A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped

Objects

Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van

Reeth

University of HasseltBelgium

Subsurface Scattering

All non-metallic objects Examples: wax, skin, marble, fruits, ...

Traditional Reflection Model Subsurface scattering

Images courtesy of Jensen et al. 2001

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

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

Diffusion Equation

Diffusion Equation

Boundary Conditions

Diffusion termSource term

Stopping term

•Large amount of memory in 3D•Badly approximates the surface•Impractical!

Overview

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Finite-Differencing (FD)

FD but… 1th order surface approximation Allows coarser grid O(h2) accurate everywhere! Badly approximates high curvature regions Still requires quite some memory

Embedded Boundary Discretization

Adaptive Grid Refinement

Discretization: example

FD vs. EBD

FD yields instabilities near the boundary EBD results in a consistent solution

FD EBD

Adaptive Grid Refinement

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

Results

Material Scale Time (sec)

Marble 5mm 444

Marble 10mm 295

Milk Mix 10mm 105

Milk Mix 20mm 62

Marble Mix 20mm 205

Marble Mix 100mm 85

Results (2)

Model Depth #tris Mem (MB)

Prep(sec)

Src(sec)

Solve(sec)

Tot(sec)

Dragon 7 200K 38.3 16.1 5.0 29.8 50.9

Buddha 8 800K 61.0 72.8 8.2 16.0 97

Venus 6 31K 32.4 3.1 1.8 83.1 88

Monte-Carlo Comparison

Jensen et al. Our method Monte-Carlo

Monte-Carlo Comparison

Jensen et al. Our method Monte-Carlo

Monte-Carlo Comparison

Jensen et al. Our method Monte-Carlo

Chromatic bias in source

Highly exponential falloff for opaque objects

Requires small cells

Workaround: use irradiance at the surface as source

Distance (mm)

Ave

rage

col

or

Monte-Carlo Comparison

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

Thank you!

Acknowledgements• tUL impulsfinanciering

• Interdisciplinair instituut voor Breed-BandTechnologie

Subsurface Scattering

Jensen vs. Multigrid

Jensen Visibility

Fine-coarse

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

Overview

Outline Construct volumetric grid Discretize diffusion eq. Solve using multigrid

Finite-Differencing (FD)

Overview

Outline Construct volumetric grid Discretize diffusion eq. Solve using multigrid

Finite-Differencing (FD)

-4

1

1

11

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