A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom...
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Transcript of A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom...
![Page 1: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/1.jpg)
A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped
Objects
Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van
Reeth
University of HasseltBelgium
![Page 2: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/2.jpg)
Subsurface Scattering
All non-metallic objects Examples: wax, skin, marble, fruits, ...
Traditional Reflection Model Subsurface scattering
Images courtesy of Jensen et al. 2001
![Page 3: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/3.jpg)
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
![Page 4: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/4.jpg)
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
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Diffusion Equation
Diffusion Equation
Boundary Conditions
Diffusion termSource term
Stopping term
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•Large amount of memory in 3D•Badly approximates the surface•Impractical!
Overview
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Finite-Differencing (FD)
![Page 7: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/7.jpg)
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
![Page 8: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/8.jpg)
Discretization: example
![Page 9: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/9.jpg)
FD vs. EBD
FD yields instabilities near the boundary EBD results in a consistent solution
FD EBD
![Page 10: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/10.jpg)
Adaptive Grid Refinement
![Page 11: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/11.jpg)
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
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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
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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
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Monte-Carlo Comparison
Jensen et al. Our method Monte-Carlo
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Monte-Carlo Comparison
Jensen et al. Our method Monte-Carlo
![Page 16: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/16.jpg)
Monte-Carlo Comparison
Jensen et al. Our method Monte-Carlo
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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
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Monte-Carlo Comparison
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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
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Thank you!
Acknowledgements• tUL impulsfinanciering
• Interdisciplinair instituut voor Breed-BandTechnologie
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Subsurface Scattering
![Page 22: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/22.jpg)
Jensen vs. Multigrid
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Jensen Visibility
![Page 24: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/24.jpg)
Fine-coarse
![Page 25: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/25.jpg)
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
![Page 26: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/26.jpg)
Overview
Outline Construct volumetric grid Discretize diffusion eq. Solve using multigrid
Finite-Differencing (FD)
![Page 27: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/27.jpg)
Overview
Outline Construct volumetric grid Discretize diffusion eq. Solve using multigrid
Finite-Differencing (FD)
-4
1
1
11
![Page 28: A Computational Approach to Simulate Light Diffusion in Arbitrarily Shaped Objects Tom Haber, Tom Mertens, Philippe Bekaert, Frank Van Reeth University.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649cc95503460f94991aeb/html5/thumbnails/28.jpg)
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