Mapping Textures on 3D Geometric Model Using Reflectance Image

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Mark D. Wheeler Mapping Textures on 3D Geometric Model Using Reflectance Image Ryo KURAZUME, Ko NISHINO, Mark D. WHEELER, and Katsushi IKEUCHI 3 3 CAD albedo 1. VR modeling-from-realitymfr 1 2 3 Institute of Industrial Science, The University of Tokyo, 4 6 1 Komaba, Meguro-ku, Tokyo, 153 8505 Japan Cyra Technologies, Inc. 8000 Capwell Drive, Oakland, CA 94621, U.S.A. (1) (2) (3) 3 [1] [3] [4] [5] [7], [13][15] OGIS Cyberwares 1038 D II Vol. J85 D II No. 6 pp. 1038 1046 2002 6

3 2 3 [11], [12] 2. Viola [8] Allen [7] Lensch [9], [10] Downhill Simplex 2D-3D [11][13] albedo Elstrom [6] 1 2 3 Closed-form 4 3. ERIM Perceptron Cyrax [7], [11][13] 1039

2002/6 Vol. J85 D II No. 6 Canny [17] Canny 3 Cyrax Cyrax G 3 1 Fig. 1 Edge sampling. 3 3 3 3 3 2 2 1 3 3 2 2 3D -2D 3D -2D 1 3 3 2 3 2 3 3. 1 Canny [17] 3 1040

P i = { visible n v 0 invisible otherwise (1) n v 3 { edge 0 <n v t P i = (2) not edge otherwise t 3. 2 3 2 2 3 P 2 u u 2 y 3 Puy 3. 3 M 2 3 M [19] 2 3 3 2 2 y l 3 3 PH 3 z i [18] z i = Z i sin θ (3) Z i 3 θ 3 E E(P )= ρ(z i) (4) i ρ P E(P ) P E P = i ρ(z i) z i z i P = 0 (5) w(z) w(z) = 1 z ρ z (6) 2 E P = z i w(z i)z i P = 0 (7) i ρ(z) (4) E ρ(z) = σ2 2 log(1 + (z/σ)2 ) (8) P 4. 2 2 3 Fig. 2 2D distance and 3D distance. 4. 1 3D -2D 10 mm 20 mm 1m 3 300 dpi 70 mm 3 1041

2002/6 Vol. J85 D II No. 6 3 Fig. 3 Simulation model. 5 Fig. 5 Reflectance image of the dish. Table 1 4 Fig. 4 Simulation results. 1 Convergence for some estimation functions. Estimation func. Number of convergence [times] L 2 70/100 Tukey 68/100 Huber 78/100 Geman-McClure 70/100 Welsch 59/100 Lorentzian 81/100 2 [mmpixel] Table 2 Position errors [mm (pixel)]. x y z θ[deg.] Average 0.14 (0.12) 0.20 (0.16) 967.81 4.0 STD. 0.13 (0.11) 1.89 (1.56) 5.94 4.1 4 M 50 mm20 6 6 Fig. 6 Texture image of the dish. 100 L 2 2 1 y 2 2 z 1042

Fig. 11 11 Texture image of the Kamakura Great Buddha. 7 Fig. 7 Aligned intensity edges with reflectance edges. 8 Fig. 8 Aligned color texture on the dish. 9 Fig. 9 Geometric model of the Kamakura Great Buddha. 12 Fig. 12 Aligned intensity edges with reflectance edges. Fig. 10 10 Reflectance image of the Kamakura Great Buddha. 32 mm (2) 1043

2002/6 Vol. J85 D II No. 6 3D -2D 4. 2 Cyrax 3 5 6 NikonD1 24 8 Canny 5 7 M CAD 8 4. 3 13 Fig. 13 Aligned color texture on the 3D geometric model. Fig. 14 14 The Kamakura Great Buddha with the color texture image. 1044

3 [16] 9 10 11 12 M 10 11 13 14 5. Canny 3 3 3 2 3 2 3 M CREST [1] vol.16, no.6, pp.29 32, 1998. [2] vol.4, no.4, pp.623 630, Dec. 1999. [3]Y. Sato, M.D. Wheeler, and K. Ikeuchi, Object shape and reflectance modeling from observation, Proc. ACM SIGGRAPH 97, In Computer Graphics Proceedings, Annual Conference Series 1997, pp.379 387, ACM SIGGRAPH, Aug. 1997. [4]K. Nishino, Y. Sato, and K. Ikeuchi, Eigen-texture method: Appearance compression based on 3D model, Proc. Computer Vision and Pattern Recognition 99, vol.1, pp.618 624, June 1999. [5]I. Sato, Y. Sato, and K. Ikeuchi, Acquiring a radiance distribution to superimpose virtual objects onto a real scene, IEEE Trans Visualization and Computer Graphics, vol.5, no.1, pp.1 12, Jan. 1999. [6]M.D. Elstrom and Philip W. Smith, Stereo-based registration of multi-sensor imagery for enhanced visualization of remote environments, Proc. 1999 IEEE International Conference on Robotics & Automation, pp.1948 1953, 1999. [7]I. Stamos and P.K. Allen, Integration of range and image sensing for photorealistic 3D modeling, Proc. 2000 IEEE International Conference on Robotics and Automation, pp.1435 1440, 2000. [8]P. Viola and W.M. Wells III, Alignment by maximization of mutual information, International J. Computer Vision, vol.24, no.2, pp.137 154, 1997. [9]H. Lensch, W. Heidrich, and H.-P. Seidel, Automated texture registration and stitching for real world models, Pacific Graphics 00, pp.317 326, Oct. 2000. [10]H. Lensch, W. Heidrich, and H.P. Seidel, Hardwareaccelerated silhouette matching, SIGGRAPH Sketches, 2000. [11]M.D. Wheeler, Automatic modeling and localization for object recognition, Technical Report (Ph.D. Thesis), CMU-CS-96-188, School of Computer Science, Carnegie Mellon University, Oct. 1996. [12]M.D. Wheeler and K. Ikeuchi, Sensor modeling, probabilistic hypothesis generation, and robust localization for object recognition, IEEE Trans. Pattern Anal. & Mach. Intell., vol.17, no.3, March 1995. [13] D-IIvol, J83-D-II, no.2, pp.525 534, Feb. 2000. [14]P. Debevec, D.J. Taylor, and J. Malik, Modeling and rendering architecture from photographs; A hybrid geometry and image-base approach, Proc. SIG- GRAPH 96, pp.11 20, 1996. 1045

2002/6 Vol. J85 D II No. 6 [15]P. Debevec, Y. Yu, and G. Borshukov, Efficient view-dependent image-based rendering with projective texture-mapping, 9th Eurographics workshop on rendering, pp.105 116, 1998. [16]D. Miyazaki, T. Ooishi, T. Nishikawa, R. Sagawa, K. Nishino, T. Tomomatsu, Y. Takase, and K. Ikeuchi, The Great Buddha project: Modelling cultural heritage through observation, VSMM2000 (6th International Conference on Virtual Systems and Multimedia), pp.138 145, 2000. [17]J.F. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. & Mach. Intell., vol.8, no.6, 1986. [18]P.J. Besl and N.D. McKay, A method for registration of 3-D shapes, IEEE Trans. Pattern Anal. & Mach. Intell., vol.14, no.2, pp.239 256, 1992, [19] 3 1998. M 4. M σ = 10[mm] L2 ρ(z) = z2 2 Tukey { (1 (1 zs/s 2 2 ) 3 )/s z s <s ρ(z)= 1/s otherwise z 2 s = z 2 /σ 2 s =3 Huber { ρ(z) = z 2 s = z 2 /σ 2 0.5zs 2 z s <s s z s 0.5s 2 otherwise s =1.5 Geman-McClure (A 1) (A 2) (A 3) (A 4) (A 5) ρ(z) = z2 /2 1+z 2 (A 6) Welsch ρ(z) = σ2 2 [1 exp(z/σ)2 ] (A 7) Lorentzian ρ(z) = σ2 2 log(1 + (z/σ)2 ) (A 8) 13 4 26 8 27 1991 1995 2000 1993 1999 VSMM2000 11 Mark Damon Wheeler 1989Tulane BSE 1996 CMU Ph.D. in Computer Science Apple Computer, Inc. Cyra Technologies, Inc. 1973 1978 MIT CMU 1996 ICCV-90CVPR- 91AIJ-92-97IEEE R&A -98 OSAIEEEFellow 1046