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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.

1 1 2 4 2.1... 4 2.2... 5 2.3... 6 2.4... 6 3 8 3.1... 8 3.2... 10 3.3... 12 3.4... 16 4 17 4.1... 17 4.2... 17 4.2.1... 17 4.2.2... 18 4.2.3... 18 4.2.4... 18 4.2.5... 21 4.2.6... 22 4.3... 24 4.4... 26 4.4.1... 27 4.4.2... 27 4.4.3... 28 5 29

5.1... 29 5.2... 31 5.3... 37 5.4... 41 5.5... 43 5.6... 46 6 47 A.1

1 [1][2] [3] [4] [5] 1

2

2 3 4 5 6 3

2 2.1 2.2 2.3 2.4 2.1 Amenta[1] Fang[2] Metaxas[3] [4] 2.1 (a) (b) 2.1: 4

2.2 5

2.3 2.4 y x z 6

2.2 y axis O 2.2: 7

3 [6][7] 2 3.1 10 3.1 a length radius 3.1 b length major axis minor axis cap height 3.1 c length radius 3.1 d [8] 8

radius length (a) (b) minor axis cap height major axis length radius length (c) (d) 3.1: 9

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 3. 3.2 a 4. 3.2 b 5. 3.2 c 6 x y z 4 3.2 d 10

: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

3.3 (a) (b) 3.3: 3.3 12

1 2 6 3.4 a M torso A(M torso ) V outline V internal A(M torso ) \ (V outline + V internal ) Voutline torso torso Vinternal 3 2 6 3.4 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

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 5 3.4 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 6 3.4 e 14

(a) (b) (c) (d) (e) 3.4: 15

3.4 16

4 4.1 4.2 4.3 4.4 4.1 4.2 x y u v 4.2.1 4.1 a 17

(a) (b) 4.1: 4.1 b 4.2.2 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 4.2.3 (r;;') 4.3 a (r; ; ') (R; ; ') R 4.3 b ' u = R'cos v = R'sin (u; v) 4.3 c 4.2.4 18

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

point cloud z y o x o (a) (b) z y o ϕ θ x (c) 4.3: 20

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: 4.2.5 [9] n u min ;u max ;v min ;v max u min u u max v min v v max 21

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 3 1. 4.5 a 2. 4.5 b 3. 2 4.5 c 4. 2 3 4.5 d 4.2.6 4.2.1 4.2.5 =0 =2 4.2.5 =0 =2 =2 =0 22

(a) (b) (c) (d) 4.5: 23

\ " 4.4 4.3 4.1 4.6 a 4.6 b 4.6 c 4.7 a 4.7 b 4.7 c 24

(a) (b) (c) 4.6: (a) (b) (c) 4.7: 25

1. 2. d 1 d 2 d 12 jd 1 0 d 2 j >Nd 12 N 4.8 d1 d12 d2 4.8: 4.4 26

1. 2. 3. 4.4.1 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 \ " 4.4.2 27

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 4.4.3 p p 1 p p 1 p p 1 28

5 5.1 5.2 5.3 5.4 5.5 5.6 5.1 Poser 5.1 5.1 29

5.1: 1 2 1 2 3 4 30

camera2 laser2 human body laser1 camera1 5.1: 5.2 3 5.2 5.3 k =5 40mm n =2 3 1 31

3 5.4 5.5 5.6 5.7 A.1 A.16 10 50mm 100mm 32

5.2: 1 2 1 2 3 4 33

5.3: 1 2 1 2 3 4 34

5.4: mm 2.86618 0.647035 14.2153 17.7393 4.09500 0.0166524 14.2384 7.53184 2.80448 22.4590 4.15640 17.3399 5.80812 34.9950 2.51065 5.45217 9.72413 48.3085 3.01422 27.0331 5.14725 23.5741 3.58954 6.66651 5.5: mm 5.69203 4.08224 5.52313 47.2329 8.03297 0.628117 171.565 63.1159 5.86306 21.8268 3.91389 24.4456 1.79900 29.9121 3.60421 91.9453 2.68234 71.6425 5.62655 72.7237 4.42353 68.6510 6.76731 69.9717 35

5.6: mm 2.86619 0.647010 14.2153 17.7393 4.09500 0.0166391 14.2384 7.53184 2.71196 12.2929 0.223114 10.8371 1.52915 12.8164 0.419123 4.26977 8.39565 41.1483 1.25942 21.0151 5.35227 23.0294 1.82488 5.45119 5.7: mm 5.69218 4.08231 5.52313 47.2329 8.03310 0.628109 171.565 63.1159 4.88057 15.0702 2.89073 17.0811 2.57955 29.3263 6.91408 90.1509 4.48550 109.220 3.49604 71.0304 7.50357 116.509 2.61863 66.1758 36

5.3 5.8 5.2 10 5.3 \ " \ " 37

5.8: 1 2 1 2 3 4 38

(a) (b) (c) (d) 5.2: 39

(a) (b) 5.3: 40

5.4 5.9 5.4 5.10 30 40% 80% 5.4 90% 41

5.9: % mm 29.6822 4.12815 15.6131 28.3926 4.84018 62.4913 36.9381 6.63414 35.0947 54.2547 8.12972 37.0994 1 30.9102 5.48314 27.0448 2 29.9522 3.92191 27.3985 1 39.8267 3.40019 32.5431 2 29.9175 3.35464 29.0999 3 30.3354 4.25137 36.4120 4 26.7038 6.85562 28.9174 (a) (b) 5.4: 42

5.10: % mm 32.7555 3.72466 0.955007 3.75211 29.5044 38.1555 9.63152 1.82919 19.2301 43.0719 93.3683 150.495 92.8046 94.6843 115.469 542.938 86.3890 0.908282 60.2453 79.8943 13.3352 101.848 42.6243 8.21024 85.9513 78.3872 2.57102 25.7281 29.2679 6.99566 53.7825 36.7438 4.81105 31.9760 5.5 5.5 5.6 5.5 5.6 4.3 43

(a) (b) (c) (d) 5.5: 44

(a) (b) (c) (d) 5.6: 45

5.6 [10] 46

6 47

48

A.1 A.1: \ " mm 3.98489 2.27577 2.54171 22.072 6.67098 6.94609 161.072 47.5848 15.3896 44.9706 13.4723 72.3374 13.1991 62.0078 11.4317 51.8894 3.81701 10.8201 3.17947 28.7548 3.28730 25.1228 4.63404 54.0535 A.2: \ " mm 3.98485 2.27574 2.54171 22.0720 6.67077 6.94586 161.072 47.5848 7.04925 22.4957 8.83141 68.8385 11.3300 48.0407 4.79125 6.68278 6.42301 31.0815 2.67553 15.4897 3.29540 35.8199 7.13511 52.8412

A.3: \ " mm 1.03603 7.00080 5.35240 28.9662 4.31372 7.35583 153.609 28.2227 2.04330 31.7596 2.72042 18.766 16.2931 61.7162 9.69264 46.4458 0.63987 80.9564 8.68465 39.6348 5.39534 21.8576 2.78728 56.3017 A.4: \ " mm 1.03607 7.00079 5.35240 28.9662 4.31373 7.35583 153.609 28.2227 2.73669 26.0142 5.07003 13.0828 9.80727 33.2831 15.0674 24.1798 6.75851 76.2643 9.26949 58.2782 9.82233 25.3081 3.83447 57.3946

A.5: \ 1" mm 0.774952 2.32355 4.63698 13.4945 8.95437 1.90004 176.622 13.4945 9.88307 49.0982 8.95248 62.7458 2.28716 32.3043 6.38882 42.9505 5.20127 32.4249 4.06519 19.4848 8.25614 25.0955 9.62454 30.9078 A.6: \ 1" mm 0.775007 2.32354 4.63698 13.4945 8.95430 1.90004 176.622 13.4945 3.84299 21.5792 14.5936 66.8880 5.24993 11.4210 5.96845 12.4118 11.4953 62.1419 4.69158 23.9164 7.09744 24.9945 1.85686 20.1063

A.7: \ 2" mm 5.99344 1.61887 3.06611 29.8497 2.80454 2.38567 176.891 15.4851 7.00862 40.0973 9.91401 52.2199 6.93339 37.4986 12.7629 84.8871 5.65127 28.6675 9.07044 40.0228 5.58144 31.1657 4.81293 24.6892 A.8: \ 2" mm 5.99349 1.61887 3.06611 29.8497 2.80455 2.38568 176.891 15.4851 2.17663 4.21570 5.35759 52.0276 4.25834 15.1473 12.4287 52.6072 3.65847 22.6600 4.32509 9.87549 3.04928 18.3133 0.674974 53.8034

A.9: \ 1" mm 0.247862 5.18329 0.933498 23.6958 1.62528 4.49109 176.330 31.8547 5.22182 28.5811 1.53484 61.7635 9.20986 54.5752 5.94033 61.6565 0.482185 55.7419 7.71130 36.5946 4.13440 42.0548 4.45584 20.0681 A.10: \ 1" mm 0.247991 5.18328 0.933498 23.6958 1.62441 4.49128 176.330 58.3396 4.54352 26.9107 2.76862 60.1491 2.17070 8.14894 7.89027 59.8069 7.22471 38.3041 2.18855 14.6305 0.295719 13.3994 4.37017 22.0460

A.11: \ 2" mm 0.644043 2.78684 1.13371 18.8495 6.79312 2.52337 177.367 14.5008 5.58562 45.9275 1.24729 38.4020 4.88772 27.2088 5.47460 87.9276 3.05842 29.3765 1.06725 19.2600 5.14730 37.9045 1.99867 27.0715 A.12: \ 2" mm 0.644063 2.78683 1.13371 18.8495 6.79305 2.52337 177.367 14.5008 5.61951 13.7147 1.11601 37.8616 5.62248 28.6946 5.69912 87.7583 2.47964 18.4202 0.55902 14.8424 5.38486 35.7457 3.97035 20.6109

A.13: \ 3" mm 3.04664 10.6598 0.0136331 53.959 2.21899 7.29525 5.44795 55.5812 10.9820 56.4071 12.5602 45.1789 17.7725 93.6127 6.06884 21.7546 6.89583 44.5710 6.19854 43.3590 6.54584 35.4901 1.25308 28.0149 A.14: \ 3" mm 3.04649 10.66 0.0136331 53.959 2.21912 7.29519 5.44795 55.5812 8.55084 42.1319 1.42941 10.1098 2.27715 55.6912 3.00059 30.2039 4.10792 43.5601 2.18255 28.9604 7.16412 28.0844 2.12424 15.8376

A.15: \ 4" mm 1.68808 6.26563 5.73820 30.0230 3.34364 4.98828 171.877 22.5404 5.40816 22.4845 6.12601 28.4646 6.10748 30.9409 9.82428 48.0906 11.8317 51.7903 2.33321 53.3637 8.08788 37.9853 8.88320 40.5798 A.16: \ 4" mm 1.68823 6.26568 5.7382 30.023 3.34363 4.9883 171.877 22.5404 6.46939 6.29222 4.51983 7.28528 11.0615 32.9421 11.8419 18.2080 8.68676 41.2593 5.12313 53.2152 9.16491 44.5475 8.96422 32.8609

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