Contents of Photorealistic Image Synthesis using Ray-bundles

1 Introduction

1.1 Global pass
1.2 Local pass.
1.3 Tone mapping

2 Global Illumination problem.

2.1 The rendering equation
2.2 Measuring the radiance.
2.3 The potential equation.
2.4 Measuring the potential
2.5 The rendering problem
2.5.1 Geometry of the surfaces
2.5.2 Bi-directional Reflection Distribution Functions
2.5.3 Lightsources
2.5.4 Measuring devices
2.6 Numerical solution of the rendering equation
2.6.1 Error measures for numeric techniques
2.6.2 Properties of the rendering equation
2.7 Classification of the solution techniques

3 Solution strategies for the global illumination problem

3.1 Inversion
3.2 Expansion.
3.2.1 Expansion of the rendering equation: gathering walks
3.2.2 Expansion of the potential equation: shooting walks
3.2.3 Merits and disadvantages of expansion methods
3.3 Iteration
3.3.1 Analysis of the iteration.
Error caused by the approximation of the transport operator
3.4 Analytical solution of the rendering equation.
3.4.1 Scenes with constant radiance
3.4.2 Scenes with constant reflected radiance

4 Finite-element methods for the Global Illumination Problem

4.1 Galerkin's method.
4.2 Point collocation method
4.3 Finite-element methods for the diffuse global illumination problem.
4.3.1 Geometric methods for form factor computation.
Discrete hemisphere algorithm and its variations.

5 Numerical quadrature for high dimensional integrals.

5.1 Monte-Carlo quadrature
5.2 Quasi-Monte Carlo quadrature
5.2.1 Error analysis for integrands of finite variation: Koksma-Hlawka inequality
5.2.2 Generation of the sample points
5.2.3 Generation of low-discrepancy sequences
5.3 Importance sampling
5.3.1 Generation of a random variable with a prescribed probability density
5.3.2 Importance sampling in quasi-Monte Carlo integration
5.3.3 Metropolis sampling

6 Random walk solution of the global illumination problem

6.1 Why should we use Monte-Carlo expansion methods?
6.2 Quasi-Monte Carlo quadrature for the rendering equation
6.2.1 Integrating functions of unbounded variation
Numerical evidence using simple functions
Numerical evidence for the rendering equation
6.3 Importance sampling for the rendering equation
6.3.1 BRDF sampling
BRDF sampling for diffuse materials
BRDF sampling for specular materials
6.3.2 Lightsource sampling
6.3.3 Sampling the lightsources in gathering random walks
6.3.4 Importance sampling in colored scenes
6.3.5 Multiple importance sampling
6.4 Handling infinite-dimensional integrals
6.4.1 Russian roulette
6.4.2 Russian roulette in quasi-Monte Carlo quadrature
BRDF sampling for materials of multiple reflection type
6.5 Review of random walk algorithms
6.5.1 Gathering-type random walk algorithms
Ray-casting
Visibility ray-tracing.
Distributed ray-tracing
Path-tracing
6.5.2 Shooting-type walk methods
Photon tracing.
Light-tracing
Random walks for the radiosity setting
6.5.3 Bi-directional random walk algorithms
Bi-directional path-tracing
Metropolis light transport
Photon-map.
Instant radiosity

7 Stochastic iteration solution of the global illumination problem

7.1 Why should we use Monte-Carlo iteration methods?
7.2 Formal definition of stochastic iteration.
7.2.1 Other averaging techniques
Self-correcting iteration.
7.3 Stochastic iteration for the diffuse radiosity
7.3.1 Stochastic radiosity
7.3.2 Transillumination radiosity
7.3.3 Randomly placed hemicubes
7.3.4 Stochastic ray-radiosity.
7.4 Definition of the random transport operator for the non-diffuse finite-element case
7.4.1 Single ray based transport operator

8 Simulating Light Transport using Ray-bundles

8.1 Reformulation of the rendering equation using finite-elements
8.2 Stochastic expansion using ray bundles.
8.2.1 Generating uniformly distributed points on the sphere
8.2.2 Simple Monte-Carlo, or quasi-Monte Carlo walks
8.2.3 Calculation of the image estimate
Bi-linear interpolation.
Phong integpolation.
8.2.4 Improved walking techniques
8.2.5 D-step iteration
8.3 Importance sampling for the evaluation of directional integrals
8.3.1 Application of the VEGAS algorithm
8.3.2 Application of Metropolis sampling
Variance reduction.
Mutation strategies
Generating an initial distribution and automatic exposure
8.3.3 Evaluation of the performance of the Metropolis method
Evaluation of the start-up bias
Starting from multiple seeds
Analysis of uniform random perturbations.
8.4 Stochastic iteration using ray-bundles
8.4.1 Can we use quasi-Monte Carlo techniques in iteration?.
8.5 Calculation of the radiance transport in a single direction.
8.5.1 Galerkin's method with piece-wise constant basis functions
Continuous algorithm with initial sorting: Local visibility map
Continuous algorithm without initial sorting: Global visibility map
Discrete algorithm with initial sorting: Global painter's algorithm
Discrete algorithm without initial sorting: software z-buffer
Discrete algorithm without initial sorting: exploitation of the hardware z-buffer
8.5.2 Analysis of the finite resolution problem of discrete methods
8.5.3 Point collocation method with piece-wise linear basis functions
Calculation of the irradiance at vertices
8.6 Handling sky-light illumination
8.7 Improving the efficiency
8.7.1 Self-correcting iteration
8.7.2 Preprocessing the small lightsources
Incoming first-shot of point lightsources
Smaller area lightsources
Diffuse shot
8.7.3 Adaptive importance sampling and resolution control in iteration
8.7.4 Reducing the power defect of the iteration.
8.7.5 Constant radiance step

9 Simulation results

9.1 Testing the walk method.
9.2 Testing stochastic iteration and self-correcting iteration
9.2.1 Self-correcting stochastic iteration
9.2.2 Self-correcting stochastic iteration with incoming first-shot

10 Conclusions.

10.1 Future improvements

BIBLIOGRAPHY

SUBJECT INDEX