a) Extraction of Similarities and Differences in Human Behavior Using Singular Value Decomposition Kenichi MISHIMA, Sayaka KANATA, Hiroaki NAKANISHI a

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1 a) Extraction of Similarities and Differences in Human Behavior Using Singular Value Decomposition Kenichi MISHIMA, Sayaka KANATA, Hiroaki NAKANISHI a), Tetsuo SAWARAGI, and Yukio HORIGUCHI 1. Johansson [1] Cutting [2], [3] Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto-shi, Japan a) [4] [5], [6] [7] A Vol. J94 A No. 4 pp c

2 2011/4 Vol. J94 A No. 4 Troje [8], [9] 2 (1) (2) [5] [9] quaternion [10] quaternion 1 z x y (1) z ψ (2) (1) y θ (3) (2) x φ φ, θ, ψ θ ±1/2π φ ψ quaternion Fig. 1 1 Definition of reference frame and human skeleton model. 294

3 quaternion q v q s r ξ quaternion ( ) q q = v r sin ξ = 2 q s cos ξ (1) 2 quaternion q q =1 (2) (2) quaternion 2. 2 α x α p R N (p =1, 2,,S) X α X α =(x α 1, x α 2, x α S) (3) N S 3 quaternion 4 X α [11] X α x α p (4) a α α a α = ({x ) α 1 } T {x α 2 } T {x α S} T T (4) M a α (α = 1, 2,,M) D(S N M) ( ) D = a 1 a 2 a M (5) rankd M rankd < M rankd = M a α a a a D 1 (λ 1a λ 2a λ M a ) a a D D D = UΣV T (6) Σ σ i(i =1, 2,,M) σ 1 σ 2...σ M 0 U u i R S N V v i R M i i α a α a α = M σ iv αiu i (7) i v αi i v i α (7) α a α u i σ i v αi σ i 295

4 2011/4 Vol. J94 A No. 4 u i v i v αi i α D 1 v α1 D 2 v αi(i 2) 2. 3 (7) 1 a 1st a 1st = σ 1v 1stu 1 (8) v 1st v 1 i i a i,p a i,n a i,p = σ 1v 1stu 1 + σ iv i,pu i (9) a i,n = σ 1v 1stu 1 + σ iv i,nu i (10) v i,p > 0,v i,n < 0 (11) (8) (9) (10) quaternion (8) (9) (10) a 1st, a i,p, a i,n quaternion (2) quaternion p t quaternion q p(t) quaternion q p(t) q p (t) = q p(t) q p (t) (12) u i 4. quaternion 1 3. Xsens MTx

20 (m) 1 2(kg) 3 M M =15 20 11 20 2 30 1 40 1 20 13 30 1 40 1 100 (Hz) N N = 115 50 (Hz) N N = 102 2 Fig. 2 Position of sensors in experiments. 4. 4. 1 S S =14 3=42 0 1 (4) a α (5) D quaternion S =14 4=56 quaternion 1 4.

5 20 (m) 1 2(kg) 3 M M = (Hz) N N = (Hz) N N = Fig. 2 Position of sensors in experiments S S =14 3= (4) a α (5) D quaternion S =14 4=56 quaternion σ i v αi 1 v αi Fig. 3 Sensor setting on an subject s body. 4 Fig. 4 Singular value of each mode (walking). 297

6 2011/4 Vol. J94 A No. 4 1 v i 1 2 Table 1 Value of right singular vector v i for each subject (walking): while contributive values of 1st mode were almost same, ones of higher modes were different for different subjects. Fig. 5 5 Tree structure of motion constructed by extracted similarities and differences (walking) v αi 5 v αi (positive) (negative) (zero) u i 6(b)

7 (a) roll (a) roll (b) pitch (b) pitch Fig. 6 (c) yaw 6 1 Characteristic motion of 1st mode (walking). Fig. 7 (c) yaw 7 2 Characteristic motion of 2nd mode (walking) (a) (c) 7(a) (c)

8 2011/4 Vol. J94 A No. 4 Fig Characteristic motion of 1st mode (loading). 9 Fig. 9 2 Characteristic motion of 2nd mode positive (loading). 10 Fig Characteristic motion of 2nd mode negative (loading)

9 % 70% S 9 80% S 100% 10 80% S 80% 100% (19GS0208) [1] G. Johansson, Visual perception of biological motion and a model for its analysis, Perception and Psychophysics, vol.14, pp , [2] J.E. Cutting and L.T. Kozlowski, Recognizing friends by their walk: Gait perception without familiarity cues, Bulletin of the Psychonomic Society, vol.9, pp , [3] L.T. Kozlowski and J.E. Cutting, Recognizing the sex of the walker from a dynamic point-light display, Perception and Psychophysics, vol.21, no.6, pp , [4] S. Runeson and G. Frykholm, Visual perception of lifted weight, J. Experimental Psychology: Human Perception and Performance, vol.7, no.4, pp , [5] M.S. Nixon and J.N. Carter, Automatic recognition by gait, Proc. IEEE, vol.94, no.11, pp , [6] J.E. Boyd and J.J. Little, Biometric gait recognition, Lect. Notes Comput. Sci., vol.3161, pp.19 42, [7] D vol.j92-d, no.8, pp , Aug [8] N.F. Troje, The little difference: Fourier-based synthesis of gender-specific biological motion, in Dynamic Perception, ed. R. Wurtz, and M. Lappe, pp , Aka Press, Berlin, [9] N.F. Troje, Retrieving information from human movement patterns, in Understanding Events: How Humans See, Represent, and Act on Events, ed. T.F. Shipley, and J.M. Zacks, pp , Oxford University Press, New York, [10] J.R. Wertz, Spacecraft Attitude Determination and Control, Kluwer Academic Pub., [11] 301

10 2011/4 Vol. J94 A No. 4 vol.22, no.8, pp , IEEE IEEE

1 Fig. 1 Extraction of motion,.,,, 4,,, 3., 1, 2. 2.,. CHLAC,. 2.1,. (256 ).,., CHLAC. CHLAC, HLAC. 2.3 (HLAC ) r,.,. HLAC. N. 2 HLAC Fig. 2

1 Fig. 1 Extraction of motion,.,,, 4,,, 3., 1, 2. 2.,. CHLAC,. 2.1,. (256 ).,., CHLAC. CHLAC, HLAC. 2.3 (HLAC ) r,.,. HLAC. N. 2 HLAC Fig. 2 CHLAC 1 2 3 3,. (CHLAC), 1).,.,, CHLAC,.,. Suspicious Behavior Detection based on CHLAC Method Hideaki Imanishi, 1 Toyohiro Hayashi, 2 Shuichi Enokida 3 and Toshiaki Ejima 3 We have proposed a method for