Estimating the Rotation of a Ball Using High Speed Camera

Transcription

1 Hough ICP 3DCG 3 6% 3% 6% Estimating the Rotation of a Ball Using High Speed Camera Hiroki Kamada, 1 Yoshinori Takeuchi, 2 Tetsuya Matsumoto, 1 Hiroaki Kudo 1 and Noburu Ohnishi 1 In table tennis, ball rotation is very important factor, since it effects ball trajectory and angle of reflection at impact. We propose a system which automatically estimates the ball rotation axis and rotation speed using high-speed camera. This system is composed of two modules ball detector and estimator of the ball rotation. The former explores the ball by applying sobel fillters and Hough transform for many edge points which make circular edge of the ball. Then, we use ball luminance information and center coordinates of detected circle to determine ball position. The latter determines corresponding point using Iterative Closest Point(ICP) algorithm and estimates rotation transform by singular value decomposition technique. We measured the performance of this system by using 3DCG animation.the mean error of the rotation axis is 3 degrees. The mean error of the rotation speed is 6%. 1. 1) [rps] 2) Hubert 3) 4) 1 Graduated School of Information Science Nagoya University 2 Information and Communications Headquarters Nagoya University 1 c 2012 Information Processing Society of Japan

2 Hough Lucas-Kanade LK 5) 2 LK 1 Hough 1 1 ICP [mm] Hough 6),7) 6),8) Hough C ki = (c x, c y, r) k i k (c x, c y ) r Hough 2 1 Fig. 1 Overview of the system Hough 2 Fig. 2 Result of ball candidate detection ( 1 ) 5 5 C l,0, C l,1,..., C l,ml L 0, L 1,..., L Ml l 2 c 2012 Information Processing Society of Japan

3 l = 5n + 1 (n = 0, 1, 2,...), M l l l = 1 1 ( 2 ) k (l + 1 k l + 4) C k,0, C k,1,..., C k,mk ( a ) k 1 L m C k,m D M m M M k 1 ( b ) D L m D L m C k,m D C k,m L M (M = M + 1) ( c ) (a) (b) 5 3. ( 3 ) 3 3. ( a ) 3 ( b ) a,b ( c ) a b. a b 0 a b < 0 (a) 3 ( 4 ) l = 1 AL m 0 m M M l = 1 ( 5 ). ( a ) AL m D ( b ) D AL m D AL m D AL M (M = M + 1) ( 6 ) 3. Iterative Closest Point ICP 9) SIFT 20[mm] 1 ICP 2 X,Y ICP ( 1 ) X x i Y y i ( 2 ) Y (RX + t) R t Y RX R R Singular Value Decomposition, SVD 10) 13) 3 ( 1 ) k, k + 1 A, B ( 2 ) A B ( 3 ) A B D ( 4 ) D,(7) ( 5 ) AB T SVD R ( 6 ) R A = RA A (2) ( 7 ) R k, k + 1 u α 3 c 2012 Information Processing Society of Japan

4 4 CG Fig. 4 Image of CG animation 5 Fig. 5 θ ϕ θ and ϕ CG Blender 14) 7 50[rps] 2000fps Fig. 3 Flow chart of the estimation of the ball rotation u = (r 32 r 23, r 13 r 31, r 21 r 12) α = cos 1 ((tr(r) 1)/2) ( 8 ) (1) (7) N-1 k 60% k+1 80% 4. CG CG 7 20mm [pixels] 4 4 CG θ ϕ 5 θ y x z x z P ϕ OP x 50[rps] 2 ϕ, θ [rps] 6.2% [rps] 1 3% 3% c 2012 Information Processing Society of Japan

5 1 3 Table 1 Rotation axis of the ball of CG Table 3 The comparison of each method x y z [ ] [ ] A B C D E F G Table 2 The error between ground truth and estimated value [rps] x y z [ ] [ ] A B C D E F G [ ] [rps] x y z ϕ θ (a) (b) (c) (a) 1 Table 4 A part of coordinates of corresponding point in first frame obtained by method(a) A B R t A (A) (R ta) (B) ( B R ta ) x y z x y z x y z B 3 (a) (c) (a). R t k A k + 1 B (b). R t ICP ICP (c). ICP ICP (c) 3 (a) R t A (a) 1 A R ta B 4 4 B R t A A a c 7 (a) (c) c 2012 Information Processing Society of Japan

6 Fig. 6 Difference of edge points between 13th frame and 14th frame Fig. 9 [1] (a) [2] (c) 9 9 Distance between corresponding points of many-to-one in 9th frame a c 7 (a) (c) [1] (a) [2] (c) Fig. 7 Difference of corresponding point between method (a) and (c) Fig. 10 Distance between corresponding points of many-to-one in 13th frame (a) (c) (a) 9 13 (a) Fig. 8 Error due to many-to-one correspondence ICP 8 9 9[1],10[1] (c) 0.5 9[2],10[2] (b) (c) ICP ICP 6 c 2012 Information Processing Society of Japan

7 Fig. 11 Many-to-one correspondence which dose Fig. 12 Many-to-one correspondence which cause not cause displacement of the center point displacement of the center point 13 Fig. 13 Shooting environment 14 Fig. 14 Example of real image ICP Vision Reserch Phantom V [fps] [pixels] 9.3[m] 13 KONICA MINOLTA CL-200 2,255[lx] 5 Pico 15) % 0.228% 5.60% 6. 2 Hough ICP 3DCG 3 6% 3% 7 c 2012 Information Processing Society of Japan

8 Table 5 5 Result of estimation of the ball rotation in real image [rps] [rps] % a A B b A B c A B d A B e A B f A B g A B h A B i A B ICP NPO JOC 1),,.. PRMU , pp , Nov ) (20) ) Hubert Shum and Taku Komura. Tracking the translational and rotational movement of the ball. Image Processing, Vol.3, pp , Sept ),,,,,,,.., pp , Nov ) B.D. Lucas and T.Kanade. An Iterative Image Registration Technique with an Application to Stereo Vision. Proc. of Int. Joint Conf. on Artificial Intelligence, pp , Aug ),.., ),. -,, -., ). - -., ) PaulJ. Besl and NeilD. McKay. A Method for Registration of 3-D Shapes. IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol.14, No.2, pp , Feb ),.., ) WilliamH. Press, SaulA. Teukolsky, WilliamT. Vetterling, and BrianP. Flannery. NUMERICAL RECIPES in C[ ] C., ),,,.., ).. SIP SIS , pp , Sept ) blender.jp. 15) Xration. 8 c 2012 Information Processing Society of Japan