Our approach enables unbiased multiple importance sampling...
1
Bailey Miller 1* Iliyan Georgiev 2* Wojciech Jarosz 1 1 Dartmouth College, 2 Autodesk *authors with equal contributions Our approach enables unbiased multiple importance sampling in heterogeneous media. A null-scattering path integral formulation of light transport Unbiased rendering of heterogeneous media uses null-collision methods to generate free flight distances and estimate transmittance. Challenge: Null-collision methods employ black-box rejection sampling algorithms such as delta tracking or ratio tracking. These algorithms do not provide path pdfs, making their combination via multiple importance sampling (MIS) difficult. Our Approach: We derive a path integral formulation of light transport from the null- scattering radiative transfer equation (RTE). We then cast null-collision methods as path sampling techniques with known pdfs, which enables their straightforward MIS combination. Previous Work: MIS in piecewise homogeneous media: [Krivenak et al. 2014], [Wilkie et al. 2014], [Georgiev et al. 2013] Spectral tracking (derived from null RTE, forgoes complete MIS): [Kutz et al. 2017] MIS through tabulated sampling: [Szirmay-Kalos et al. 2017], [Gamito 2018] Classical RTE [Chandrasekhar 1960] Unable to adjust density. Only can compute transmittance analytically in simple media, Recursive estimation of the volume rendering equation can be done via a series of direction ωi and distance samples ti: Null RTE [Galtier et al. 2013] Able to add fictitious particles. Always can compute transmittance analytically. Classical path integral Considers real scattering only Evaluates heterogeneous transmittance Our null-scattering path integral Considers real and null scattering Evaluates simple homogeneous transmittance ω 0 ω 2 ω 4 t 1 t 3 t 5 ω 0 t 1 t 2 ω 3 t 4 t 5 t 6 t 8 t 9 ω 7 0XOWLSOH VFDHULQJ 6LQJOH VFDHULQJ 5HIHUHQFH ,QGHSHQGHQW WUDFNLQJ 6SHFWUDO WUDFNLQJ Spectral MIS (ours) Spectral+NEE MIS (ours) Independent tracking Spectral tracking Spectral MIS (ours) Spectral+NEE MIS (ours) Single scattering Multiple scattering RMSE 0.045 LTUV 4.33M Time 252s \ RMSE 0.088 LTUV 16.0M Time 237s RMSE 0.089 LTUV 16.5M Time 234s RMSE 0.074 LTUV 12.0M Time 275s RMSE 0.069 LTUV 10.5M Time 270s RMSE 0.041 LTUV 3.91M Time 267s RMSE 0.037 LTUV 3.02M Time 273s RMSE 0.032 LTUV 2.31M Time 275s μ t μ s Our path integral formulation allows us to combine unbiased null-collision techniques and their spectral variants through MIS into more robust volumetric light transport estimators. Project page: References: Subrahmanyan, Chandrasekhar.1960. Radiative Transfer. Dover Publications. Manuel Gamito. 2018. Path Tracing in Production: Path Tracing the Framestorian Way. In ACM SIGGRAPH 2018 Courses. ACM, New York, NY, USA, Article 15. Iliyan Georgiev, Jaroslav Křivánek, Toshiya Hachisuka, Derek Nowrouzezahrai, and Wojciech Jarosz. 2013. Joint Importance Sampling of Low-Order Volumetric Scattering. ACM Transactions on Graphics (Proc. SIGGRAPH Asia) 32, 6 (Nov. 2013). Peter Kutz, Ralf Habel, Yining Karl Li, and Jan Novák. 2017. Spectral and Decomposition Tracking for Rendering Heterogeneous Volumes. ACM Transactions on Graphics (Proc. SIGGRAPH) 36, 4 (July 2017). Jaroslav Křivánek, Iliyan Georgiev, Toshiya Hachisuka, Petr Vévoda, Martin Šik, Derek Nowrouzezahrai, and Wojciech Jarosz. 2014. Unifying Points, Beams, and Paths in Volumetric Light Transport Simulation. ACM Transactions on Graphics (Proc. SIGGRAPH) 33, 4 (July 2014). László Szirmay-Kalos, Iliyan Georgiev, Milán Magdics, Balázs Molnár, and Dávid Légrády. 2017. Unbiased Estimators to Render Procedurally Generated Inhomogeneous Participating Media. Computer Graphics Forum (Proc. Eurographics) 36, 2 (2017). Alexander Wilkie, Sehera Nawaz, Mark Droske, Andrea Weidlich, and Johannes Hanika. 2014. Hero wavelength spectral sampling. Computer Graphics Forum (Proc. Eurographics Symposium on Rendering) 33, 4 (June 2014). along connection from camera from light Unidirectional sampling Next-event estimation Equiangular sampling Bidirectional path tracing (t=0,s=3) Come to our talk to learn more! Tuesday, 9 - 10:30 am in Room 152. x 2 x 3 x 4 ≡ x r 2 T (x 2 , x 3 )G (x 2 , x 3 ) μ s (x 2 )ρ m (x 2 ) ρ s (x 3 ) x 7 ≡ x r 3 x 5 μ s (x 2 )ρ m (x 2 ) ρ s (x 7 ) x 6 T (x 4 , x 5 ) T (x 5 , x 6 ) T (x 6 , x 7 ) G (x 4 , x 7 ) ≡ G (x r 2 , x r 3 ) μ n (x 5 ) μ n (x 6 )
Transcript of Our approach enables unbiased multiple importance sampling...
Bailey Miller1* Iliyan Georgiev2* Wojciech Jarosz1 1Dartmouth College, 2Autodesk *authors with equal contributions
Our approach enables unbiased multiple importance sampling in
heterogeneous media.
A null-scattering path integral formulation of light transport
Unbiased rendering of heterogeneous media uses null-collision methods to generate free flight distances and estimate transmittance. Challenge: Null-collision methods employ black-box rejection sampling algorithms such as delta tracking or ratio tracking. These algorithms do not provide path pdfs, making their combination via multiple importance sampling (MIS) difficult. Our Approach: We derive a path integral formulation of light transport from the null-scattering radiative transfer equation (RTE). We then cast null-collision methods as path sampling techniques with known pdfs, which enables their straightforward MIS combination. Previous Work: MIS in piecewise homogeneous media:
[Krivenak et al. 2014], [Wilkie et al. 2014], [Georgiev et al. 2013] Spectral tracking (derived from null RTE, forgoes complete MIS):
[Kutz et al. 2017] MIS through tabulated sampling:
[Szirmay-Kalos et al. 2017], [Gamito 2018]
Classical RTE [Chandrasekhar 1960]
Unable to adjust density. Only can compute transmittance
analytically in simple media,
Recursive estimation of the volume rendering equation can be done via a series of direction ωi and distance samples ti:
Null RTE [Galtier et al. 2013] Able to add fictitious particles. Always can compute transmittance analytically.
Classical path integral Considers real scattering only
Evaluates heterogeneous transmittance
Our null-scattering path integral Considers real and null scattering Evaluates simple homogeneous transmittance
ω0
ω2
ω4
t1t3
t5ω0 t1
t2 ω3
t4t5
t6t8
t9
ω70XOWLSOH�VFDࣚ
HULQJ
6LQJOH�VFDࣚHULQJ
0XOWLSOH�VFDࣚ
HULQJ6LQJOH�VFDࣚ
HULQJ
5HIHUHQFH ,QGHSHQGHQW�WUDFNLQJ 6SHFWUDO�WUDFNLQJ Spectral MIS (ours) Spectral+NEE MIS (ours)
Independent tracking
Spectral tracking Spectral MIS (ours)
Spectral+NEE MIS (ours)
Single scatteringM
ultiple scattering
RMSE 0.045 LTUV 4.33M Time 252s
\
RMSE 0.088 LTUV 16.0M Time 237s RMSE 0.089 LTUV 16.5M Time 234s RMSE 0.074 LTUV 12.0M Time 275s RMSE 0.069 LTUV 10.5M Time 270s
RMSE 0.041 LTUV 3.91M Time 267s RMSE 0.037 LTUV 3.02M Time 273s RMSE 0.032 LTUV 2.31M Time 275s
μtμs
Our path integral formulation allows us to combine unbiased null-collision techniques and their spectral variants through MIS into more robust volumetric light transport estimators.
Project page:References:Subrahmanyan, Chandrasekhar.1960. Radiative Transfer. Dover
Publications. Manuel Gamito. 2018. Path Tracing in Production: Path Tracing the
Framestorian Way. In ACM SIGGRAPH 2018 Courses. ACM, New York, NY, USA, Article 15.
Iliyan Georgiev, Jaroslav Křivánek, Toshiya Hachisuka, Derek Nowrouzezahrai, and Wojciech Jarosz. 2013. Joint Importance Sampling of Low-Order Volumetric Scattering. ACM Transactions on Graphics (Proc. SIGGRAPH Asia) 32, 6 (Nov. 2013).
Peter Kutz, Ralf Habel, Yining Karl Li, and Jan Novák. 2017. Spectral and Decomposition Tracking for Rendering Heterogeneous Volumes. ACM Transactions on Graphics (Proc. SIGGRAPH) 36, 4 (July 2017).
Jaroslav Křivánek, Iliyan Georgiev, Toshiya Hachisuka, Petr Vévoda, Martin Šik, Derek Nowrouzezahrai, and Wojciech Jarosz. 2014. Unifying Points, Beams, and Paths in Volumetric Light Transport Simulation. ACM Transactions on Graphics (Proc. SIGGRAPH) 33, 4 (July 2014).
László Szirmay-Kalos, Iliyan Georgiev, Milán Magdics, Balázs Molnár, and Dávid Légrády. 2017. Unbiased Estimators to Render Procedurally Generated Inhomogeneous Participating Media. Computer Graphics Forum (Proc. Eurographics) 36, 2 (2017).
Alexander Wilkie, Sehera Nawaz, Mark Droske, Andrea Weidlich, and Johannes Hanika. 2014. Hero wavelength spectral sampling. Computer Graphics Forum (Proc. Eurographics Symposium on Rendering) 33, 4 (June 2014).
along connectionfrom camera
from light
Unidirectional sampling
Next-event estimation
Equiangular sampling
Bidirectional path tracing (t=0,s=3)
Come to our talk to learn more! Tuesday, 9 - 10:30 am in Room 152.
x2x3
x4 ≡ xr2
T (x2, x3)G (x2, x3)μs(x2)ρm(x2)
ρs(x3)
x7 ≡ xr3
x5
μs(x2)ρm(x2)
ρs(x7)x6
T (x4, x5) T (x5, x6)T (x6, x7)
G (x4, x7) ≡ G (xr2 , xr3)
μn(x5)μn(x6)
