A Hybrid Monte Carlo Method for Accurate and Efficient Subsurface - - PowerPoint PPT Presentation

A Hybrid Monte Carlo Method for Accurate and Efficient Subsurface Scattering

Li, Pellacini, Torrance Cornell University

Subsurface Scattering

• Looks good

without subsurface with subsurface

[Jensen et al. ‘02]

Subsurface Scattering

directional- diffuse behavior uniform- diffuse behavior

Optically thin/thick materials

translucent transparent

• ptical thickness = “size”/mfp

thick thin appearance

Previous work

• Accurate for all materials, but inefficient

– Monte Carlo path/light tracing

• Efficient, but inaccurate for most materials

– First-order approximation [H&K93] – Diffusion approximation [Stam95] – Jensen at el. BSSRDF approximation [Jen01,Jen02] – Shell Texture Functions [Chen04]

Goal

• Accurate and Efficient for all materials

– As accurate as Monte Carlo – More efficient than Monte Carlo

• Hybrid algorithm

– Monte Carlo to capture directional-diffuse behavior – Dipole approx. to capture uniform-diffuse behavior

Hybrid method

• Isotropic core region

– 1 mfp below surface mfp isotropic core region directional- diffuse behavior uniform- diffuse behavior

Hybrid method

• Monte Carlo path-trace until core region

– Check for distance to surface using kd tree lookup mfp isotropic core region directional- diffuse behavior uniform- diffuse behavior

Hybrid method

• Determine kud constant to conserve energy

– k < 1 in most cases, k = 0 in regions of high curvature mfp isotropic core region directional- diffuse behavior uniform- diffuse behavior

Hybrid method

• Use dipole approx. for uniform-diffuse

mfp isotropic core region directional- diffuse behavior uniform- diffuse behavior

Monte Carlo path tracing solution

• =

n i

• i

i i

• i

i

x x S x x S ) , ; , ( ) , ; , (

• r

r r r

Jensen et al. BSSRDF approximation

) , ; , ( ) , ; , ( ) , ; , (

1

• i

i d

• i

i

• i

i

x x S x x S x x S

• r

r r r r r + +

• First-order approx.

Dipole-diffusion approx.

Comprehensive BSSRDF model

) , ; , ( ) , ; , ( ) , ; , ( ) , ; , (

• i

i ud

• i

i ud

• i

i dd

• i

i

x x S x x k x x S x x S

• r

r r r r r r r

• +

+

• Directional-diffuse

Uniform-diffuse Isotropic core

Comparison with pure Monte Carlo

• Key insight: use dipole approx. when

appropriate

• Same Accuracy

– Photons contributes to uniform diffuse behavior only when entering core region – Otherwise contributes to directional-diffuse, i.e. angular dependence is well represented

• Efficiency

– MC methods are inefficient when many scattering events are needed – Use dipole approx. in this case

Comparison with Jensen et al.

• Jensen et al. approximations come from

– One scattering event for directional-diffuse – Uniform-diffuse behavior always present, i.e. k = 1

• Inaccurate for optically-thin

– Multiple scattering before entering core region – Often no uniform-diffuse behavior

Results – Armadillo

Monte Carlo Hybrid Jensen et al. 246 min 33 min 10 min

Results – Thick Dragon

Monte Carlo Hybrid Jensen et al. 1992 min 209 min 45 min

Results – Thin Dragon

Monte Carlo Hybrid Jensen et al. 1328 min 191 min 46 min

Conclusion

• Accurate and Efficient Subsurface Scattering

– Extend accuracy to optically-thin materials – Maintain efficiency compared to full simulation – Explanation of artifacts introduced in other approx.

Future work

• Increase efficiency further

– Hierarchical estimation [Jensen et al. 2002] – Speed up distance-to-surface calculation

• Extend to more materials

– Inhomogeneous materials – Layered materials

• Comprehensive model

– Introduce more accurate refraction distribution