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1 1 PC 2 Geometric and Photometric Integration System for Large Objects Ryusuke Sagawa Ko Nishino Ryo Kurazume Katsushi Ikeuchi The University of Tokyo Kyushu University Some researchers have begun projects to model Japanese cultural heritage objects. Some of Japanese cultural heritage objects are large, but their shapes may be intricate. Thus, the measurement becomes difficult and the large data set must be handled. We propose a new geometric and photometric integration framework of range images of those objects. First, we propose a new method which integrates photometric attributes as well as 3D geometric information. Next, we have developed the following methods by two different approach to build the detailed models of cultural heritages: 1. Parallel computation using a PC cluster. 2. Merging by adaptive resolution according to the data. 1 3 [2, 14, 13] [7,4,16] Wheeler [16] Wheeler 3 1

2 Lambertian inside surface outside PC surface Wheeler [16, 15] 3 surface (signed distance) 1: 0 (isosurface) marching cubes algorithm [9]( MC) MC 2 [1, 10] PC Wheeler Wheeler 1 PC 2 octree octree - x f (x) f (x) 0 ( 1) f (x) [8] N MC x f (x) 2 Wheeler Wheeler (consensus 3 surface algorithm) 4 5 f (x) x x 2

3 Normal vector of range image center point x' f(x') f(x) center point x 2D slice of octree closest surface point to x Range images surface 2: : 4: octree center point x' center point x 3: : k-d tree [6] SameSurface( p 0, n 0, p 1, n 1 )= { (1) True ( p 0 p 1 δ d ) (n 0 n 1 cosθ n ) False otherwise δ d θ n (consensus surface) ( 3) 2.2 Octree [4] Wheeler octree 0 1 ( 4) MC [9] ,3, MC 1 [15, 16] 3

4 5: LRS 3 6: LRS [8] LRS(laser reflectance strength) [15] LRS LRS [12] PC LRS PC LRS LRS 2 LRS LRS ( 6) LRS [8] 20kg [5]

5 surface Octree nodes center point x' PC2 center point x CPU1 CPU2... CPU3 CPU CPU1 CPU2 CPU3,... PC1 Data1 Data2 Data3 PC3 8: octree PC 7: 4. (4-1) PC (4-2) PC PC 2, (2-1) PC 4.3 (2-2) PC PC 7 1,2,3 PC1,2,3 x 1 PC1 2 PC2 PC GB OS PC PC PC 4 5

6 2D slice of a voxel edges of cubes for marching High curvature area n 2 n n _ n 3 1 n4 Neighboring range image points Approximated plane 9: n 5 octree 5.1 n n i n ( 9) n i n 5.2 2D slice of adaptive octree 10: octree MC ( ) ( ) ( ) - [8] octree marching cubes algorithm MC () MC 8 6

7 11: MC 1: # of Traversals Computation Time min min min min. MC 10 octree min. 2 PC MC octree ( ) ( ) 1 ( ) 6.2 MC 11 MC ( 11 ) A B A C Metro[3] LRS (B3) (A3) 6 8 PC (C3) LRS Minolta VIVID RGB PC PC VIVID 800MHz PentiumIII 1GB RGB 100BASE-TX Cyrax[5] 6.3 Minolta VIVID[11] Cyrax GB Cyrax Cyrax GB LRS MB 1.7GB

8 2: : # of points Time for Integration Mean Error (A) 3.0 million 61 min. N/A (B) 1.4 million 25 min mm (C) 1.7 million 30 min mm : 3 [1] D. Bartz and W. Straßer. Parallel construction and isosurface extraction of recursive tree structures. In Pro- ceedings of WSCG 98, volume III, Plzen, PC 2 [2] P.J. Besl and N.D. McKay. A method for registration of 3-d shapes. IEEE Trans. Patt. Anal. Machine Intell., 14(2): , Feb PC [3] P. Cignoni, C. Rocchini, and R. Scopigno. Metro: measuring error on simplified surfaces. Computer Graphics 2 Forum, 17(2): , June PC [4] Brian Curless and Marc Levoy. A volumetric method for 2 octree building complex models from range images. In Proc. SIGGRAPH 96, pages ACM, [5] [6] Jerome H. Friedman, Jon Bentley, and Raphael Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3): , [7] A. Hilton, A.J. Stoddart, J. Illingworth, and T. Windeatt. Reliable surface reconstruction from multiple range images. In Proceedings of European Conference on Com- puter Vision, pages , Springer-Verlag, [8] R. Kurazume, K. Nishino, Zhengyou Zhang, and Katsushi Ikeuchi. Simultaneous 2d images and 3d geometric model registration for texture mapping utilizing reflectance attribute. In Proc. The 5th Asian Conference (CREST) on Computer Vision, volume 1, pages , January

9 図 14: 統合処理によって生成された奈良大仏のモデル 図 15: 生成されたアチャナ仏とその周囲の壁のモデル [9] W. Lorensen and H. Cline. Marching cubes: a high resolution 3d surface construction algorithm. In Proc. SIGGRAPH 87, pages ACM, [10] P. Mackerras. A fast parallel marching-cubes implementation on the fujitsu ap1000. Technical report, Australian National University, TR-CS-92-10, [11] Minolta. Vivid 900 non-contact digitizer. [12] S.K. Nayar and M. Oren. Generalization of the lambertian model and implications for machine vision. International Journal of Computer Vision, 14: , [13] K. Nishino and K. Ikeuchi. Robust simultaneous registration of multiple range images. In Proc. of Fifth Asian Conference on Computer Vision ACCV 02, pages , Jan [14] K. Pulli. Multiview registration for large data sets. In Second Int. Conf. on 3D Digital Imaging and Modeling, pages , Oct [15] Mark D. Wheeler. Automatic Modeling and Localization for Object Recognition. PhD thesis, School of Computer Science, Carnegie Mellon University, [16] M.D. Wheeler, Y. Sato, and K. Ikeuchi. Consensus surfaces for modeling 3d objects from multiple range images. In Proc. International Conference on Computer Vision, January 図 13: 竜門石仏 光学的情報として RGB 値を用いた統合 処理結果 9

10 (A) (B) (C) (1) (2) (3) 図 16: 鎌倉大仏の統合結果: 列 A,B,C はそれぞれ 適応的統合を行わなかった場合 曲率のみを考慮した場合 曲率 と LRS 値の両方を考慮した場合である 行 1,2,3 はそれぞれ ワイヤフレーム表示 面表示 LRS 値を輝度値として 表示した場合である 最上段 最下段は枠で囲まれた大仏の額部分の拡大図である 10

2003 : ( ) :80226561 1 1 1.1............................ 1 1.2......................... 1 1.3........................ 1 1.4......................... 4 2 5 2.1......................... 5 2.2........................

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