1 Kinect for Windows M = [X Y Z] T M = [X Y Z ] T f (u,v) w 3.2 [11] [7] u = f X +u Z 0 δ u (X,Y,Z ) (5) v = f Y Z +v 0 δ v (X,Y,Z ) (6) w = Z +

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3 3D 1,a) 1 1 Kinect (X, Y) 3D 3D 1. 2010 Microsoft Kinect for Windows SDK( (Kinect) SDK ) 3D [1], [2] [3] [4] [5] [10] 30fps [10] 3 Kinect 3 Kinect Kinect for Windows SDK 3 Microsoft 3 Kinect for Windows SDK 3 Zhang Zhang Kinect RGB [6] Khoshelham Elberink Microsoft Kinect for Windows [7] Smisek [8] Herrera C. [9] RGB RGB Karan [10] Kinect 1 The University of Shiga Prefecture 1 Presently with Graduate school of The University of Shiga Prefecture a) oo23kgouhara@ec.usp.ac.jp Microsoft Kinect 2. Kinect 1 Kinect 2 O b Kinect Z 0 Q y Kinect c 2015 Information Processing Society of Japan 1

1 Kinect for Windows 3.1 3 M = [X Y Z] T M = [X Y Z ] T f (u,v) w 3.2 [11] [7] u = f X +u Z 0 δ u (X,Y,Z ) (5) v = f Y Z +v 0 δ v (X,Y,Z ) (6) w = Z +δz(u,v)+z 0 (7) (u 0,v 0 ) δ u (X,Y,Z ) δ v (X,Y,Z ) 2 w Z k δz(u,v) z w Z 0 y z d M M y Y M = RM +t R Y Z D QOP X Y Z θ x θ y θ z QYZ D b = Z 0 Z k (1) 1 0 0 Z 0 R = 0 cosθ x sinθ x OYZ Oyz 0 sinθ x cosθ x d f = D (2) cosθ Z k y 0 sinθ y 0 1 0 (1) (2) sinθ y 0 cosθ y Z k Z 0 Z k = 1+ Z0 fb d (3) cosθ z sinθ z 0 sinθ z cosθ z 0 0 0 1 2 OWZ Owz X k = x t [t x t y t z ] T k (4) Z k f (u k,v k,w k ) f Z k (5) (6) (7) û k ˆv k ŵ k x k X k n e = ( u k û k 2 + v k ˆv k 2 + w k ŵ k 2 ) (8) 3. k=1 f u 0 v 0 δ u δ v δz Z 0 θ x θ y θ z t (8) c 2015 Information Processing Society of Japan 2

3 (c): θ x θ y (d):(c) δz (5) (6) δz 3 (3D) (8) δz δz δz 4 (a): (b):(a) 3.3 δz δz θ x θ y 4(a) 5 4 (d) 4(b) w u w X Z w Z known Z 0 X Z θ y δz = (w Z 0 ) Z known u w θ y (u,v) 5 4 (d) θ x θ z δz 0 4(a) θ y 4(a) 3.4 3D θ x θ y θ x 4(c) (d) 3D 4(c) w 4(d) 4(d) w w w c 2015 Information Processing Society of Japan 3

3.5 2 (X 1,Y 1,Z 1 ) (X 2,Y 2,Z 2 ) 3D (u 1,v 1,w 1 ) (u 2,v 2,w 2 ) (5) (6) u θ z θ 2 u 1 = f X 2 X 1 z = 0 Z +(u 2r2 2 u 1r1)k 2 1 (13) 2 3.3 3D v 2 v 1 = f Y 2 Y 1 θ x θ y θ x θ y Z +(v 2r 2 2 v 1r 1)k 2 1 (14) 2 R Z 1 Z 2 R t 2 (X 1,Y 1,Z 1 ) (X 2,Y 2,Z 2 ) t z t = [0 0 t z ] T (X 1,Y 1,Z 1 ) (X 2,Y 2,Z 2 ) u 0 v 0 f (13) (14) ŭ 0 v 0 k 1 k 1 2 k 1 [u v w] T R [u v w ] T = R 1 [u v w] T 3.6 w 3.3 3.2 δz Z 0 Z 0 (u k,v k,w k ) (û k,ˆv k,ŵ k f f u 0 v 0 k 1 Z 0 θ x θ y θ z t 2 (8) (X a,y a,z a ) (X b,y b,z b ) [u v w ] T (u a v a w a ) (u b v b w b ) (5) (6) u a u b = fx a X b Z a v a v b = f Y a Y b Z a (9) (10) R t Z (5) (6) (11) (12) p = X /Z 2 (X a,y a,z a ) (X b,y b,z b ) q = Y /Z (5) (6) p q 2 (X a,y a,z a ) (X b,y b,z b ) Z X Y [u v w ] T = R 1 [u v w] T M X a X b Y a Y b X a X b Y a Y b M = R 1( M t ) Z a = Z b Z a = Z b Z a t z 2 δz 3.7 (u,v,w) M = [X Y Z] T w δz Z 0 4. Kinect f (9) (10) f 3 4.1 3D δ u = uk 1 r 2 (11) 3D 6 δ v = vk 1 r 2 (12) ( ) X r 2 2 ) Y 2 7 = +( Z Z 1200mm 900mm [12] 100mm 50mm k 1 100mm 6 c 2015 Information Processing Society of Japan 4

6 7 8 δz.(a):δz. (b): 7 4.2 δz Kinect 1000 mm 10 9 1 1 θ x {(u,v) u = 319,10 v 59} 4.3.1 {(u,v) u = 319,420 v 469} f k 1 θ y {(u,v) 10 u 59,v = 239} {(u,v) 580 u 629,v = 239} 3.3 δz 945mm 8 [u v w ] T 4.2 δz 1000 mm Z 0 Z 0 = 16 mm ŭ 0 = 319 v 0 = 239 [u v w ] T (u,v ) 4.3 (u,v ) w 4.2 Kinect 3D 1000 mm f θ z = 0 f 4.2 θ x θ y R (9) f f 2 t = [0 0 1000] T 31 32,32 33,33 40,40 41,41 49,49 50 θ x θ y 4.2 48 w R 1 c 2015 Information Processing Society of Japan 5

9 (a): (b): θ x θ y = 100 (c): δz Z 0, 13.6 2.65 5.78 1 (i) (ii) θ x [deg] -0.1249 5.453 10 2 4.547 10 2 θ y [deg] 6.720 10 2 2.858 10 2 1.156 10 2 θ z [deg] 0 8.213 10 3 0.3507 t x [mm] 0 129.0 132.0 t y [mm] 0 125.7 160.4 t z [mm] 1000 960.5 669.6 k 1 4.690 10 7 0 0.8425 f [mm] 593.0 562.4 520.7 u 0 [pixel] 319 415.3 275 v 0 [pixel] 239 315.1 330 Z 0 [mm] 16 16.83 16 k 1 2 (13) k 1 48 k 1 2 10 11,11 18,18 63,63 71 1 (i) (ii) k 1 1 5. SDK (i)(ii) 2 2 2 6. 1 Khoshelham Elberink[7] 5.453±0.012 mm (i)(ii) f 2 (i)(ii) SDK (i) Kinect Kinect Kinect 4.4 7 X,Y,Z u,v,w (8) f k 1 c 2015 Information Processing Society of Japan 6

2 2 SDK (i) (ii) [mm] [mm] [ ] [mm] [ ] [mm] [ ] 14-15 100 115.5 15.5 97.94 2.06 106.3 6.29 15-20 608.3 702.9 15.6 586.1 3.64 633.7 4.18 20-21 100 116.6 16.6 97.55 2.45 103.8 3.83 21-22 100 117.6 17.6 96.79 3.21 106.1 6.14 22-23 100 110.1 10.1 93.60 6.40 102.3 2.32 23-24 100 118.1 18.1 97.64 2.36 104.8 4.85 24-26 200 227.5 13.7 195.1 2.43 210.8 5.42 26-30 608.3 692.3 13.8 586.7 3.54 635.3 4.44 30-34 400 452.1 13.0 385.2 3.70 417.5 4.39 34-39 412.3 468.7 13.7 398.3 3.40 431.8 4.72 39-42 400 454.8 13.7 386.9 3.28 418.2 4.54 42-47 412.3 479.7 16.4 400.7 2.81 433.8 5.21 47-51 400 463.0 15.8 388.5 2.87 421.1 5.27 51-55 608.3 672.7 10.6 603.4 0.799 650.3 6.90 55-57 200 214.8 7.38 202.8 1.39 216.7 8.34 57-58 100 109.0 8.98 100.6 0.591 109.1 9.09 58-59 100 116.0 16.0 100.6 0.616 107.5 7.51 59-60 100 110.5 10.5 95.51 4.49 105.0 4.99 60-61 100 114.6 14.6 98.78 1.22 107.5 7.53 61-66 608.3 670.0 10.1 618.8 1.74 667.5 9.72 34(15), pp. 1995 2006, Nov., 2013. [6] Cha Zhang and Zhengyou Zhang, Calibration between 7. depth and color sensors for commodity depth cameras, IEEE International Conference on Multimedia and Expo Kinect 3D (ICME) 2011, pp. 1 6, July 11 15, 2011. [7] Kourosh Khoshelham and Sander Oude Elberink, Accuracy and Resolution of Kinect Depth Data for Indoor (i) Mapping Application, Sensors 12, pp. 1437 1454, 2012. Kinect [8] Jan Smisek, et al., 3D with Kinect, Consumer Depth Cameras for Computer Vision, Advances in Computer Vision and Pattern Recognition 2013, pp. 3 25, Springer. [9] Daniel Herrera C., et al. Joint Depth and Color Camera Calibration with Distortion Correction, IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(10), pp. 2058 2064, Oct., 2012. [10] Branko Karan, Calibration of Depth Measurement [1] Alexander Weiss et al., Home 3D Body Scans form Model for Kinect-Type 3D Vison Sensors, Poster Proceedings of 21st International Conference in Central Eu- Noisy Image and Range Data, IEEE International Conference on Computer Vision 2011, pp. 1951 1958, Nov. rope on Computer Graphics, Visualization and Computer Vision, pp. 61 64, June 24 27, 2013 6 13, 2011. [2] Jing Tong, et al., Scanning 3D Full Human Bodies Using Kinects, IEEE Trans. on Visualization and Com- [11] Zhengyou Zhang, Flexible camera calibration by viewing a plane from unknown orientations, The Proceedings of the Seventh IEEE International Conference on puter Graphics, 18(4), pp. 643 650, April, 2012. [3] Richard A. Newcombe et al., KinectFusion: Real-Time Computer Vision 1999, Vol. 1, pp. 666 673, 20 Sep, Dense Surface mapping and Tracking, 10th IEEE International Sypmposium on Mixed and Augumented Real- 1999. [12] R. Y. Tsai, A versatile camera calibration technique ity 2011, pp. 127 136, Oct. 26-29, 2011. for high-accuracy 3D machine vision metrology using [4] Lu Xia, et al., Human Detection Using Depth Information by Kinect, International Workshop on Human off-the-shelf TV cameras and lenses, IEEE Journal of Robotics and Automation, 3(4), pp. 323-344, August Activity Understanding from 3D Data 2011, pp. 15-22, 1987. Jun. 24, 2011. [5] Lulu Chen, et al., A survay of human motion analysis using depth imagery, Pattern Recognition Letters, c 2015 Information Processing Society of Japan 7

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