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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1 3 3D 1,a) 1 1 Kinect (X, Y) 3D 3D 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
2 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 +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) 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 (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 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 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
4 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) D 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 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 D 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
5 6 7 8 δz.(a):δz. (b): δz Kinect 1000 mm θ x {(u,v) u = 319,10 v 59} {(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 = [ ] T 31 32,32 33,33 40,40 41,41 49,49 50 θ x θ y w R 1 c 2015 Information Processing Society of Japan 5
6 9 (a): (b): θ x θ y = 100 (c): δz Z 0, (i) (ii) θ x [deg] θ y [deg] θ z [deg] t x [mm] t y [mm] t z [mm] k f [mm] u 0 [pixel] v 0 [pixel] Z 0 [mm] k 1 2 (13) k 1 48 k ,11 18,18 63, (i) (ii) k SDK (i)(ii) Khoshelham Elberink[7] 5.453±0.012 mm (i)(ii) f 2 (i)(ii) SDK (i) Kinect Kinect Kinect X,Y,Z u,v,w (8) f k 1 c 2015 Information Processing Society of Japan 6
7 2 2 SDK (i) (ii) [mm] [mm] [ ] [mm] [ ] [mm] [ ] (15), pp , Nov., [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, [7] Kourosh Khoshelham and Sander Oude Elberink, Accuracy and Resolution of Kinect Depth Data for Indoor (i) Mapping Application, Sensors 12, pp , 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 , Oct., [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 , Nov. rope on Computer Graphics, Visualization and Computer Vision, pp , June 24 27, , [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 , April, [3] Richard A. Newcombe et al., KinectFusion: Real-Time Computer Vision 1999, Vol. 1, pp , 20 Sep, Dense Surface mapping and Tracking, 10th IEEE International Sypmposium on Mixed and Augumented Real [12] R. Y. Tsai, A versatile camera calibration technique ity 2011, pp , Oct , 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 , August Activity Understanding from 3D Data 2011, pp , Jun. 24, [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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