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Second-Order Occlusion-Aware Volumetric Radiance Caching
Julio Marco1 Adrian Jarabo1 Wojciech Jarosz2 Diego Gutierrez1
1 Universidad de Zaragoza, I3A 2 Dartmouth College
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Second-Order Occlusion-Aware Volumetric Radiance Caching Julio Marco - - PowerPoint PPT Presentation
Second-Order Occlusion-Aware Volumetric Radiance Caching Julio Marco - - PowerPoint PPT Presentation
Second-Order Occlusion-Aware Volumetric Radiance Caching Julio Marco 1 Adrian Jarabo 1 Wojciech Jarosz 2 Diego Gutierrez 1 1 Universidad de Zaragoza, I3A 2 Dartmouth College 1 2 3 4 5 [Schwarzhaupt et al. 2012] 6 OUR METHOD L +
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≈
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≈
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[Schwarzhaupt et al. 2012]
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OUR METHOD
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?
L
L + ∆x · dL dx
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Related Work
- Photon-based methods
POINTS [Jensen and Christensen 98] [Knaus and Zwicker 11]
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[Jarosz et al. 11] [Jarosz et al. 11] BEAMS POINTS + BEAMS + PATHS [Krivanek et al. 14] [Bitterli and Jarosz 17] Higher-dimensional
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Related Work
Frequency and gradient-domain
- Frequency and first-order analysis
[Durand et al. 2005, Ramamoorthi et al. 2007]
- Media frequency analysis
[Belcour et al. 2014]
- Image-space gradients for MLT
[Lehtinen et al. 2013, Manzi et al. 2014]
- Gradient-domain path tracing methods
[Kettunen et al. 2015, Manzi et al. 2015]
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Related Work
- Irradiance/radiance caching methods
[Ward et al. 88] [Ward and Heckbert 91]
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Related Work
- Irradiance/radiance caching methods
[Krivanek et al. 2005] [Krivanek et al. 2006]
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Related Work
- Irradiance/radiance caching methods
[Jarosz et al. 2008]
- Media gradients
è YES
- Occlusions
è NO
- Higher-order
è NO
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Related Work
[Jarosz et al. 2008]
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Related Work
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2nd order Occlusions
SURFACES MEDIA
[Jarosz et al. 2008] [Schwarzhaupt et al. 2012] [Jarosz et al. 2008]
✘
OURS
✘ ✘
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Radiance extrapolation
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Radiance extrapolation
Radiance value at x n-th translational derivative at x
TAYLOR EXPANSION
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Radiance extrapolation
TRUNCATED TAYLOR EXPANSION
Extrapolated value at x’ (first order) Error Actual value
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Radiance extrapolation
TRUNCATED TAYLOR EXPANSION
Extrapolated value at x’ (first order) Error Actual value
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Radiance extrapolation
Eigenvalues
- f Hessian
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Rλ1 Rλ2 Rλ3
Error threshold
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? L + ∆x · dL
dx
How to compute them?
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Derivative computation
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PHASE FUNCTION TRANSMITTANCE FORESHORTENING VISIBILITY INCOMING RADIANCE
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Derivative computation
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Ignored in gradient computation
[Jarosz et al. 2008]
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Derivative computation
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?
[Jarosz et al. 2008]
Ignored in gradient computation
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Derivative computation
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[Jarosz et al. 2008]
Ignored in gradient computation
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Derivative computation
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[Jarosz et al. 2008]
Ignored in gradient computation
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Derivative computation
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Gone!
Our method
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Derivative computation
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Our method
RAY MARCHING
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Derivative computation
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Our method
Triangle-to-medium form factor
For a single triangle
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Derivative computation
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Our method
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Derivative computation
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2D visualization of derivatives
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PENUMBRA OCCLUDER LIGHT SHADOW Ours SINGLE SCATTERING ROI
- Occ. Unaware
[Jarosz 2008] 1 0.1 Reference (finite diff.) Orientation Magnitude
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2D visualization of derivatives
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ROI Ours MULTIPLE SCATTERING PENUMBRA LIGHT OCCLUDER Magnitude 0.1 0.01
- Occ. Unaware
[Jarosz 2008] Reference (finite diff.) Orientation
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Results
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Statues – Render comparison
Reference [Jarosz et al. 2008] Ours
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Statues – Render comparison
Reference [Jarosz et al. 2008] Ours
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[Jarosz et al. 2008] Occlusion-unaware, 1st order metric Single scattering Multiple scattering
Statues – Cache distribution
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(TOP VIEW) (TOP VIEW)
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Statues – Cache distribution
Ours Occlusion-aware, 2nd-order metric Single scattering Multiple scattering
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(TOP VIEW) (TOP VIEW)
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Patio – Time performance
Our computational overhead
- Triangulation
- Hessian computation
+9%
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Patio – Time performance
Our computational overhead
- Triangulation
- Hessian computation
+9%
Ours (iso. cache) 135 min., 32k points
Equal-time
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Patio – Time performance
Our computational overhead
- Triangulation
- Hessian computation
+9%
[Jarosz et al. 2008] 136 min., 36k points
Equal-time
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Patio – Time performance
Our computational overhead
- Triangulation
- Hessian computation
+9%
Ours (aniso. cache) 94 min., 21k points
30% faster Same error threshold
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Equal-time comparison
Reference Path tracing [Jarosz et al. 2011] Progressive photon beams [Jarosz et al. 2008] Occlusion-unaware first-order Ours Second-order
- cclusion-aware
EQUAL TIME
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Future work
- Extend to support scattering from glossy materials
- Limited to finite light sources
- Extend to anisotropic media and heterogeneous materials
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Conclusions
- Computation of occlusion-aware media derivatives
- Second-order error metric for volumetric radiance caching
- … radiance derivatives useful for other applications!
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