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A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects

Explore a novel computational method for simulating light diffusion in irregularly shaped objects with subsurface scattering. Discover how this approach extends on previous works to accurately resolve internal visibility and handle heterogeneous media such as marble. Learn about the implementation and results of this innovative technique using adaptive grid refinement and embedded boundary discretization.

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A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects

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  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!

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