Quick survey about PRT Valentin JANIAUT KAIST (Korea Advanced Institute of Science and Technology)
Transcript of 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]