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Quick survey about PRT. Valentin JANIAUT KAIST (Korea Advanced Institute of Science and Technology). Some Math before. Wavelet Spherical Harmonic Spherical Radial Basis Function. Wavelet: How to compress signal. Goal: Express a function as a set of coefficients. Sum of sinus and cosinus.

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Quick survey about PRT

Valentin JANIAUT

KAIST (Korea Advanced Institute of Science and Technology)


Some math before
Some Math before.

  • Wavelet

  • Spherical Harmonic

  • Spherical Radial Basis Function


Wavelet how to compress signal
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.


Wavelet intuitive approach
Wavelet: Intuitive approach

FEATURES

  • Orthonormal basis

  • Catch the high-frequency

  • Quite complicate

  • Used in JPEG-2000

  • A lot of possible kernels


Spherical harmonic
Spherical Harmonic

FEATURES

  • Spherical basis

  • Catch large features

  • Quite complicate

  • Used in geology

  • Use Legendre polynomial as kernel.


Spherical radial basis function
Spherical Radial Basis Function

FEATURES

  • Spherical basis

  • Catch high and low frequency.

  • Fairly simple

  • Use Gaussian or Poison kernel

Gaussian Distribution


What is prt
What is PRT?

  • A set of technique to pre-compute various function related to the Radiance Transfer.

Problem

How to integrate the rendering equation over large-scale lighting environment?

  • Monte-Carlo Ray Tracing

  • Radiosity

  • Multi-pass rendering

No real-time


Some key paper in this field
Some key paper in this field

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]

2002

2003

2005

2008

2010


An example of transfer matrix
An example of Transfer Matrix

Rendering Equation

Geometry relighting

Image Relighting

B = TL


Precomputed radiance transfer for real time rendering in dynamic low frequency lighting environment
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.


Clustered principal components for precomputed radiance transfer
Clustered principal components for precomputed radiance transfer

  • Similar than the previous approach.

  • Add support for diffuse multiple scattering


All frequency shadows using non linear wavelet lighting approximation
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.


All frequency interactive relighting of translucent objects with single and multiple scattering
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].


Importance sampling of products from illumination and brdf using spherical radial basis functions
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.


Real time editing and relighting of homogeneous translucent materials
Real-time editing and relighting of homogeneous translucent materials.

  • Improved version of the previous article.

  • Reading not done yet.


All frequency rendering of dynamic spatially varying reflectance
All-frequency Rendering of Dynamic, Spatially-Varying Reflectance

  • Proposed an unified technique to represent SVBRDF using SRBF.

  • Using the micro-facet model.


Back to our problem
Back to our problem Reflectance


Current solution
Current solution Reflectance

Implemented using marschner model.

Extract the SRBF coefficient using L-BFGS-B solver like [Tsai08]

DOES NOT SOLVE THE HAIR GEOMETRY DEPENDANT TERMS


Better approach
Better approach Reflectance

  • 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


Papers to read
Papers to read Reflectance

  • 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]


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