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]