Quick survey about PRT
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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

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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.

NO TIME (OR SPACE) RESOLUTION

Fourier transform restricted to cosinus.

Cut the signal into different window for better analysis.


Wavelet: Intuitive approach

FEATURES

  • Orthonormal basis

  • Catch the high-frequency

  • Quite complicate

  • Used in JPEG-2000

  • A lot of possible kernels


Spherical Harmonic

FEATURES

  • Spherical basis

  • Catch large features

  • Quite complicate

  • Used in geology

  • Use Legendre polynomial as kernel.


Spherical Radial Basis Function

FEATURES

  • Spherical basis

  • Catch high and low frequency.

  • Fairly simple

  • Use Gaussian or Poison kernel

Gaussian Distribution


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

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

Rendering Equation

Geometry relighting

Image Relighting

B = TL


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

  • Similar than the previous approach.

  • Add support for diffuse multiple scattering


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.

  • 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.

  • 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.

  • Improved version of the previous article.

  • Reading not done yet.


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


Current solution

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

  • 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

  • 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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