Gaze Estimation from Low Resolution Images Insensitive to Segmentation Error

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Ἐλισάβετ Λαύρα Βιλαέτης
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1 (MIRU2005) {onoy,takahiro,ysato}@iis.u-tokyo.ac.jp appearance-based methods SVDSingular Value Decomposition N-mode SVD N-mode SVD, PCAPrincipal Component Analysis appearance-based method, N-modeSVD Gaze Estimation from Low Resolution Images Insensitive to Segmentation Error Yasuhiro ONO, Takahiro OKABE, and Yoichi SATO Institute of Indusctiral Science, The University of Tokyo 4 6 1, Meguro-ku, Tokyo, Japan {onoy,takahiro,ysato}@iis.u-tokyo.ac.jp Abstract We propose an appearance-based method for estimating gaze directions from low resolution images. In estimation of gaze directions from low resolution images, there exist inevitable errors in segmentation of eye regions. To improve the accuracy of gaze estimation, two key ideas are introduced in our method: using a set of training images of eye regions with artificially added segmentation error, and using N-mode singular value decomposition in order to treat image variation due to different gaze directions and segmentation errors separately. In this paper, we describe the details of our proposed method and report experimental results demonstrating the advantage of our method over the conventional PCA-based method. Key words gaze estimationlow resolutionappearance-based methodsegmentation, N-mode SVD 1.,, model-based methods appearance-based methods model-based methods [2], [3], [7], [17] [4], [5], [15] 96

2 model-based methods 3 model-based methods appearance-based methods [1], [9], [16] [10] 3 appearance-based methods Appearance-based methods [6], N-mode SVD [11][14] SVDSingular Value Decomposition N-mode SVD Vasilescu N-mode SVD [12] N-mode SVD PCAPrincipal Component Analysis 2 N-mode SVD ,,, N-mode SVD [11],,,,,,, N-mode SVD, 2. 1 N-mode SVD N-mode SVD [11] N-mode SVD N,,,,, 3-mode SVD ,,, D ijk i(1< = i< = I),j(1< = j< = J),k(1< = k< = K), 97

3 , ,, SVD SVD, 2, i(1< = i< = I) j(1< = j< = J) 2 D ij, D ij D ij = U gazeσv pixel SVD, U gaze V pixel 3-mode SVD 3 D ijk SVD,, SVD, D ijk,,, i D i(kj) (gaze) R I KJ D i(kj) (gaze) =[D ij1, D ij2, D ij3,..., D ijk] (1) D ij1, D ij2, D ij3,..., D ijk D ijk () (A 1) (A 2) D ijk SVD D i(kj) (gaze) SVD D i(kj) (gaze) =U gazeσ gazev gaze (2) [ def U gaze = u (1) gaze, u (2) gaze, u (3) gaze u (I) gaze u (i) gaze R I (1< = i< = I),u (i) gaze,u gaze u (j) cut R J (1< = j< = J) u (k) pixel RK (1< = k< = K) () (A 4) (A 6) ] (3) u (i) gaze, u (j) cut, u (k) pixel D ijk D ijk = I J K i=1 j=1 k=1 Z ijk u (i) gazeu (j) cutu (k) pixel (4) Z ijk R I J K D = Z U gaze U cut U pixel (5) Z = D Ugaze Ucut Upixel N-mode SVD, gaze(i)(1< = i< = I) c gaze(i) U gaze ( 2. ) U gaze def =[c gaze(1), c gaze(2), c gaze(3),..., c gaze(i) ] (6) gaze(i) cut(1< = cut< = J) d gaze(i),cut, c gaze(i) ( 2. ) c gaze(i) = ( B cut (gaze) ) 1 dgaze(i),cut (7), d gaze(i),cut ( B cut (gaze) ) 1, c gaze(i) PC 2, D ijk, (1), D i(kj) (gaze) (2) (6) c gaze(i). 3 (A 14) ( Bcut (gaze) ) 1 (0 < = cut< = J) ( B cut (gaze) ) 1 ( ) = D 1 cut (gaze) U gaze (8),

4 , , 2 m n d mn ( B cut (gaze) ) 1 cut(0< = j< = J) c m(cut) c m(cut) = ( B cut (gaze) ) 1 dmn (9) c m(cut) m m c m(cut) cut cut ( B cut (gaze) ) 1 3, gaze cut (gaze,cut) =arg min gaze,cut c m(cut) c gaze 2 (10) (gaze,cut) =(gaze(1),cut(1)) c gaze(1) gaze(1) c m(cut(1)), cut(1) cut(1) gaze(2),gaze(3) 2 3 c gaze(1), c gaze(2), c gaze(3) 3 3, 2 3 ɛ = c m(cut(1)) w ic gaze(i) 2 (11) i=1 3 wi< i=1 = 1 0 < = w i < = 1(i =1, 2, 3) g(test) 3 g(test) = w ig(i) (12) i=1 g(i)(0< = i< = I) 3 c gaze(i) ,, [8], IEEE1394 (Point Grey Research Flea) 3 1,, PC(OS: Windows XPCPU: Intel Pentium4 3.0GHz), cm, , 30, 1 50,

5 3 4 1 () () , ( ), ( ) ,, [8] 1 ( 3 ) ,, 2 81, ,,,, = = 4050, 5., 12 4=48. 5 x, y, 5,,., , c ( gaze(i) Bcut (gaze) ) 1., 2. 3 c m(cut). 3. 3,3-mode SVD,3-mode SVD PCA 3-mode SVD, ,2,3,

6 ,2,3,...., 7 x, y, z 3 3 7, mode SVD PCA =48,24 8 = 192,48 16 = 768 3, 8, 3-mode SVD PCA.,.,, PCA mode SVD PCA 9., ,3 6., 3-mode SVD PCA mode SVD PCA , , mode SVD PCA. 3-mode SVD PCA mode SVD PCA. 4. appearance-based methods,,,n-mode SVD N-mode SVD PCA, 101

7 C [1] S. Baluja and D. Pomerleau, Non-intrusive gaze tracking using artificial neural networks, CMU CS Technical Report, CMU-CS , [2] D. Beymer and M. Flickner, Eye Gaze Tracking Using an Active Stereo Head, In Proc. IEEE CVPR 2003, pp. II , [3] T. Hutchinson, K. White, JR., W. Martin, K. Reichert, and L. Frey, Human-Computer Interaction Using Eye-Gaze Input, IEEE Trans. SMAC, Vol. 19, No. 6, pp , [4] T. Ishikawa, S. Baker, I. Matthews, and T. Kanade, Passive Driver Gaze Tracking with Active Appearance Models, In Proc. WCITS 2004, [5] Y. Matsumoto and A. Zelinsky, An algorithm for real-time stereo vision implementation of head pose and gaze direction measurement, In Proc. IEEE FG 2000, pp , [6],,,,,, Vol. J64-D, No.3, pp , [7] T. Ohno and N. Mukawa, A Free-head, Simple Calibration, Gaze Tracking System That Enables Gaze-Based Interaction, In Proc. ACM ETRA 2004, pp , [8] Kenji Oka, Yoichi Sato, Yasuto Nakanishi, and Hideki Koike, Head pose estimation system based on particle filtering with adaptive diffusion control, In Proc. IAPR MVA 2005, pp , [9] R. Stiefelhagen, J. Yang, and A. Waibel, Tracking Eyes and Monitoring Eye Gaze, In Proc. WPUI, [10] K. Tan, D. Kriegman, and N. Ahuja, Appearance-based EyeGazeEstimation, InProc. IEEE WACV, pp , [11] M. A. O. Vasilescu and D. Terzopoulos, Multilinear Analysis of Image Ensembles: TensorFaces, In Proc. ECCV 2002, pp , [12] M. A. O. Vasilescu and D. Terzopoulos, Multilinear Image Analysis for Facial Recognition, In Proc. IAPR ICPR 2002, pp. II , [13] M. A. O. Vasilescu, Human Motion Signatures: Analysis, Synthesis, Recognition, In Proc. IAPR ICPR 2002, pp. III , [14] M. A. O. Vasilescu and D. Terzopoulos, TensorTextures: Multilinear Image-Based Rendering, In Proc. ACM SIG- GRAGH 2004, Vol. 23, No. 3, pp , [15] J. Wang, E. Sung, and R. Venkteswarlu, Eye gaze Estimation from a Single Image of One Eye, In Proc. IEEE ICCV 2003, pp. I , [16] L. Xu, D. Machin, and P. Sheppard, A Novel Approach to Real-time Non-intrusive Gaze Finding, In British Machine Vision Conference, [17] D. Yoo and M. Chung, Non-intrusive Eye Gaze Estimation without Knowledge of Eye Pose, In Proc. IEEE FG 2004, pp , D ijk D j(ik) (cut) =[D 1jk, D 2jk,..., D Ijk ] (A 1) D j(ik) (cut) R J IK 3 D ijk D k(ji) (pixel) =[D k1i, D k2i,..., D kji ] (A 2) D k(ji) (pixel) R K JI D j(ik) (cut) SVD D j(ik) (cut) =U cutσ cutv cut U cut = [ ] u (1) cut, u (2) cut, u (3) cut,..., u (J) cut (A 3) (A 4) u (j) cut R J U cut R J J D k(ji) (pixel) SVD D k(ji) (pixel) =U pixel Σ pixel V pixel U pixel = [ ] u (1) pixel, u(2) pixel, u(3) pixel,..., u(k) pixel (A 5) (A 6) u (k) pixel RK U pixel R K K 2. B B def = Z U cut U pixel (A 7) 3 D D = B U gaze D N N N N [11] D = Z U 1 U 2 U N (A 8) D n D(n) [11] D(n) =U nz(n)(u n+1 U n+2 U N U 1 U n 1), 3 D N =3,n=1 D(gaze) =U gazez(gaze)(u cut U pixel ) (A 10) = U gazeb(gaze) (A 11) D(gaze) (A 9) 102

8 D i(kj) (gaze) =[D ij1, D ij2,..., D ijk] (A 12) j = cut D ijk D i(k,cut) (gaze) =[D i,cut,1, D i,cut,2,..., D i,cut,k] (A 13) i ( J ) c i = j=1 cij /J 2. 3 D cut(gaze),b cut(gaze) j = cut B, (A 11), D cut(gaze) =U gazeb cut(gaze) (A 14), c gaze(i) R I (1< = i< = I) U gaze def =[c gaze(1), c gaze(2),..., c gaze(i) ] (A 15), d gaze(i),cut R K (1< = i< = I) D cut(gaze) def =[d gaze(1),cut, d gaze(2),cut,..., d gaze(i),cut ] (A 16), d gaze(i),cut, gaze(i), cut (A 15) (A 16), (A 14) c gaze(i) = ( B cut (gaze) ) 1 dgaze(i),cut (A 17), (B cut (gaze)) 1 gaze(i), cut d gaze(i),cut c gaze(i), c gaze(i), 2 1 c gaze(i) 2 (A 17) c gaze(i) 3. PCA PCA, i, j d ij D 1< = i< = I,1< = j< = J D =[d 1,1, d 2,1,..., d I,1, d 1,2, d 2,2,..., d I,2,..., d 1,J, d 2,J,..., d IJ] (A 18) D = UΣV U d ij c ij c ij = U d ij 103

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