IX (ug; upos; up )= JX KX i=1 j=1 k=1 arg minu G 2< I ;u POS 2< J ;u P 2< K f(ug; upos; up ) (ug; upos; up ) (4) ug, upos, up (4) f 1 @f=@(u G)i =0 (1 < = i< = I) ; (5) @f=@(u POS)j =0 (1 < = j< = J) ; (6) @f=@(u P )k =0 (1< = k< = K) : (7) UG, UPOS, UP g, o, p (TG) (G) Φ(z test )2< I Φ (T G)(G) (T G)(G) = P T i;j J P K P J P K onpmo n=1 m=1 l=1 k=1 lp k k(z inm ; z jlk ), (TG)(G) Φ(z test ) i = P J j=1 P K k=1 ojp kk(z ijk ; z test )! 2 Dijkm(u G)i(uPOS)j(uP )k (4) (3), i (1)= arg min i2f1;2;:::;ig kug u i Gk 2 u i(1) G i(1) 2 3 u i(2) G, ui(3) G, P 3 ffl = kug p=1 wpui(p) P G k2 3 p=1 wp =1 0 < = w p < = 1(p =1; 2; 3) P 3 g = wpg(p) p=1 g g(p)(1< = p< = 3) u i(p) G 3 2 g := UGuG; o := UPOSuPOS; p := UP up (8) 4 T G2< I 1 1 M T G := W 2 o T 3 p T (9) z test 2< L Φ(Z test ) (G) Φ(Z test ) (G) = Φ z test T 2< 1 M (10) (1), (4), (8), (9), (10) (5) ug ug = U T G T + test (TG) (G) Φ(z ) = UG T T 1 (TG) (G) (TG) (G) (TG)(G) Φ(z test ) (11) (TG) (G) 4 T G M + + T I I (11) (TG) (G) (TG) (G) 2< 3 1,, [9], 3 2 3 IEEE1394 (Point Grey Research Flea) 3 1, 10 5 10, 1280 1024 18 50cm, 598
1 LCD Fig 1 Alayout of targets displayed on the surface on an LCD monitor: circles for training and crosses for test 2 (a), (b),(c),(d) Fig 2 (a)candidates of eye corners (b),(c),(d)a schematic diagram of segmented eye images 3 2 (1) (2) (3) (1), (2) (1) 1 1, 20, 1 32 144 144 (2), (144 144 ), (144 144 ) 36 36, [9] ( 2 ) 1 ( 2 ), 2 (b),(c),(d) 12 4=48, 25,,,, 3 :(a), (b) Fig 3 Examples of training images for (a)different gaze points and (b)different segmentations, 20 20 25 20 25 = 500 32 32 25 = 800, 3 3(a),,, 3(b) 3 3 N SVD N SVD (1) 0 9 4( ) 4( ) 0 4 5 9 10 4( ) 4 (2) 5 10 5 5 4 599
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