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NAIST-IS-MT0251072 2004 2 6

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,,,.,,.,,.,,,,.,,,.,,,.,,,.,,,,, NAIST-IS- MT0251072, 2004 2 6. i

Wearable 3D Shape Measurement System with Estimating Self Pose and Position Masanobu Tsuchiya Abstract At present, when the user let someone know a shape of some object, the user can take the shape as a photograph and send someone it instantly by using mobile phone attached small camera. However, 2 dimensional image such as this photograph cannot represents 3 dimensional shape of someobject strictly. By using 3 dimensional information, the user can see the object from free position and direction and know the shape more closely. The present method taking the 3 dimensional shape spents various time in order to take the shapes from pictures and photographs manually. There are few 3D measurement system which can take 3 dimensional information easily, such as the mobile phone attached a camera which can take a picture easily and send it immediately. This paper proposes the newly 3D shape measurement system. This system can take 3D shape of hand-held size object without pre-preparation and send it straightaway. The user can measure the shape of the object by natural operations that the user looks at it from free direction. Keywords: Three-Dimensional Information, 3D Measurement, Wearable Computer, Marker, Slit-Light Detection Master s Thesis, Department of Information Processing, Graduate School of Information Science, Nara Institute of Science and Technology, NAIST-IS-MT0251072, February 6, 2004. ii

1 1 2 3 2.1............................ 3 2.1.1............... 3 2.2............................ 8 2.2.1..................... 9 2.3............. 13 2.4....................... 15 3 19 3.1............................ 19 3.2................................ 20 3.2.1........................ 21 3.2.2......................... 22 3.2.3........................ 28 4 29 4.1........................... 29 4.1.1.................... 30 4.2........................... 31 4.3............................ 34 4.3.1... 34 4.3.2......... 37 4.3.3.......... 37 iii

5 41 5.1................... 41 5.2................... 41 6 43 44 45 iv

2.1........................ 4 2.2................. 5 2.3 GPT-8000A................. 7 2.4........................... 8 2.5 KONICA MINOLTA VIVID910................... 8 2.6 FARO Technologies Inc. FaroArm Gold............. 10 2.7 Kreon Technologies KLS51 Model................. 10 2.8 Faro Arm Kreon 3D laser sensor....... 10 2.9 Polhemus 3SPACE FASTRAK.................. 11 2.10 Ascension Flock of Birds...................... 11 2.11 Northern Digital hybrid POLARIS................ 12 2.12 ARToolKit............................... 12 2.13 3....... 14 2.14 A Self-Referenced Hand-Held Range Sensor............ 16 2.15 Interactive Shape Acquisition using Marker Attached Laser Projector................................. 17 3.1......................... 20 3.2............................. 21 3.3........................ 22 3.4............................. 24 3.5............ 27 4.1.............................. 30 v

4.2.................. 32 4.3.................. 33 4.4........................... 33 4.5...................... 35 4.6...................... 35 4.7.................... 36 4.8........................ 38 4.9......................... 39 4.10........ 40 vi

4.1........... 34 vii

1,.,.,,,,.,,.,,., 3D [1] [2], [3].,,.,,.,,,,,.,,,,.,,.,,,,.,,, 1

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2.3: GPT-8000A[7],.,, 1 1, 2.4.,.,,,,,.,.,..,. 7

2.4: 2.5: KONICA MINOLTA VIVID910 [8] KONIKA MINOLTA VIVID [8]. VIVID,, 0.2[mm]. 2.2 2.1,,.,,, 8

.,. 2.2.1,.,,., Faro FaroArm[9] Kreon 3D laser sensors[10] 2.6, 2.7,??. 10[µm], 25[µm].,,.,,.,,.., Polhemus 3SPACE FASTRAK[11] [11] 2.9. Fastrak 1.5[m], 1[mm], 0.15., Ascension Flock of Birds[12] [12] 9

2.6: FARO Technologies Inc. FaroArm Gold [9] 2.7: Kreon Technologies KLS51 Model [10] 2.8: Faro Arm Kreon 3D laser sensor 10

2.10. Flock of Birds 1.2[m], 0.5[mm], 0.15.,,,.,,,. 2.9: Polhemus 3SPACE FASTRAK [11] 2.10: Ascension Flock of Birds [12],,., 1., 2.,. 1,. LED, LED., Northern Digital hybrid POLARIS Active [13]., 11

LED, LED,,. 2,,., ARToolKit[14]. ARToolKit,.,,., Mixed Realty,,.,,,.,. 2.11: Northern Digital hybrid POLARIS [13] 2.12: ARToolKit[15] 12

2.3, [16].,,,.,.,.. 1., 3. 2., 3,. 3..,., 10 20,., 2,., Hebèrt A Self-Referenced Hand-Held Range Sensor [17] Fukukawa [18] Interactive Shape Acquisition using Marker Attached Laser Projector. 13

(a) (b) (c) 2.13: 3 [16] 14

A Self-Referenced Hand-Held Range Sensor 2,.,.,., 2. 250[µm]. Interactive Shape Acquisition using Marker Attached Laser Projector 5 LED,.,,. LED 5,,.. A Self-Referenced Hand-Held Range Sensor.,,., Interactive Shape Acquisition using Marker Attached Laser Projector,,,. 2.4, 1.. 2.. 15

(a) (c) (b) 2.14: A Self-Referenced Hand-Held Range Sensor [17] 16

(a) [18] (b) [19] 2.15: Interactive Shape Acquisition using Marker Attached Laser Projector 17

, 1., 2,. 18

3,...,,.,,. 3.1,,,, PC, 3.1.,, 2.1.1,.,, 3.2.1.,.,,,., Head Mounted Display,., PC. 19

3.1: 3.2.,.,,.,,.,,.,.,.,. 20

3.2.1,,.,,.,. 3.2. 3.2:,,.?? P n P cn (X cn, Y cn ) P n X n X 0n a n = Y n Y 0n b n = Z n Z 0n c n (3.1) a n, bn, cn, X0n, Y 0n, Z0n Pcn 3.1 k P n 21

P n+1 P n+3 = P n l n = P n P n+1 {(a n k + X 0n ) (a n+1 k + X 0n+1 )} 2 + = {(b n k + Y 0n ) (b n+1 k + Y 0n+1 )} 2 + (3.2) {(b n k + Z 0n ) (b n+1 k + Z 0n+1 )} 2 l n k 3.3: 2.2.1, ARToolKit. 3.2.2,,, 1. 1., 1,, 22

3.4.,.,,. t t F RGB (t)., RGB,. RGB, Y C R C B Y. RGB r, g, b, Y(r, g, b) = (0.2990 r) + (0.5870 g) + (0.1140 b) (3.3) [20]., rgb, 8[bit], 0 r, g, b 255.,,,.,,,.,,,,,.. F RGB (t) F Y (t), F Y (t 1),, F Diff (t) = F Y (t) A F Y (t 1) (3.4) 23

(a) (b) 3.4: 24

. A,. A now, A prev, A A = A 1 now A prev (3.5). x, y x, y, a xx a xy a xz 0 [ ] [ ] x y z 1 = x y z a yx a yy a yz 0 1 a zx a zy a zz 0 a lx a ly a lz 1 [ ] = x y z 1 A z = z = 0. [ ] [ ] x y 0 1 = x y 0 1 A (3.6),,,??..,??, 25

., x h c x c h c y c = C y h z c 1 x h c x c c 11 c 12 c 13 c 14 h c y c = c 21 c 22 c 23 c 24 y (3.7) h c c 31 c 32 c 33 c z 34 1. C, x c, y c, x, y, z..,,,., 3.7, x c, y c, h c. 3.7, x c = 0, y c = 0,, ] ] x [h p = [p 1 p 2 p 3 y (3.8) z., h p 0. 3.5, q, q, q.,,. 3.7 26

3.8,, c 34 x c c 14 c 11 c 31 x c c 12 c 32 x c c 13 c 33 x c x c 34 y c c 24 = c 21 c 31 y c c 22 c 32 y c c 23 c 33 y c y h p p 1 p 2 p 3 z F = Q V (3.9)., V V = Q 1 F (3.10)., 3.10,,,. 3.5: 27

3.2.3 3.2.2,.. M o, M now,, [ ] T [ T x o y o z o 1 = M 1 o M now x y z 1] (3.11).,,,.,. 28

4,,,. 4.1, 4.1.. PC CPU.................................... Intel Pentium 4 1.2[GHz]................................................ 1[GB]........ ATI MOBILITY RADEON 9000 I O DATA magictv..................... : 320 240[P ixel] WATEC WAT-240R................ : NTSC Composite Video 29

TAKENAKA OPTONIC 赤色スリット光レーザ.... 波長 : 635[nm] 図 4.1: 試作計測器 4.1.1 カメラと計測器の調整 レンズ歪の補正 歪みのない三次元形状を得るためにレンズ歪を補正する. 補正式は, Tsai のモ デルのレンズ歪補正式 [21] Xu = Xd + Dx (4.1) Yu = Yd + Dy (4.2) を用いる. Xu, Yu は補正後の座標値, Xd, Yd は補正前の座標値である. Dx, Dy が 補正値であり, レンズの半径方向の歪係数 κ1, κ2 を用いて, 以下のように表すこ 30

??. D x = X d (κ 1 r 2 + κ 2 r 4 ) (4.3) D y = Y d (κ 1 r 2 + κ 2 r 4 ) (4.4) r = Xd 2 + Y d 2 (4.5), (X u, Y u ), (X d, Y d ), D x, D y., κ 1, κ 2., C P. 4.3. 30[cm]. 4.3 O Z, X, Y. Z 2[cm], g,, X, Y Z, x c, y c.,., 30[cm] 4[cm]. C P.. 4.2 4.3,.,,......................................... 2788.................................... 32 31

4.2: 32

Y X O Z 図 4.3: キャリブレーション時の機材配置 カメラから約 22[cm] カメラから約 4[cm] 図 4.4: 方眼撮影画像の例 33

4.1: X [cm] Y [cm] Z [cm] 4[cm] 16[cm] 0.14 0.29 0.77 18[cm] 28[cm] 0.71 0.72 1.67 0.16 0.50 1.13., 32,,. 4.1. 18[cm] 28[cm] 1.67[cm].,,,. 4[cm] 16[cm], 2[mm],., 4.3 30[cm] 8[cm] 2[cm],.,. 4.5. 4.3 4.3.1 4.6. 4.6,,, 4.7 34

図 4.5: スリット光断面の計測結果 図 4.6: スリット光抽出実験の様子 35

1[cm] 2[cm] 3[cm] 4[cm] 5[cm] 4.7: 36

4.3.2 4.8. 4.9,,.. 4.3.3 4.10 37

(a) (b) 4.8: 38

(a) (b) 4.9: 39

(a) 4.10: 40

5 5.1, 18[cm] 28[cm] 1.67[cm].,,,. 4[cm] 16[cm], 2[mm],.,.,. 5.2 5[cm]..,,,.,,..,.,,,, 41

, 42

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[20].., 1990. [21].., 1998. 47