A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects

1. A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University of Hasselt Belgium

2. Subsurface Scattering • All non-metallic objects • Examples: wax, skin, marble, fruits, ... Traditional Reflection Model Subsurface scattering Images courtesy of Jensen et al. 2001

3. Previous Work • Monte-Carlo volume light transport • Accurate, but slow for highly-scattering media • Analytical dipole model [Jensen01] • Inaccurate (semi-infinite plane, no internal visibility) • Fast (basis for interactive methods) • Inherently limited to homogeneous media • Multigrid [Stam95] • Simple Finite Differencing • Only illustrative examples in 2D • Our method extends on this work

4. Goals • Simulate subsurface scattering • Accurate for arbitrarily shaped objects • Capable of resolving internal visibility • Heterogeneous media • Varying material coefficients • E.g. Marble • Only highly scattering media

5. Diffusion Equation Diffusion Equation Stopping term Source term Diffusion term Boundary Conditions

6. 1 1 -4 1 1 Overview Finite-Differencing (FD) • Large amount of memory in 3D • Badly approximates the surface • Impractical!

7. Adaptive Grid Refinement Embedded Boundary Discretization • FD but… • 1th order surface approximation • Allows coarser grid • O(h2) accurate everywhere! • Badly approximates high curvature regions • Still requires quite some memory

8. Discretization: example

9. FD vs. EBD • FD yields instabilities near the boundary • EBD results in a consistent solution FD EBD

10. Adaptive Grid Refinement

11. Implementation • Preprocessing (prep) • Construction of volumetric grid • Adaptive mesh refinement • Source term computation (src) • Visibility tests to light sources • Attenuation • Solve using multigrid • Visualization Implemented on a pentium 4 1.7 Ghz with 512 MB RAM

12. Results

13. Results (2)

14. Monte-Carlo Comparison Jensen et al. Our method Monte-Carlo

15. Monte-Carlo Comparison Jensen et al. Our method Monte-Carlo

16. Monte-Carlo Comparison Jensen et al. Our method Monte-Carlo

17. Chromatic bias in source • Highly exponential falloff for opaque objects • Requires small cells • Workaround: use irradiance at the surface as source Average color Distance (mm)

18. Monte-Carlo Comparison

19. Conclusion • Contributions • Multigrid made practical in 3D • Embedded boundary discretization • Adaptive Grid Refinement • Heterogeneous materials • Limitations • Grid size • Assumptions of the diffusion eq. • Future Work • More efficient subdivision scheme • Perceptual metrics

20. Thank you! • Acknowledgements • tUL impulsfinanciering • Interdisciplinair instituut voor Breed-BandTechnologie

21. Subsurface Scattering

22. Jensen vs. Multigrid

23. Jensen Visibility

24. Fine-coarse

25. Adaptive Mesh Refinement • Three-point interpolation scheme • Implies several constraints • Neighboring cells cannot differ by more than one level • Cells neighboring a cut-cell must all be on the same level

26. Overview • Outline • Construct volumetric grid • Discretize diffusion eq. • Solve using multigrid • Finite-Differencing (FD)

27. 1 1 -4 1 1 Overview • Outline • Construct volumetric grid • Discretize diffusion eq. • Solve using multigrid • Finite-Differencing (FD)

28. 1 1 -4 1 1 Overview • Outline • Construct volumetric grid • Discretize diffusion eq. • Solve using multigrid • Finite-Differencing (FD) • Requires large amount of memory in 3D • Badly approximates the surface • Impractical!