3 3 Sampling and Modeling of Shape and Reflectance of 3-D Objects Ryo Furukawa, Hiroshi Kawasaki, Yasuaki Nakamura and Yutaka Ohsawa Abstract In this
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1 3 3 Sampling and Modeling of Shape and Reflectance of 3-D Objects Ryo Furukawa, Hiroshi Kawasaki, Yasuaki Nakamura and Yutaka Ohsawa Abstract In this paper, we developed a method for sampling and modeling reflectance of 3-D objects and performing real-time rendering of modeled objects. Our method can be used to render modeled objects from an arbitrary viewing direction with illuminations from point lights at any given place or with any illumination map. To achieve this goal, we developed a platform that can sample appearances of target objects with 4DOFs parameters of light and viewing directions. Light-dependent variations of sampled data were approximated using spherical harmonics functions as bases. To render a modeled object, we generated its appearance by synthesizing the effects of illuminations using spherical harmonics functions and by interpolating between sampled viewing directions. The appearance was then texture-mapped to the shape model. Using our method, we could represent reflectance properties of surfaces of 3-D objects that were parametrized by 4DOFs light and viewing directions. We also successfully rendered the modeled objects using programmable vertex/pixel shaders with real-time performance ) , TEL , TEL Faculty of information science, Hiroshima city university (3 4 1, Ozuka-higashi, Asaminami-ku, Hiroshima , Japan) Faculty of engineering, Saitama universiyt (255, Shimo-ohkubo, Sakura-ku, Saitama, Saitama , Japan) CPU 5fps 11)14) Vol. 60, No. 4, pp. 1 8 (2006) ( 1 ) 1
2 BRDF 3)5)8)10)12)17). BRDF Kauts McCool BRDF 2 BRDF 6)9) Chen 1) Ramamoorthi 11) Sloan (PRT) 14) Malzbender (PTM) 7) PTM (BTF) BTF 2 6 2) Sattler BTF 13) Suykens BTF 16) Sloan BTF (BRT) 15) BTF BTF 3 BTF Sloan BRT 15) Sloan BTF BRDF BTF 2 ( 2 ) Vol. 60, No. 4 (2006)
3 4 2)16) 3 BRDF BTF Debvec (2 ) 3) PTM 7) (2 ) Wood (2 ) 17) 3 (4 ) 1 5) 2 CCD CCD PC PC Image sampling platform. 2 Shape measurement with light sectioning method. (1) (2) (3) BTF T (i v, l, s, t, c), i v l (s, t) c {0, 1, 2} (R,G,B) 3 ( 3 ) 3
4 ) T M c m (i v, s, t, c)y m (l) m=1 Y m m M l i v, (s, t) c P M = P 2 P P = 5 Sloan 14) P P = 6,M = 36 PRT 14) (PCA) PCA PCA PCA (i v, s, t) c m k b k,m,c (1 < = k < = K) W k (i v, s, t) K i v (s, t) : T (i v, l, s, t, c) M m=1 k=1 K W k (i v, s, t)b k,m,c Y m (l)(1) m L(l, k, c) M m=1 b k,m,cy m (l) T (i v, l, s, t, c) K W k (i v, s, t)l(l, k, c) (2) k=1 T (i v, l, s, t, c) K l (1) (VDTM) 4) v v v v v (v) 0, 1, 2 (v) v V (v; 0),V (v; 1),V (v; 2) λ ι(λ) I(v; n) ι(v (v; n)) v v H(v; 0),H(v; 1),H(v; 2) H(v; n) H(v; n) v (v) (v) abc p abc a,b,c (α, β, γ) pbc, pca, pab α : β : γ (v) 4 ( 4 ) Vol. 60, No. 4 (2006)
5 v (B(v; 0), B(v; 1), B(v; 2)) H(v; n) B(v; n) I(v; n) H(v; n) 5. W k (i v, s, t), I(v; n), H(v; n), L(l, k, c) W k (i v, s, t) 2 L(l, k, c) k I(v; n) H(v; n) v v, l 3 2 I(v 0 ; n) 3 3 v 0 I(v 0 ; n) H(v 0 ; n) 3 P IX IV W V W L 2 3 I(v; n) H(v; n) (CPU) Step 1 PIX[c] 0, c = 0, 1, 2 Step 2 IV[n] I(v; n), n = 0, 1, 2. Step 3 WV[n] H(v; n), n = 0, 1, 2 Step 4 k = 0, 1,, K 1 Step 4.1 WL[k] 2 n=0 WV[n] W k (IV[n], s, t) Step 4.2 PIX[c] PIX[c]+WL[k] L(l, k, c), c = 0, 1, 2 Step 5 PIX[c] L(l, k, c) M m=1 b k,m,cy m (l) Step4.2 L(l, k, c) = ( 5 ) 5
6 ( 2 ) ( 4 ) 5 PCA. Weights obtained by PCA. 3. Sampled ancient mirror. 4. Obtained polygon mesh = M 6 2 = 36 CPU Intel Pentium4(2.0GHz) 2.0GB PC 11 PCA 1% 2 PCA W K 12, 256MB nvidia GeForceFX 5950 Ultra fps 60fps 6 ( 6 ) Vol. 60, No. 4 (2006)
7 (左側の点光源による照明.) (手前の点光源による照明.) 図 7 異なる視点からの描画結果 Rendered images with different viewpoints. および光源方向のパラメータを用いてすべて標本化し 各 視点における 2 次元の光源パラメータ空間を球面調和関 数基底によって表現した また 視点方向に関しては 標 (遠くの点光源による照明.) 本化した視点間を補間して 投影テクスチャマッピングに より描画する手法を提案した 提案した手法を ピクセル シェーダ機能を持ったビデオハードウェアを用いて実装し 実際に計測した 3 次元物体を実時間で描画可能であること を確認した 文 (近くの点光源による照明.) 図 6 異なる光源方向での描画結果 Rendered images with different light positions. 本論文で提案した見えに基づくモデルは 実時間描画のた めの BTF のモデルとしても利用できる 何種類かの BTF を標本化し 球面に貼り付けて描画した例を図 9 に示す それぞれの画像において BTF が視点および光源に依存し て正しく描画されていることがわかる 7. む す び 本論文では 3 次元形状物体の表面特性を獲得し 実時間 描画に適したモデルとして表現する手法を提案した これ を実現するため 我々は 実物体の見えを 4 自由度の視点 論 文 3 次元物体の形状 表面特性の獲得および表現手法 献 1 W.-C. Chen, J.-Y. Bouguet, M. H. Chu and R. Grzeszczuk. Light field mapping: Efficient representation and hardware rendering of surface light fields. In J. Hughes, SIGGRAPH 2002 Conference Proceedings, Annual Conference Series, pp , (2002). 2 K. Dana, B. V. Ginneken, S.Nayar and J. Koenderink, Reflectance and texture of real-world surfaces, ACM Transactions on Graphics, pp.1 34, (1999). 3 P. Debevec, T. Hawkins, C. Tchou, H.-P. Duiker, W. Sarokin and M. Sagar. Acquiring the reflectance field of a human face. In K. Akeley, Siggraph 2000, Computer Graphics Proceedings, pp , (2000). 4 P. E. Debevec, G. Borshukov and Y. Yu. Efficient view-dependent image-based rendering with projective texture-mapping. In 9th Eurographics Rendering Workshop, pp , (1998). 5 R. Furukawa, H. Kawasaki, R. Kawatsu, D. Miyazaki, K. Ikeuchi and M. Sakauchi. Appearance based object modeling using texture database: Acquisition, compression and rendering. In Rendering Techniques 2002 (Eurographics Workshop Proceedings), pp & 333, (2002). 6 J. Kautz and M. D. McCool. Interactive rendering with arbitrary brdfs using separable approximations. In Rendering Techniques (Eurographics Workshop Proceedings), pp , (1999). 7 T. Malzbender, D. Gelb and H. Wolters, Polynomial texture maps, Proceedings of SIGGRAPH 2001, pp , (2001). 8 W. Matusik, H. Pfister, A. Ngan, P. Beardsley, R. Ziegler and L. McMillan, Image-based 3d photography using opacity hulls, acm Transactions on Graphics, pp , (2002). (7) 7
8 15 P.-P. Sloan, X. Liu, H.-Y. Shum and J. Snyder, Bi-scale radiance transfer, ACM Trans. Graph., vol.22, no.3, pp , (2003). 16 F. Suykens, K. v Berge, A. Lagae and P. Dutre. Interactive rendering with bidirectional texture functions. In Proceedings of Eurographics 2003, pp , (2003). 17 D. N. Wood, D. I. Azuma, K. Aldinger, B. Curless, T. Duchamp, D. H. Salesin and W. Stuetzle. Surface light fields for 3D photography. In K. Akeley, Siggraph 2000, Computer Graphics Proceedings, pp , (2000). ( ) ( ) ( ) 8 : , 23 fps 60 fps Examples for measuring the rendering speed: the client areas of the windows were , the frame rates were approximately 23 fps for the per-pixel-view implementation and 60 fps for the per-object-view implementaton IEEE GIS ACM ( ) ( ) 9 BTF. Modeling and rendering of measured BTFs. 9 M. D. McCool, J. Ang and A. Ahmad, Homomorphic factorization of brdfs for high-performance rendering, Proceedings of SIG- GRAPH 2001, pp , (2001). 10 K. Nishino, Y. Sato and K. Ikeuchi. Eigen-texture method: Appearance compression based on 3D model. In IEEE Conf. on Comp. Vision and Patt. Recog, pp , (1999). 11 R. Ramamoorthi and P. Hanrahan. An efficient representation for irradiance environment maps. In SIGGRAPH 01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp , (2001). 12 R. Ramamoorthi and P. Hanrahan. A signal-processing framework for inverse rendering. In E. Fiume, SIGGRAPH 2001, Computer Graphics Proceedings, pp , (2001). 13 M. Sattler, R. Sarlette and R. Klein. Efficient and realistic visualization of cloth. In EGSR 03: Proceedings of the 14th Eurographics Symposium on Rendering, pp , (2003). 14 P.-P. Sloan, J. Kautz and J. Snyder, Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments, ACM Transactions on Graphics (TOG), pp , (2002). 8 ( 8 ) Vol. 60, No. 4 (2006)
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