Master Thesis - Computer Graphics and Visualization - TU Delft

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9.2 ERPT mutation Energy Redistribution Path Tracer (ERPT) 98 (a) (b) Figure 9.2: High correlation between mutations in a mutation chain cause distinct errors. (a) Correlation between lens mutations cause sharp shadows. (b) Correlation between caustic mutations cause splotchy caustics. apparent errors in the final image. The type of visible errors also depend on the distribution of energy within the feature. For example, a local optimum in the energy distribution of a feature results in a small region within the feature that is easy to find through mutations but hard to escape. An important example of this are paths in corners (see figure 9.3). The shown feature is relatively large thus most mutations will result in valid light transport paths. However, the energy is very unevenly distributed over the feature. The further the first path vertex lies from the second vertex, the smaller will be the energy flowing over this path. This is mainly due to the cosine term in the rendering equation on the angle between the normal of the horizontal surface and the connection edge. A consequence is a local optimum in the energy distribution around the unconnected path (unbroken line) in figure 9.3. Therefore, mutation chains will tend to mutate towards this local optimum and will have a hard time escaping the corner. Actually, the real problem here is not the local optimum within the feature, but the fact that the total energy of the feature is quite small. Each mutation chain has a fixed amount of energy to redistribute. All this energy will be distributed over paths within a single feature. If the total feature energy is very small, the probability of generating a mutation chain for this feature is also small, but if one is generated, all chain energy is distributed over this low energy feature. If many low energy features are present in the scene, the result is that only a few such features appear in the image, but they will seem to be oversampled and too bright. In the example case, this becomes visible as bright splotchy errors in corners. Figure 9.4 shows an example of such errors. This shows that not only the size of the features, but also the energy distribution within the features determines the kind of errors in the resulting image.
Energy Redistribution Path Tracer (ERPT) 9.2 ERPT mutation Figure 9.3: Mutations have a hard time escaping small corners due to a local optimum in mutation acceptance probabilities. Image space feature Figure 9.4: Splotchy errors in the corners due to low energy feature. We use ERPT to compute an image, so it seems natural to look at feature properties in image space. The feature energy E(Φ) is the amount of energy reaching the image plane along the feature paths. This energy is distributed over the pixels in the image plane. However, a feature does not contribute equally to all image pixels. The image space contribution of a feature is defined by the distribution of feature energy over the image plane. Let us say 99
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Unbiased physically based rendering
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c○ 2010 Dietger van Antwerpen. Co
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ii memory-footprint independent of
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Contents Preface iii Contents v Lis
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CONTENTS CONTENTS Bibliography 131
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List of Figures List of Figures x 7
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List of Tables 5.1 Test scenes . .
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Chapter 1 Introduction Since the in
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Introduction 1.1 Summary of Contrib
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Part I Preliminaries 5
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2.1 Rendering equation Unbiased Ren
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2.3 Unbiased Monte Carlo estimate U
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2.5 Importance sampling Unbiased Re
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2.7 BiDirectional Path Tracing Unbi
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2.7 BiDirectional Path Tracing Unbi
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2.9 Metropolis Light Transport Unbi
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2.9 Metropolis Light Transport Unbi
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2.10 Energy Redistribution Path Tra
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Chapter 3 3.1 Introduction GPGPU Mo
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GPGPU 3.3 Memory Hierarchy divergin
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GPGPU 3.3 Memory Hierarchy (1 trans
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GPGPU 3.5 Parallel scan Algorithm 3
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4.1 GPU ray tracing Related Work 34
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4.2 Unbiased rendering Related Work
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Chapter 5 The Problem Statement In
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The Problem Statement 5.1 Related w
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Chapter 6 6.1 Introduction Hybrid T
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Hybrid Tracer 6.2 Hybrid architectu
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Page 78 and 79: 7.5 Results Path Tracer (PT) 58 sam
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Page 82 and 83: 7.5 Results Path Tracer (PT) 62 Mil
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Page 89 and 90: Streaming BiDirectional Path Tracer
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Page 114 and 115: 9.2 ERPT mutation Energy Redistribu
Page 124 and 125: 9.3 GPU ERPT Energy Redistribution
Page 143 and 144: Chapter 10 Comparison In this secti
Page 145 and 146: Comparison 10.1 Performance Million
Page 147 and 148: Comparison 10.2 Convergence (a) (b)
Page 149 and 150: Chapter 11 Conclusions and Future W
Page 151 and 152: Bibliography [1] Timo Aila and Samu
Page 153 and 154: BIBLIOGRAPHY BIBLIOGRAPHY [25] Jare
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Page 159 and 160: Appendix B Sample probability When
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Appendix E BDPT Algorithm This appe
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BDPT Algorithm E.2 Algorithm Figure
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BDPT Algorithm E.2 Algorithm Algori
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Appendix F MLT Mutations This appen
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MLT Mutations F.1 Acceptance probab
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MLT Mutations F.2 Algorithm Algorit
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Master Thesis - Computer Graphics and Visualization - TU Delft

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