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3 ii Surface Reconstruction from Point Cloud of Human Body in Arbitrary Postures Isao MORO Abstract We propose a method for surface reconstruction from point cloud of human body in arbitrary postures. In this method, we make volume data from the point cloud. Then a human model is matched to the volume data and human body posture is estimated. Point cloud is classied into parts by the estimated posture. For each classied point cloud, surface is reconstructed with 2D delaunay triangulation. Then whole body surface is reconstructed by collecting surfaces of parts. In our experiments, postures are estimated and surfaces are reconstructed from synthetic data and real data.
4
5 A.1
6 1 [1][2] [3] [4] [5] 1
7 2
8
9 Amenta[1] Fang[2] Metaxas[3] [4] 2.1 (a) (b) 2.1: 4
10 2.2 5
11 y x z 6
12 2.2 y axis O 2.2: 7
13 3 [6][7] a length radius 3.1 b length major axis minor axis cap height 3.1 c length radius 3.1 d [8] 8
14 radius length (a) (b) minor axis cap height major axis length radius length (c) (d) 3.1: 9
15 3.2 [4] 1. P = p 1 ;p 2 ; 111;p n p i k N bhd (p i )=n bhd (1);n bhd (2); 111;n bhd (k) n bhd (j) N bhd (p i ) p i j p i n bhd (k) p i A disk A disk = 1kp i 0 n bhd (k)k 2 p i p i n bhf (k) k p i i i = k +1 A disk i min 2. min a b c 6 x y z d 10
16 :Point :Voxel :Outline Voxel :External Voxel (a) (b) scan scan :Outline Voxel :Internal Voxel :External Voxel :Outline Voxel :Internal Voxel :External Voxel (c) (d) 3.2: 11
17 3.3 (a) (b) 3.3:
18 a M torso A(M torso ) V outline V internal A(M torso ) \ (V outline + V internal ) Voutline torso torso Vinternal b M chest A(M chest ) B(M chest ) n 2 (B(M chest ) \ V torso outline )+(A(M chest ) \ V torso internal ) n 13
19 4 3.4 c n 2 (B(M weist ) \ (V outlinse 0 V matched outline )+(A(M weist ) \ (V internal 0 V matched) internal Voutline matched Vinternal matched d n 2 (B(M weist ) \ (V outline 0 V matched outline ))+(A(M weist ) \ (V internal 0 V matched internal )) Voutline matched Vinternal matched e 14
20 (a) (b) (c) (d) (e) 3.4: 15
21 3.4 16
22 x y u v a 17
23 (a) (b) 4.1: 4.1 b h r (0 2) (r; ; h) 4.2 a 0 (r; ; h) (R; ; h) R 4.2 b u = R v = h (u; v) 4.2 c (r;;') 4.3 a (r; ; ') (R; ; ') R 4.3 b ' u = R'cos v = R'sin (u; v) 4.3 c
24 point cloud 3π 2 0 R h 0 r θ π π 2 3π 2 0 R h 0 R θ π π 2 (a) (b) v h 0 Rθ πr πr 3πR 2 2 2πR u (c) 4.2: 19
25 point cloud z y o x o (a) (b) z y o ϕ θ x (c) 4.3: 20
26 p i =(u i ;v i ) V (p i ) V (p i )=fp =(u; v)jd(p,p i ) <d(p,p j ); 8j 6= ig d(p,p i ) (p) (p i ) p i p p i 4.4 a 4.4 b (a) (b) 4.4: [9] n u min ;u max ;v min ;v max u min u u max v min v v max 21
27 u min < 8u k ;u max > 8u k v min < 8v k ;v max > 8v k (k =1; 2; 3;:::;n) P 1 (u min ;v min ) P 2 (u min ;v max ) P 3 (u max ;v min ) P 4 (u max ;v max ) P 1 P 2 P 4 P 1 P 4 P a b c d =0 = =0 =2 =2 =0 22
28 (a) (b) (c) (d) 4.5: 23
29 \ " a 4.6 b 4.6 c 4.7 a 4.7 b 4.7 c 24
30 (a) (b) (c) 4.6: (a) (b) (c) 4.7: 25
31 1. 2. d 1 d 2 d 12 jd 1 0 d 2 j >Nd 12 N 4.8 d1 d12 d2 4.8:
32 A B 1 A B 4.9 a A B 2 A B A B 4.9 b A B A B 3 A B 4.9 c \ "
33 only A A and B only A A and B only A A and B only B (a) 1 (b) 2 (c) 3 4.9: 2 A B A B p p 1 p p 1 p p 1 28
34 Poser
35 5.1:
36 camera2 laser2 human body laser1 camera1 5.1: k =5 40mm n =
37 A.1 A mm 100mm 32
38 5.2:
39 5.3:
40 5.4: mm : mm
41 5.6: mm : mm
42 \ " \ " 37
43 5.8:
44 (a) (b) (c) (d) 5.2: 39
45 (a) (b) 5.3: 40
46 % 80% % 41
47 5.9: % mm (a) (b) 5.4: 42
48 5.10: % mm
49 (a) (b) (c) (d) 5.5: 44
50 (a) (b) (c) (d) 5.6: 45
51 5.6 [10] 46
52 6 47
53 48
54 A.1 A.1: \ " mm A.2: \ " mm
55 A.3: \ " mm A.4: \ " mm
56 A.5: \ 1" mm A.6: \ 1" mm
57 A.7: \ 2" mm A.8: \ 2" mm
58 A.9: \ 1" mm A.10: \ 1" mm
59 A.11: \ 2" mm A.12: \ 2" mm
60 A.13: \ 3" mm A.14: \ 3" mm
61 A.15: \ 4" mm A.16: \ 4" mm
62
63 [1] Nina Amenta,Marshall Bern,Manolis Kamvysselis: A New Voronoi-Based Surface Reconstruction Algorithm, SIGGRAPH 1998 Conference Proceedings, pp (1998) [2] Thung-Pao Fang,Les A.Piegl: Delaunay Triangulation in Three Dimensions IEEE Computer Graphics and Applications september 1995,pp (1995) [3] Dimitris Metaxas,Eunyoung Koh,Norman I.Badler: Multi-Level Shape Representation Using Global Deformations and Locally Adaptive Finite Elements, International Journal of Computer Vision 25(1), 49-61(1997) [4] : Vol.40, No.5, pp (1999) [5] : 2000 No.D-12-42,pp. 229,2000. [6],, : J79-D-II, No.1, pp (1996) [7] : Volume Data (1999) [8] : [9] : 3 (1998) [10] : J83-D-II No.7 pp (2001).
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