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2 i ( )

3 1 1 (Virtual Reality : VR) VR [1] VR VR VR [2][3] VR 3 SONY Play Station VR [4] Oculus VR Oculus Rift [5] VR VR VR [6] 2

4 1 2 [7] [8] Wang [9] Pamplona [10] ARToolKit ( AR ) (Inverse KInematic : IK) [11] 2 6 ( ) AR [12] [13] 4 1

5

6 4 2 [14] IP MP CM () ( ) 4 ( ) 0% 100% 4 0pt 400pt 2.1 ( 2.1) IP MP 1 CM 2 4 DIP PIP 1 MP

7 2 5 DIP PIP IP MP MP CM 2 自由度 1 自由度 2.1: () DIP PIP MP IP CM 2.1: ( [15] ) 2.2 i (i = 1 4) i = 1 i = 4 0 i DIP PIP [16] ( 2.2 ) PIP MP ( ) S [17] ( 2.2 )

8 2 6 IP MP ( 2.3 ) MP CM ( ) S ( 2.3 ) i MP [17] 2.1 MP ( ) θ i3 i MP ( ) θ i4 i MP ( ) { ( (θ i3 60.0)) θ i4 ( (θ i3 60.0)) (θ i3 60 ) 25 θ i4 25 (θ i3 < 60 ) (2.1) IP MP CM ( ) CM ( ) DIP PIP MP ( ) MP ( ) : DIP( 度 ) PIP( 度 ) PIP( 度 ) MP( 度 ) 2.2: i (DIP PIP PIP MP ( ) )

9 IP( 度 ) MP( 度 ) MP( 度 ) CM( 掌側内転 外転 )( 度 ) 2.3: (IP MP MP CM ( ) ) ( 2.4) 6 AR AR Cyclic-Coordinate Descent(CCD) [18] CCD 1 CCD 2.5 e g CCD 1. c e E c g G 2. 1 E G 3. c 2 () c b 1 4 b a

10 CCD damping () i F K i (θ i4, θ i3, θ i2 ) i DIP θ i1 PIP θ i2 f θi1 (θ i2 ) F K 0 (θ 04, θ 03, θ 02 ) IP θ 01 MP θ 02 f θ01 (θ 02 ) f θi1 (θ i2 ) f θ01 (θ 02 ) damping () DIP IP PIP θ i2 MP θ 02 f θi1 (θ i2 ) f θ01 (θ 02 ) DIP θ i1 IP θ 01 e G PIP MP damping f θi1 (θ i2 ) f θ01 (θ 02 ) 2.4:

11 2 9 e E c e E G c g b g b (1) ベクトル算出 a (2) 回転角算出 a e E c e E c b g (3) 回転角を加える a g 比較 b (4) 指先位置の更新判定 a e c E c g G b g e b (5) 注目関節を変更 a a (6)(1)~(5) をルートまで繰り返す 2.5: CCD 2.2

12 ( ( (mm)) 2 ) : ( (mm) (mm)) :

13 : 2.7: [14] 2.8 y x AR x y h max w max x y AR x 2 h1 h2 [14] 2.2 h1 h2 h max 2.10 AR 2 w1 w2 2.3 w1 w2 w max 2.4 aspect h max = h1 + h2 (2.2) w max = w1 + w2 (2.3) aspect = h max w max (2.4)

14 2 12 Z 軸 Y 軸 X 軸 2.8: AR h1 と h2 2.9:

15 2 13 w1 と w2 2.10: : α (α + β) (α + 2β)

16 2 14 R N α R N < (α + β) α (α + β) R N α (α + β) : 2.3 [19]

17 親指の屈曲に対する凸包輪郭線の減少量 親指の合計関節角度 2.12: 親指の屈曲に対する手の面積の減少量 親指の合計関節角度 2.13: [19] α(α + β) (α + 2β) T N α T N < (α + β) α (α + β) T N α (α + β)

18 : DIP PIP MP %

19 yaw roll pitch x pitch y roll z yaw roll pitch roll pitch

20 第3章 手首の回転を考慮した推定手法 18 roll Y軸 yaw Z軸 X軸 pitch 図 3.1: 手の yaw roll pitch 3.2 手首の回転による手の面積及び手の凸包輪郭線長の変化 手首の回転によって 手の面積及び手の凸包輪郭線長が三角関数的な変化をすることを期 待して いくつかの姿勢に対して手首の回転による手の面積及びと凸包輪郭線長の変化を調 査した 調査は 親指の合計関節角度を 50 度で固定したグー チョキ パーのような姿勢 に対して行った roll 方向は-60 度から 60 度の範囲を 1 度間隔でデータを取得し pitch 方 向は -50 度から 50 度の範囲を 1 度間隔でデータを取得した ただし roll 方向の回転の際 は pitch は 0 度で固定し pitch 方向の回転を行う際は roll を 0 度に固定した状態でそれ ぞれ調査を行った 調査によって得られたデータをグラフ化したものが図 である 図 3.2 図 3.3 は それぞれ roll 方向の回転による手の面積及び手の凸包輪郭線長の変化を 示しており 図 3.4 図 3.5 は それぞれ pitch 方向の回転による手の面積及び手の凸包輪郭 線長の変化を示している グラフにおける縦軸は 手の面積もしくは手の凸包輪郭線長の値 を表しており 横軸は roll もしくは pitch の回転角度を表している グラフを考察した結果 手の姿勢及び回転方向による値の変化の仕方には違いがあることが分かったが 規則性を見 つけ出すことができなかった これは 手には厚みはあり 手の姿勢によっては手首の回転 によりカメラ画像中において見えてなかった部分が見えるようになる状況が多く存在すため であると考えられる

21 : roll 3.3: roll 3.4: pitch

22 : pitch 3.3 roll pitch roll roll

23 : : 3.6: 1 3.7: 30

24 : 1 3.9: roll pitch roll pitch (roll pitch) = (40 15) (30 0) (30 30) 2 2 2

25 : roll-pitch

26 CPU : Pentium(R) Dual-Core CPU E GHz PC C++ BUFFALO USB BSW20K pixel ( 30fps) pixel pixel CG :

27 (Immersion CyberTouch) pich =20 roll = : () IP MP CM CM ( ) ( ) :

28 4 26 DIP PIP MP : DIP PIP MP : DIP PIP MP : DIP PIP MP : :

29 IP MP CM CM ( ) ( ) : DIP PIP MP : DIP PIP MP : :

30 ( ) ( ) ( ) IP MP CM CM ( ) ( ) : DIP PIP MP : DIP PIP MP : DIP PIP MP :

31 4 29 DIP PIP MP : : [14]

32 30 5

33 31

34 32 [1] 2010 [2] Vol.112 No.4 pp [3] Vol.11 No.4 pp [4] Play Station VR [5] Oculus VR Oculus Rift [6] Yutaro Mori Kenji Funahashi A Data Adjustment Method of Low-priced Dataglove Corresponding with each User Hand Proc SCIS - ISIS 2014 pp [7] IS [8] 3 Vol.63 No.6 pp [9] Robert Y. Wang Jovan Popovi Real-Time Hand-Tracking with a Color Glove ACM Transaction on Graphics(SIGGRAPH 2009) Vol.28 No [10] Vitor F. Pamplona Leandro A. F. Fernandes Joao L. Prauchner Luciana P. Nedel Manuel M. Oliveira The Image-Based Data Glove Proceedings of X Symposium on Virtual Reality pp [11],,pp ,2006. [12] Billinghurst Mark, Vol.4 No.4 pp [13] Sanshiro Yamamoto Kenji Funahashi Yuji Iwahori Study for Vision Based Data Glove Considering Hidden Fingertip with Self-Occlusion Proc.SNPD2012 pp

35 33 [14] [15], 1989 [16] George ElKoura Karan Singh Handrix: Animating the Human Hand ACM SIG- GRAPH/EG Symposium on Computer Animation 2003 [17] [18] Chris Welman, Inverse kinematics and geometric constraints for articulated figure manipulation M.Sc Thesis Simon Fraser University [19]

24 21 21115025 i 1 1 2 5 2.1.................................. 6 2.1.1........................... 6 2.1.2........................... 7 2.2...................................... 8 2.3............................

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