Miyazaki-3DForum dvi

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きよあつあさま
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BRDF http://www.cvl.iis.u-tokyo.ac.jp/ Abstract In order to create a photorealistic VR model, we have to record the appearance of the object from dierent directions under dierent illuminations.

1 BRDF Abstract In order to create a photorealistic VR model, we have to record the appearance of the object from dierent directions under dierent illuminations. In this paper, we propose a method which renders photorealistic images from small size of data. First, we separates the images of the object into diuse reection component and specular reection component by using circular polarizers. Then, we estimates the parameters of reection model for each components. Finally, we compressed the dierence between the input images and the rendered images by using wavelet transform. At the rendering stage, we rst calculate the diuse and specular reection images from the reection parameters, then add the dierence decompressed by wavelet inverse transform into the calculated reection images, and nally obtain the photorealistic image of the object. 1. Sato [9] Nishino 1 Wavelet Texture: BRDF Compression by using Daubechies Wavelet, Reection Model, and Circular Polarizer Daisuke Miyazaki, Takushi Shibata, and Katsushi Ikeuchi Institute of Industrial Science, The University oftokyo Keywords: Daubechies wavelet, circular polarization, Torrance-Sparrow model, BRDF, image compression, VR model Wavelet compression (a) Photo (b) Reflection model (c) Our result (5%) 1: (a) (b) (c) [6] Shibata [10] Nishino Eigen-Texture [5] Furukawa

2 1: MPEG Nishino (Eigen-Texture [5]) (KL ) Furukawa [3] Vasilescu (Tensor-Texture [12]) N Wang [13] out-of-core Ma [4] Lambertian Phong Nishino [6] Lambertian Torrance-Sparrow Sato [9] Lambertian Torrance-Sparrow Shibata [10] Lambertian Torrance-Sparrow (Wavelet-Texture) Lambertian Torrance-Sparrow [3] Vasilescu Tensor-Texture [12] N Wang out-ofcore [13] Ma [4] 1 N outof-core Lambertian Phong Torrance-Sparrow 1 1(a) 1(b) 1(b) 1(c)

Range sensor Light source Object Image sensor Polarizer Rotary

waveplate Right circular polarized light [observed from

waveplate Diffuse reflection Unpolarized light Right circular

3 Range sensor Light source Object Image sensor Polarizer Rotary table 2: Right circular polarizer Linear polarizer 1/4 waveplate Right circular polarized light [observed from emitting direction] Specular reflection Linear polarizer 1/4 waveplate Diffuse reflection Unpolarized light Right circular polarizer Left circular polarized light [observed from emitting direction] 4: Alignment, merging, polygon reduction 3: (1) I c = I d c + I s c (c = fr G Bg) (1) I I d I s \c" 3.2. [1] 4

$I o I on I d I s I on I o I on = I d (2) I o = I d + I s (3) I d I s I d = I on (4) I s = I o ; I on (5) 90 90 5 \(n)" n (a) (b) (c) 2) 5: (a) (b) (c) Light source L Surface$

4 I o I on I d I s I on I o I on = I d (2) I o = I d + I s (3) I d I s I d = I on (4) I s = I o ; I on (5) \(n)" n (a) (b) (c) 2) 5: (a) (b) (c) Light source L Surface normal θ i N α Bisector θr H Object surface View 6: Lambertian I d = K d (N L) (6) = K d cos i (7) I d K d N L i 6 K d K d R K d G K d B Torrance-Sparrow [11] Torrance- V

Sparrow (8) I s = K s exp ; 2 (8) cos r 2 2 I s K s

= L + V (11) kl + Vk N L V H K s R K s G K s B

Wavelet (a) (b) (c) (d) 8: : (a), (b) (a), (c) 8,

5 Sparrow (8) I s = K s exp ; 2 (8) cos r 2 2 I s K s r 2) 2) 4) 6 K s r cos r = N V (9) cos = N H (10) H = L + V (11) kl + Vk N L V H K s R K s G K s B Levenberg-Marquardt (8) 5. Wavelet-Texture 7(a) 7(b) (a) (b) (c) 7: : (a), (b), (c) Images Level 0 Array Wavelet Level 1 Level 2 Wavelet (a) (b) (c) (d) 8: : (a), (b) (a), (c) 8, (d) (c) 8 7(c) 7(c) [2] Gabor Haar Daubechies Daubechies Haar Gabor Daubechies a% 8 MPEG MPEG

MPEG (7) (8) 6. 6.1. 9(b) 9(c) 10 RGB 6.2. PSNR (peak signal-to-noise ratio) PSNR db 40dB 20dB Intensity 200 150 100 50 0 Pixel position Input Wavelet texture (1.

6 MPEG (7) (8) (b) 9(c) 10 RGB 6.2. PSNR (peak signal-to-noise ratio) PSNR db 40dB 20dB Intensity Pixel position Input Wavelet texture (1.5%) Model-based texture 10: Wavelet-Texture (1.5% ) PSNR [db] specular diffuse Compression ratio [%] 11: PSNR PSNR (PSNR) 11 50% 80dB 50% 0 2% 40dB 12 12(a) 100% 50% 5% PSNR 11 40dB 1.5% PSNR 40dB 0% PSNR 30dB

7 2) 2) 2) (a) (b) (c) 9: : (a), (b), (c) Wavelet-Texture 5% 2) 2) 2) (a) (b) (c) 12: : (a), (b) 5%, (c) 1.5% 6.3. Eigen-Texture [5] (i) 13(a)(b)(e)(f) 13(c)(d)(g)(h) 13(a)(c)(e)(g) 2% 13(b)(d)(f)(h) 26% 13(a)(b)(c)(d) 13(e)(f)(g)(h) 26% PSNR 51 PSNR 46 13(b)(d)(f)(h) 2% PSNR 38 PSNR 33 13(a)(c)(e)(g) 7.

(a) (b) (c) 2% 26% 2% Image-based Texture 2% (i) Input 2% 16) 16 26% 16) 16 8) (e) 26% Wavelet Texture 26% 16) 16 (d) 8) 16) 16 8) (f) (g) 8) (h) 図

(e)(f)(g)(h) レンダリング画像と入力画像との差分であるといえる今回の実験では Lambertian モデル TorranceSparrow モデル Daubechies ウェーブレットを用いて十分満足のいく結果が得られたしかし現在

線偏光板にはそれぞれ長所と短所があるのでそれらを組み合わせて効果的な反射成分分離方法を見いだすことも重要であろう謝辞本研究の一部は文部科学省知的資産の電子的な保存活用を支援するソフトウェア基盤技術の構築事業の助成により行われたアラインメン 7] を使用した

関して猪狩壮文および川上玲から多数の助言を頂いた記して謝意を表す参考文献 1] M. Born and E. Wolf, Principles of optics, Pergamon Press, London, 1959. 2] I.

$Ikeuchi, and M. Sakauchi, \Appearance based object modeling using texture database: acquisition compression and rendering," Proc.$ $Ouhyoung, \Level-of-detail representation of bidirectional texture functions for realtime rendering," Proc.$ $Ikeuchi, \Eigentexture method: appearance compression and synthesis based on a 3D model," IEEE Trans. Pattern Analysis and Machine Intelligence, vol.$

8 (a) (b) (c) 2% 26% 2% Image-based Texture 2% (i) Input 2% 16) 16 26% 16) 16 8) (e) 26% Wavelet Texture 26% 16) 16 (d) 8) 16) 16 8) (f) (g) 8) (h) 図 13: 画像ベースの手法と提案手法との比較 (i) 入力画像 (a)(b)(e)(f) 画像ベースの手法の結果 (c)(d)(g)(h) 提案手法の結果 (a)(c)(e)(g) 圧縮率 2% の結果 (b)(d)(f)(h) 圧縮率 26% の結果 (a)(b)(c)(d) レンダリング結果 (e)(f)(g)(h) レンダリング画像と入力画像との差分であるといえる今回の実験では Lambertian モデル TorranceSparrow モデル Daubechies ウェーブレットを用いて十分満足のいく結果が得られたしかし現在より精度の高い反射モデルやウェーブレットが提案されているのでそれらを採用することも今後検討していきたいまた今回物体を一方向のみに回転させてサンプリングを行ったが今後視点を二方向に回転し光源を二方向に回転してサンプリングを行うことを考えているまた円偏光板と直線偏光板にはそれぞれ長所と短所があるのでそれらを組み合わせて効果的な反射成分分離方法を見いだすことも重要であろう謝辞本研究の一部は文部科学省知的資産の電子的な保存活用を支援するソフトウェア基盤技術の構築事業の助成により行われたアラインメン 7] を使用したマージングには佐川立昌らのソフトウェア 8] を使トには大石岳史らのソフトウェア用したカメラキャリブレーションには運天弘樹大久保亮および富士通株式会社のソフトウェアを使用したなおカメラキャリブレーションには阪野貴彦および川上玲の協力を頂いたまた研究に関して猪狩壮文および川上玲から多数の助言を頂いた記して謝意を表す参考文献 1] M. Born and E. Wolf, Principles of optics, Pergamon Press, London, ] I. Daubechies, Ten lectures on wavelets, Society for Industrial and Applied Mathematics, Philadelphia, ] R. Furukawa, H. Kawasaki, K. Ikeuchi, and M. Sakauchi, \Appearance based object modeling using texture database: acquisition compression and rendering," Proc. Eurographics Workshop on Rendering, pp. 257{266, ] W. Ma, S. Chao, Y. Chuang, C. Chang, B. Chen, and M. Ouhyoung, \Level-of-detail representation of bidirectional texture functions for realtime rendering," Proc. Symposium on Interactive 3D Graphics and Games, pp. 187{194, ] K. Nishino, Y. Sato, and K. Ikeuchi, \Eigentexture method: appearance compression and synthesis based on a 3D model," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 23, pp. 1257{1265, ] K. Nishino, Z. Zhang, and K. Ikeuchi, \Determining re ectance parameters and illumination distribution from a sparse set of images for viewdependent image synthesis," Proc. IEEE Int'l Conf. Computer Vision, vol. 1, pp. 599{606, ] T. Oishi, A. Nakazawa, R. Kurazume, and K. Ikeuchi, \Fast simultaneous alignment of multiple range images using index images," Proc.

9 Int'l Conf. 3-D Digital Imaging and Modeling, pp. 476{483, [8] R. Sagawa, K. Nishino, and K. Ikeuchi, \Adaptively merging large-scale range data with reectance properties," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 3, pp. 392{405, [9] Y. Sato, M. D. Wheeler, K. Ikeuchi, \Object shape and reectance modeling from observation," Proc. ACM SIGGRAPH 1997, pp. 379{387, [10] T. Shibata, T. Takahashi, D. Miyazaki, Y. Sato, and K. Ikeuchi, \Creating photorealistic virtual model with polarization based vision system," Proc. SPIE, vol. 5888, pp. 25{35, [11] K. E. Torrance and E. M. Sparrow, \Theory for o-specular reection from roughened surfaces," J. Optical Society of America, vol. 57, no. 9, pp. 1105{ 1114, [12] M.A.O. Vasilescu and D. Terzopoulos, \Tensortextures: multilinear image-based rendering," ACM Trans. Graphics (Proc. ACM SIGGRAPH 2004), vol. 23, no. 3, pp. 336{342, [13] H. Wang, Q. Wu, L. Shi, Y. Yu, N. Ahuja, \Outof-core tensor approximation of multi-dimensional matrices of visual data," ACM Trans. Graphics (Proc. ACM SIGGRAPH 2005), vol. 24, no. 3, pp. 527{535, 2005.

Vol. 44 No. SIG 9(CVIM 7) ) 2) 1) 1 2) 3 7) 1) 2) 3 3) 4) 5) (a) (d) (g) (b) (e) (h) No Convergence? End (f) (c) Yes * ** * ** 1

Vol. 44 No. SIG 9(CVIM 7) ) 2) 1) 1 2) 3 7) 1) 2) 3 3) 4) 5) (a) (d) (g) (b) (e) (h) No Convergence? End (f) (c) Yes * ** * ** 1 Vol. 44 No. SIG 9(CVIM 7) July 2003, Robby T. Tan, 1 Estimating Illumination Position, Color and Surface Reflectance Properties from a Single Image Kenji Hara,, Robby T. Tan, Ko Nishino, Atsushi Nakazawa,