11) 13) 11),12) 13) Y c Z c Image plane Y m iy O m Z m Marker coordinate system T, d X m f O c X c Camera coordinate system 1 Coordinates and problem

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1 1 1 1 Posture Esimation by Using 2-D Fourier Transform Yuya Ono, 1 Yoshio Iwai 1 and Hiroshi Ishiguro 1 Recently, research fields of augmented reality and robot navigation are actively investigated. Estimating a relative posture between an object and a camera is an import task in these fields. In this paper, we propose a novel method for posture estimation by using 2-D Fourier Transform. The markers are embedded in an object s texture in the high frequency domain. We observe the change of spatial frequency of the object texture to estimate a current posture of the object. We conduct experiments to show the effectiveness of our method. 1. CG 1 Graduate School of Engineering Science, Osaka University 1) 2) 3),4) 5) 13) GPS 3) GPS (INS) GPS INS 4) 5) Lepetit 6) 7),8) 7) 8) 9),10) 1 c2010 Information Processing Society of Japan

2 11) 13) 11),12) 13) Y c Z c Image plane Y m iy O m Z m Marker coordinate system T, d X m f O c X c Camera coordinate system 1 Coordinates and problem settings iz ix 2. x, y, z X c,y c,z c O m X m,y m Z m 1 T X m,y m,z m θ x,θ y,θ z X m Y m Z m (θ x = θ y = θ z =0[deg]) θ x,θ y,θ z d Overview of marker embedding 14) 16) 2 c2010 Information Processing Society of Japan

3 Features in the frequency domain 5 Power spectrum 6 Estimation result Input Image Low-cut Filter Binarization Marker Detection Parameter Estimation 3.

3 3 Features in the frequency domain 5 Power spectrum 6 Estimation result Input Image Low-cut Filter Binarization Marker Detection Parameter Estimation Process flows of parameter estimation α, β, θ 1 α, β γ = α/β θ 2 5 α, β, γ, θ 1,θ 2 ( 3) (1) a, b, c, f, g, h α, β, θ 1 Q 2 =(a x 2 + b y 2 + c +2f x +2g y +2h xy) (1) θ 2 θ 1 0 s(θ) s 1(θ) s 2(θ) θ 2 (2) 2π θ 2 =argmax s 1(θ +Δθ) s 2(θ)dθ (2) Δθ (θ x,θ y,θ z,d) (α, β, γ, θ 1,θ 2) Kernel Support Vector Regression (SVR) 17) Kernel K SVR D w i (i =1 D) b (3) D y = f(x) = w ik(x i, x)+b (3) i=1 K (4) s, o, d K(x, y) =(s x T y + o) d (4) SVR w i (3) θ x,θ y,θ z α, β, γ, θ 1,θ 2 α, β θ x,θ y,θ z γ,θ 1,θ 2 3 c2010 Information Processing Society of Japan

4 1 Training data Training data range of posture Set1 θ x [0, 60],θ y [0, 60],θ z [0, 60] Set2 θ x [0, 60],θ y [0, 60],θ z [ 60, 0] Set3 θ x [0, 60],θ y [ 60, 0],θ z [0, 60] Set4 θ x [0, 60],θ y [ 60, 0],θ z [ 60, 0] k d 1,α 1 d 2,α 2 7 Training error α 1 α 2 = k d1 d 2 (5) 4. (α, β, γ, θ 1,θ 2) (θ x,θ y,θ z) SVR (θ x,θ y,θ z,d) 7 1 (θ x,t 1,θ y,t 1,θ z,t 1) (Δθ x, Δθ y, Δθ z) (γ,θ 1,θ 2,θ x,t 1,θ y,t 1,θ z,t 1) SVR 5. SVR SVR w i, (d, s, o) 3000[mm] θ x,θ y,θ z {0, 10, 20,...,50, 60} [deg] (d, s, o) d s = o =1 d 8,9 θ x,θ y,θ z SVR d =5 SVR d =4 w i SVR , 11, 12, 13 θ x,θ y,θ z d 2 θ x,θ y,θ z γ,θ 1,θ 2 4 c2010 Information Processing Society of Japan

5 2 Mean square errors of estimation results Parameters θ x θ y θ z d Mean square error 1.8 [deg] 1.5 [deg] 0.7 [deg] [mm] 8 Training errors of θ x,θ y,θ z 9 Training error of d 14 Estimation errors with varying the distance 15 Estimation errors with varying the distance 10 Estimation results of θ x 11 Estimation results θ y 12 Estimation results of θ z 13 Estimation results of d θ x,θ y,θ z d 15 k [mm] ±50 [mm] 4000 [mm] ±100[mm] B [mm] 3 17,18, c2010 Information Processing Society of Japan

device size 3 focal length image size Camera specification FOVEON X3 (CMOS) 20.7 13.

6 device size 3 focal length image size Camera specification FOVEON X3 (CMOS) [mm] 200 [mm] [pixels] 19 Estimation results of θ z 20 Estimation results of distance 16 Wallpaperusedinthisexperiment 4 Evaluation of estimation results in real images parameter θ x θ y θ z d mean square error 11.0 [deg] 9.2 [deg] 0.6 [deg] [mm] 5 Estimation error 17 Estimation results of θ x 18 Estimation results of θ y parameter mean square error [deg] θ x 16.0 θ y 17.6 θ z 1.1 θ x,θ y,θ z ±3.3 [deg] d ± [mm] Train.1 Train.4 5 θ x,θ y [ 60, 60],θ z [ 180, 180] SVR 21,22, 23 θ x,θ y,θ z 9.5, 6.9, 5.2 [deg] 24,25,26 27,28 γ,θ 1,θ Train.1 Train.4 29 x y 6 c2010 Information Processing Society of Japan

21 estimation results of θ x 22 estimation results of θ y 27 (θ x,θ y,θ z)=(20, 30, 40) 28 (θ x,θ y,θ z)=( 20, 30, 40) 6 Frobenius norms of estimation results simulation real scene R true R f 0.

7 21 estimation results of θ x 22 estimation results of θ y 27 (θ x,θ y,θ z)=(20, 30, 40) 28 (θ x,θ y,θ z)=( 20, 30, 40) 6 Frobenius norms of estimation results simulation real scene R true R f estimation results of θ z 24 estimation results of θ y 7 Prediction values of estimation errors estimation parameter θ x θ y θ z mean square error 24.8 [deg] 27.3 [deg] 1.8 [deg] 25 estimation results of θ y 26 estimation results of θ z ( 29(a)) ( 29(b)) R true R 6 m m = 1.55 (6) e mse E =(1 cos( e mse)) (7) m e e = arccos(1 m E) (8) 7 7 c2010 Information Processing Society of Japan

(a) initial position 29 6. examples of posture estimation results (b) after rotation 1) Zhou, F., Duh, H. B.-L. and Billinghurst, M.

572, pp.37 42 (2005). 4) Vol.106, No.535, pp.5 10 (2007). 5) Vol.10, No.3, pp.285 294 (2005). 6) Lepetit, V., Vacchetti, L., Thalmann, D. and Fua, P.

8 (a) initial position examples of posture estimation results (b) after rotation 1) Zhou, F., Duh, H. B.-L. and Billinghurst, M.: Trends in Augmented Reality Tracking, Interaction and Display: A Review of Ten Years of ISMAR, Proc. ISMAR, pp (2008). 2) Vol.20, No.5, pp (2002). 3) RTK-GPS. PRMU Vol.104, No.572, pp (2005). 4) Vol.106, No.535, pp.5 10 (2007). 5) Vol.10, No.3, pp (2005). 6) Lepetit, V., Vacchetti, L., Thalmann, D. and Fua, P.: Fully Automated and Stable Registration for Augmented Reality Applications, Proc. 2nd IEEE/ACM Int. Symp. on Mixed and Augmented Reality, pp (2003). 7) Billinghurst, M. Vol.4, No.4, pp (1999). 8) PC IE Vol.103, No.643, pp (2004). 9) Vol.13, No.2, pp (2008). 10) Park, H. and Park, J.-I.: Invisible Marker Tracking for AR, Proc. 3rd IEEE/ACM Int. Symp. on Mixd and Augmented Reality, pp (2004). 11) ( ) CVIM Vol.107, No.427, pp (2008). 12) Vol.14, No.3, pp (2009). 13) MVE Vol.106, No.91, pp.1 6 (2006). 14) Witkin, A.P.: Recovering Surface Shape and Orientaion from Texture, Artificial Intelligence, Vol.17, pp (1981). 15) Toshio, T. and Yasuo, Y.: Estimation of Rotation and Slant Angles of a Textured Plane Using Spectral Moments, IEICE Trans. on information and systems, Vol.85, No.3, p.600 (2002). 16) Super, B.J. and Bovik, A.C.: Planar surface orientation from texture spatial frequencies, Pattern Recognition, Vol.28, No.5, pp (1995). 17) Smola, A.J., Schölkopf, B. and Olkopf, B.S.: A tutorial on support vector regression, Statistics and Computing, Vol.14, No.3, pp (2004). 8 c2010 Information Processing Society of Japan

IPSJ SIG Technical Report GPS LAN GPS LAN GPS LAN Location Identification by sphere image and hybrid sensing Takayuki Katahira, 1 Yoshio Iwai 1

IPSJ SIG Technical Report GPS LAN GPS LAN GPS LAN Location Identification by sphere image and hybrid sensing Takayuki Katahira, 1 Yoshio Iwai 1 1 1 1 GPS LAN GPS LAN GPS LAN Location Identification by sphere image and hybrid sensing Takayuki Katahira, 1 Yoshio Iwai 1 and Hiroshi Ishiguro 1 Self-location is very informative for wearable systems.