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
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 3. 3.1 2 2 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 3.2 4 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) 3.3 4 5 6 (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 0 3.4 (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
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 3 4 5.1 5.1.1 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 5.1.2 10, 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
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] 0.9 10 4 [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 14 0.1 θ x,θ y,θ z d 15 k 1.0 2000 [mm] ±50 [mm] 4000 [mm] ±100[mm] 5.1.3 16 B1 3000 [mm] 3 17,18, 19 20 4 5 c2010 Information Processing Society of Japan
device size 3 focal length image size Camera specification FOVEON X3 (CMOS) 20.7 13.8 [mm] 200 [mm] 2640 1760 [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] 5.1 10 4 [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 ±2.3 10 2 [mm] 5.2 5.2.1 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 2 5.2.2 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 0.959 10 2 1.49 10 2 23 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 1.49 10 2 m = 1.55 (6) 0.959 10 2 e mse E =(1 cos( e mse)) (7) m e e = arccos(1 m E) (8) 7 7 c2010 Information Processing Society of Japan
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