Importance Sampling using Spherical Radial Basis Functions

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Importance Sampling usingSpherical Radial Basis
Functions

• Student Ching-Zhen Jiang (???)
• Advisor Prof. Zen-Chung Shih

Department of Computer Science National Chiao
Tung University, Taiwan
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Outline

• Introduction
• Related Work
• Our Concept

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Introduction
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Introduction

• The goal of global illumination is to solve the
  rendering equation Kajiya 1986
• Monte Carlo Technique
• To increase efficiency, importance sampling is a
  powerful technique.

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Introduction
Uniform Sampling
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Introduction
Importance Sampling
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Introduction
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Environment map importance sampling
BRDF importance sampling

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Related Work
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Related Work BRDF importance sampling

• Analytical BRDF
• Shirley PhD thesis 1991
• Phong model
• Lafortune et al. 1994
• Modified Phong model

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Related Work BRDF importance sampling

• Data-measured BRDF
• Elliptical Gaussian Model
• Ward SIGGRPAH 1992
• Non-linear fitting
• Stochastic sampling method

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Related Work BRDF importance sampling

• Data-measured BRDF
• Multiple Cosine Lobes Model
• Lafortune et al. SIGGRAPH 1997
• Non-linear fitting
• Apply to Monte Carlo importance sampling
  efficiently
• Hard to approximate the complex BRDF by using his
  fitting process

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Related Work BRDF importance sampling

• Data-measured BRDF
• Multiple Cosine Lobes Model

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Related Work BRDF importance sampling

• Data-measured BRDF
• Matrix factorization
• Lawrence et al. SIGGRAPH 2004
• Project 4D BRDF into sum of products of 2D
  function dependent on view direction and 2D
  function dependent on light direction.

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Related Work BRDF importance sampling
Re-parameterization
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Related Work BRDF importance sampling
Factorization
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Related Work BRDF importance sampling
Factorization
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Related Work BRDF importance sampling

• Final factored BRDF representation is
• Need non-negative entries in factorization
  because interpreted as probabilities.
• SVD does not guarantee non-negativity.
• Non-Negative Matrix Factorization Lee99

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Related Work BRDF importance sampling

• Wavelet
• Matusik et al. SIGGRAPH 2003
• Lalonde PhD thesis 1997

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Related Work BRDF importance sampling

• Spherical Radial Basis Functions (SRBFs)
• Shr-Ching Weng et al. PhD thesis 2006

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Related Work BRDF importance sampling
Lighting Direction
Viewing Direction

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Related Work BRDF importance sampling
Viewing Direction
Weighted Sum
Generate Samples
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Related Work Environment map sampling

• According the brightness
• Cohen and Debevec 2001, Agarwal et al. 2003,
  Kollig and Keller 2003, Ostromoukhov 2004.
• Spherical Harmonics
• Ramamoorthi and Hanrahan 2002
• Used spherical harmonics to directly filter the
  environment map according to the BRDF
• Efficient only when the BRDF is smooth and
  non-specular

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Related Work product of BRDF and environment

• Wavelet Important Sampling
• Clarberg et al. SIGGRAPH 2005

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Related Work product of BRDF and environment

• Hierarchical Sampling
• Wavelet decomposes the original function into a
  hierarchical representation.
• Importance sampling is performed within each
  level in the hierarchical structure.
• The importance of each region can be determined
  by the magnitude of coefficients.

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Related Work product of BRDF and environment

• Importance Image Warping
• The warped maps can be pre-computed and stored in
  a kD-tree for efficient searching.

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Our Concept
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Our Concept
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Environment map importance sampling
BRDF importance sampling

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Our Concept

• Represent BRDF and lighting environment using
  scattered SRBFs.
• fit the scattering data on sphere without
  reparameterization
• Avoid artificial boundaries and distortions

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Our Concept

• Develop a sampling scheme to analyze the product
  of BRDF and lighting environment.
• The convolution of two SRBF kernels in some
  situation has a simple mathematical form
• Rotation invariant
• Be able to estimate the densities and generate
  sample at run-time.

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Our Concept

• The major computation cost for ray tracing is the
  visibility testing.
• Generate samples smarter based on some heuristic
  approach.