3 3 3 Knecht (2-3fps) AR [3] 2. 2 Debevec High Dynamic Range( HDR) [4] HDR Derek [5] 2. 3 [6] 3. [6] x E(x) E(x) = 2π π 2 V (x, θ i, ϕ i )L(θ

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1 (MIRU212) RGB-D {ikeda,charmie,saito}@hvrl.ics.keio.ac.jp, sugimoto@ics.keio.ac.jp RGB-D Lambert RGB-D 1. Augmented Reality AR [1] AR AR 2 [2], [3] [4], [5] [6] RGB-D RGB-D RGB-D [2]

2 3 3 3 Knecht (2-3fps) AR [3] 2. 2 Debevec High Dynamic Range( HDR) [4] HDR Derek [5] 2. 3 [6] 3. [6] x E(x) E(x) = 2π π 2 V (x, θ i, ϕ i )L(θ i, ϕ i ) cos θ i sin θ i dθdϕ, (1) L(θ i, ϕ i ) (θ i, ϕ i ) cos θ i sin θ i dθ i dϕ i E(x) V (x, θ i, ϕ i ) x (θ i, ϕ i ) V = V = 1 x x (θ r, ϕ r ) u i(θ r, ϕ r ) (θ i, ϕ i ) (θ r, ϕ r ) (Bidirectional Reflectance Distribution Function: BRDF) i(θ r, ϕ r ) = k 2π π 2 V (θ i, ϕ i )R(θ i, ϕ i, θ r, ϕ r ) L(θ i, ϕ i ) cos θ i sin θ i dθdϕ, (2) k k R(θ i, ϕ i, θ r, ϕ r ) BRDF Lambert BRDF R d i(θ r, ϕ r ) = k 2π π 2 V (x, θ i, ϕ i )R d L(θ i, ϕ i ) cos θ i sin θ i dθdϕ (3) 2 θ i ϕ i N

3 i(u) = = V n (x)r d L n cos θ n S n L n, (4) i(u) u V n (x) n x R d L n k n θ n z n S n = V n (x)r d cos θ n L n S n N < = M L n. i = SL i(u 1 ) S 11 S 1N. =.. S.. mn i(u M ) S M1 S MN L 1.. L N (5) (5) [7], [8] (5) L n V n (x) cos θ n R d R d R d V n (x) u i (u) i (u) = R d L n cos θ n (6) (4) R d i(u) N i (u) = L n N j=1 L V n (x) cos θ n (7) j cos θ j R d (7) L n L n N j=1 L j cos θ j R d V n (x) cos θ n 3 4. RGB-D V n (x) cos θ n 3. 2 x E in (x) L E in (x) = L n cos θ n (8) (1) x E out (x) E out (x) = V n (x)l n cos θ n (9) V n (x) x n x u i in (u) E in (x) u i out (u) E out (x) E in (x) E out (x) i out (u) 4. i out (u) = i in (u) E out(x) E in (x) (1) RGB-D 3 V n (x) cos θ n V n (x) cos θ n 3 RGB RGB 3 3

otherwise d obj if d obj d bg > τ d d diff = (12) otherwise τ d diff a obj = d diff (13) RGB RGB RGB RGB c

4 2 V n (x) cos θ n L L RGB 4 (c obj, c bg, d obj, d bg ) 2 c, d RGB obj, bg diff c obj if c obj c bg > τ c c diff = (11) otherwise d obj if d obj d bg > τ d d diff = (12) otherwise τ d diff a obj = d diff (13) RGB RGB RGB RGB c diff d diff 3 3 a shadow = c diff ddiff (14) a obj a shadow d obj V n (x) cos θ n 4. 2 V n (x) cos θ n 3 V n (x) cos θ n V n (x), 3 x n V n (x) = 2 V n (x) = V n (x) 3 V n (x) = 1 3 V n (x) = 1

5 V n (x) = 1 cos θ n 3 x n θ n. 5.,, (4) (5) 4 Box 7 [6] Box Box V n (x) cos θ n Box RGB-D 5 2 RGB-D Microsoft Kinect < = θ < = 7 5 < = ϕ < θ (Box, Duck2, Hemisphere) 7 (Combined) Box ( ) 5 2 RGB-D V n (x) V n (x) = 5. 3 Ground truth 5 3 Box Ground truth 5 Ground truth Real scene 2 Real scene 2 Box 2 Box Duck2 2 Box Duck2 Box RGB-D

6 4. V n (x) Hemisphere Box 2 Combined Duck2 Box Duck2 Duck2 V n (x) 5. 4 Box Duck2 2 1 Box Duck2 V n (x) 3(c) 2 3(a) (b) Hemisphere Box, Combined (Duck2 Hemisphere ) Hemisphere 6. RGB-D RGB-D V n (x) V n (x)., [9] [1] R. Azuma, A survey of augmented reality, Presence: Teleoperators and Virtual Environments, 6 (1997). [2], VRSJ, 4, 4, pp

7 5 (1999). [3] M. knecht, et al., Differential instant radiosity for mixed reality, in Proc. ISMAR (21). [4] P. Debevec, Rendering synthetic objects into real scenes: Bridging traditional and aimagebased graphics with global illumination and high dynamic range photography, in Proc. ACM SIGGRAPH, pp (1998). [5] N. derek et al. Light Factorization for Mixed- Frequency Shadows in Augmented Reality, in Proc. ISMAR (211). [6], 41 SIG1(CVIM1) pp.31-4(2). [7] Gillm R.E, W. Murray M.H. Wright, Practical Optimization, Academic Press, London, UK(1981). [8] Coleman, R.F, Y. Li, A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables, SIAM Journal on Optimization, 6, 4, pp (1996). [9], CVIM pp.21-28(22).

情報処理学会研究報告 IPSJ SIG Technical Report Vol.2014-CVIM-190 No /1/24 RGB-D 1 1 *1 Relighting with Dynamic Light Environments Using an RGB-D Camera

情報処理学会研究報告 IPSJ SIG Technical Report Vol.2014-CVIM-190 No /1/24 RGB-D *1 *1 *1 Relighting with Dynamic Light Environments Using an RGB-D Camera RGB-D *1 *1 *1 Relighting with Dynamic Light Environments Using an RGB-D Camera Takuya Ikeda *1 Francois de Sorbier *1 and Saito Hideo *1 Abstract RGB-D GPU 10fps Keywords : Relighting, Lambertian model,