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

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Presentation on theme: "A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University."— Presentation transcript:

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 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 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) Dragon7200K Buddha8800K Venus631K

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)

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!


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