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1 The Great Buddha Project Λ1 Λ2 Λ2 Λ2 Λ3 Λ2 Λ1 Λ2 Λ3 ( (VR) VR (1) (2) (3) modeling-from-reality (MFR) The Great Buddha Project Digital archive of large-scale cultural heritage Ryo Kurazume Λ1 Ko Nishino Λ2 Ryusuke Sagawa Λ2 Takeshi Oishi Λ2 Yutaka Takase Λ3 Katsushi Ikeuchi Λ2 Λ1 Japan Science and Λ2 The University of Tokyo Λ3 CADCENTER, Inc Technology Corporation This paper presents an overview of our efforts in modeling the Great Buddha of Kamakura through observation. The Kamakura Great Buddha, built in the 13th Century, is one of the national treasures of Japan; of its height is about 12.4m, including its pedestal. Currently, the Buddha is standing in the open air. We have started this modeling as the kick-off step of our project to model Japanese cultural heritages by using the modeling-from-reality techniques that make virtual models of real objects through observing the real objects. Due to the size and the circumstance concerning the great Buddha, we have encountered several research issues. For geometric modeling, we have developed a simultaneous registration and parallel volumetric merging algorithms. We have constructed a CG model of the Main Hall of the Great Buddha, widely briefed its existence from the literature survey, and created a video of the Buddha, measured and constructed with our techniques, in the virtual Main Hall created through the literature survey. We have demonstrated the effectiveness of the algorithms as well as the importance of restoring cultural heritage through these techniques. 1

1 3 3 1. [14],[15] 2. [6],[10] 3. [11],[12] 4. [18] 2 1 12 12.

2 [14],[15] 2. [6],[10] 3. [11],[12] 4. [18] m Figure 1: [17] mm 12.5mm (1) (2) (3) modelingfrom-reality (MFR) [14],[15] MFR Stanford [8] IBM [3] Levoy 2

1 Cyrax 2400( 2) 100m mm Cyrax 2400 1 3 4

3 Bernardini Rushmeier 5m 15m MFR Figure 2: Cyrax 2400 CG Cyrax 2400( 2) 100m mm Cyrax Table 1: Cyrax 2400 Range 100[m] Accuracy 6 [mm] Resolution 0.25 [mm] at 50[m] N. of points Figure 3: [13] 2 3

Figure 4: [2] : Euclidian [7] closed form 3 Besl Kay ICP [4] [5] [1] 1 2 3 1 Cyrax for(each model)f for(eachmodel point)f for(each scene)f scene point = findpointmate(modelpoint); dist += computedist

4 Figure 4: [2] : Euclidian [7] closed form 3 Besl Kay ICP [4] [5] [1] Cyrax for(each model)f for(eachmodel point)f for(each scene)f scene point = findpointmate(modelpoint); dist += computedist (model point, scene point); g g step[model] = computestep(dist); g for(each model)f transform(model,step[model]); g model scene step 1 computestep M [14] M ComputeStep E(P )= 1 N X i2n ρ(z i (P )) (1) P model t 4 q P = (t; q) T N z i (P ) i 3 4

ρ E(P ) E(P ) 0 @E(P ) X @ρ @z i (P ) = =0 (2) @P @z i @P i2n w(z i ) w(z i )= 1 z i @ρ @z i

1+ 1 z 2 1 (5) 2 ff z i z i (P )=j R(q)x i + t y i j (6) R(q) P t x i y i model scene 4 z i P

5 ρ E(P ) E(P ) i (P ) = i2n w(z i ) w(z i )= 1 i ) X = i2n w(z i )z i (P random sample consensus [16] w(z i ) w(z) = 1+ 1 z 2 1 (5) 2 ff z i z i (P )=j R(q)x i + t y i j (6) R(q) P t x i y i model scene 4 z i i (P ) 2(x i + t y) 4x i (t y) (7) Figure 5: consensus [14] ,3 5

6 5. 8 marching-cubes algorithm[9] [14] Dual Pentium III 800MHz 1GB 8 PC CPU 16 PC PC PC 2 2. (2-1) PC (2-2) PC 6 1,2,3 PC1,2,3 x 1 PC1 2 PC2 PC 3 Figure 6: 7 PC PC PC 3 3. (3-1) (3-1) PC PC 2,3 Surface PC1 PC3 PC2 PC4 Octtree PC1 PC2 PC3,... Figure 7: PC PC 1 PC 6

7 PC 8 PC 2 CPU PC CAD 30 CG CG 11 Figure 9: Figure 10: Figure 8: D

Figure 11: CREST References [1] R. Benjemma and F. Schmitt. Fast global registration of 3D sampled surfaces using a multi-z-buffer technique. In Proc. Int. Conf.

Patt. Anal. Machine Intell., 18(5)540-547, May. 1996. [3] F.Bernardini and H.Rushmeier, The 3D Model Acquisition Pipeline Eurographics 2000. [4] P.J. Besl and N. D. McKay.

Image and Vision Computing, 10(3):145-155, Apr. 1992. [6] Y. Sato, M. D. Wheeler, and K.

8 Figure 11: CREST References [1] R. Benjemma and F. Schmitt. Fast global registration of 3D sampled surfaces using a multi-z-buffer technique. In Proc. Int. Conf. On Recent Advances in 3-D Digital Imaging and Modeling, pp , May [2] R. Bergevin, M. Soucy, H. Gagnon and D. Laurendeau. Towards a general multi-view registration technique. IEEE Trans. Patt. Anal. Machine Intell., 18(5) , May [3] F.Bernardini and H.Rushmeier, The 3D Model Acquisition Pipeline Eurographics [4] P.J. Besl and N. D. McKay. A method for registration of 3-D shapes. IEEE Trans. Patt. Anal. Machine Intell., 14(2): , Feb [5] Y. Chen and G. Medioni. Object modeling by registration of multiple range images. Image and Vision Computing, 10(3): , Apr [6] Y. Sato, M. D. Wheeler, and K. Ikeuchi, Object shape and reflectance modeling from observation, Proceedings of ACM SIGGRAPH 97, In Computer Graphics Proceedings, Annual Conference Series 1997, ACM SIGGRAPH, pp , August [7] A. Johnson and M. Hebert. Surface registration by matching oriented points. In Proc. Int. Conf. on Recent Advances in 3-D Digital Imaging and Modeling, pp , May [8] M. Levoy et. al. The Digital Michelangelo Project. In Proc. SIGGRAPH 00, pp [9] W.E. Lorensen, W.E. and H.E. Cline. Marching Cubes: a high resolution 3D surface reconstruction algorithm. In Proc. SIG- GRAPH96, pp [10] K.Nishino, Y.Sato and K.Ikeuchi, Eigen-Texture Method: Appearance Compression based on 3D Model, in Proc. of Computer Vision and Pattern Recognition 99, vol.1, pp , Jun., [11] 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, January [12] I. Sato, Y. Sato, and K. Ikeuchi, Illumination distribution from brightness in shadows: adaptive estimation of illumination distribution with unknown reflectance properties in shadow regions, Proceedings of IEEE ICCV 99, pp , September [13] G. Turk and M. Levoy. Zippered polygon meshes from range images. In Proc. of SIGGRAPH 94, pp , Jul [14] M. Wheeler, Y. Sato, and K. Ikeuchi, Consensus surfacs for modeling 3D objects from multiple range images, Proc. ICCV pp , Jan, [15] M. D. Wheeler and Katsushi Ikeuchi, Sensor Modeling, Probabilistic Hypothesis Generation, and Robust Localization for Object Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence,Vol. 17, No. 3, March [16] M.A. Fischler and R.C. Bolles,Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography, Communications of the ACM, Vol.16, No.24, [17] - -,Vol.12, No.6,pp ,1960 [18] :-)2001,1-B-(4),2001 8

proc.dvi

proc.dvi TVRSJ Vol.7 No.1, 2002 The Great Buddha Project Λ1 Λ2 Λ1 Λ1 Λ1 Λ3 The Great Buddha Project Digital archive of large-scale cultural heritage Katsushi Ikeuchi Λ1, Ryo Kurazume Λ2, Ko Nishino Λ1, Ryusuke