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 ModelSubsurface 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 Boundary Conditions Diffusion term Source term Stopping term

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

7.  FD but…  1th order surface approximation  Allows coarser grid  O(h 2 ) accurate everywhere!  Badly approximates high curvature regions  Still requires quite some memory Embedded Boundary Discretization Adaptive Grid Refinement

8. Discretization: example

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

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 MaterialScaleTime (sec) Marble5mm444 Marble10mm295 Milk Mix10mm105 Milk Mix20mm62 Marble Mix20mm205 Marble Mix100mm85

13. Results (2) ModelDepth#trisMem (MB) Prep (sec) Src (sec) Solve (sec) Tot (sec) Dragon7200K38.316.15.029.850.9 Buddha8800K61.072.88.216.097 Venus631K32.43.11.883.188

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

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

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

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

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. Overview  Outline Construct volumetric grid Discretize diffusion eq. Solve using multigrid  Finite-Differencing (FD) -4 1 1 11

28. 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! -4 1 1 11