Download - Quick survey about PRT Valentin JANIAUT KAIST (Korea Advanced Institute of Science and Technology)
Quick survey about PRT
Valentin JANIAUT
KAIST (Korea Advanced Institute of Science and Technology)
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Some Math before.
● Wavelet● Spherical Harmonic● Spherical Radial Basis Function
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Wavelet: How to compress signal
Goal: Express a function as a set of coefficients.
Sum of sinus and cosinus.
NO TIME (OR SPACE) RESOLUTION
Fourier transform restricted to cosinus.
Cut the signal into different window for better analysis.
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Wavelet: Intuitive approach
FEATURES
• Orthonormal basis
• Catch the high-frequency
• Quite complicate
• Used in JPEG-2000
• A lot of possible kernels
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Spherical Harmonic
FEATURES
• Spherical basis
• Catch large features
• Quite complicate
• Used in geology
• Use Legendre polynomial as kernel.
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Spherical Radial Basis Function
Gaussian Distribution
FEATURES
• Spherical basis
• Catch high and low frequency.
• Fairly simple
• Use Gaussian or Poison kernel
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What is PRT?
● A set of technique to pre-compute various function related to the Radiance Transfer.
How to integrate the rendering equation over large-scale lighting environment?
● Monte-Carlo Ray Tracing● Radiosity● Multi-pass rendering
No real-time
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Some key paper in this field
2002 Precomputed Radiance Transfer for Real-Time Rendering in dynamic, low-frequency lighting environment. [Sloan]
Clustered principal components for precomputed radiance transfer. [Sloan]All frequency shadows using non-linear wavelet lighting approximation. [Ng]
Precomputed Radiance Transfer: Theory and Practice SIGGRAPH05 Course All frequency interactive relighting of translucent objects with Single and Multiple Scattering. [Wang]
Importance sampling of products from illumination and BRDF using spherical radial basis functions. [Tsai]Real-time editing and relighting of homogeneous translucent materials. [Wang]
All-frequency Rendering of Dynamic, Spatially-Varying Reflectance. [Wang]
2005
2008
2010
2003
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An example of Transfer Matrix
Rendering Equation
Geometry relighting Image Relighting
B = TL
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Precomputed Radiance Transfer for Real-Time Rendering in
dynamic, low-frequency lighting environment.
● Use Spherical Harmonic to represent how an object scatter light.
LIMITS● No High-Frequency (too many SH
coeff.)● Only diffuse and glossy surface.
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Clustered principal components for precomputed radiance transfer
● Similar than the previous approach.● Add support for diffuse multiple
scattering
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All frequency shadows using non-linear wavelet lighting approximation
● Same framework than [SLOAN02]● Approximate the environment map in a
wavelet basis keeping only the largest terms (=non-linear approximation)
LIMITS● Rigid scene (but relighting is OK)● Only diffuse and glossy surface.
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All frequency interactive relighting of translucent objects with Single and Multiple Scattering.
● Add support for Diffuse Multiple Scattering in [Ng] framework.
with
T is precomputed into Wavelet like in [Ng].
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Importance sampling of products from illumination and BRDF using spherical radial basis functions.
● No transfer function, use directly precomputation of BRDF and the environment map into SRBF.
LIMITS● Support only
BRDF.● Needs more
data, but only one product at the Running time.
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Real-time editing and relighting of homogeneous translucent materials.
● Improved version of the previous article.
● Reading not done yet.
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All-frequency Rendering of Dynamic, Spatially-Varying Reflectance
● Proposed an unified technique to represent SVBRDF using SRBF.
● Using the micro-facet model.
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Back to our problem
€
L(ωo) = D L(ω i)T(ω i)Ω∫ S(ω i,ωo)cosθ idω i
€
L(ωo) = D L jj =1
N
∑ ˜ T (ξ j ,λ j ) G j (ω i)Ω∫ S(ω i,ωo)cosθ idω i
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Current solution
€
S(ω i,ωo) Implemented using marschner model.
Extract the SRBF coefficient using L-BFGS-B solver like
[Tsai08]
DOES NOT SOLVE THE HAIR GEOMETRY DEPENDANT
TERMS
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Better approach
● Find a way to pre-compute the different terms of the equation using SRBF.
● Look to the visibility map● Look to PRT techniques with support to
geometry modification
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Papers to read
● Local, deformable precomputed radiance transfer [Sloan05]
● Generalized wavelet product integral for rendering dynamic glossy objects [Sun06]
● Real-time soft shadows in dynamic scenes using spherical harmonic exponentiation [Ren06]
● Real-time, all-frequency shadows in dynamic scenes [Annen08]