Master Thesis - Computer Graphics and Visualization - TU Delft

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9.2 ERPT mutation Energy Redistribution Path Tracer (ERPT) 102 (a) (b) (c) (d) (e) (f) Figure 9.5: Original mutation strategy (a),(c),(e) vs. Improved mutation strategy (b),(d),(f). Computation times were similar for both strategies. Our improvement trades structural noise for more uniform noise, reducing visible artifacts. tation strategy proposed by Kelemen also mutate the length of the path. Therefore, it is not trivial to efficiently implement the mutation strategy from Kelemen on the GPU. How-
Energy Redistribution Path Tracer (ERPT) 9.3 GPU ERPT ever, by letting the perturbation size for the outgoing direction of a vertex depend on the incoming direction and the local BSDF of a vertex, the acceptance probability may be further increased. This seems especially beneficial for near-specular materials. Furthermore, in our implementation a specular vertex must remain specular after mutation. This results in smaller features, especially when complex caustics are present. Dropping this constraint will increase feature size even further, reducing speckles which are caused by difficult caustic features. 9.2.4 Filter For most mutation strategies, including ours, it is unavoidable that some scenes will contain high energy features with a small image space size. As discussed earlier, this may result in high energy speckles. One cause of speckles that is hard to completely prevent is that of floating point imprecisions. For example, in most ray tracing implementations, it is possible (although unlikely) for a ray to pass through two triangles at their connecting edge due to arithmatic imprecisions in the intersection computations. If the energy on such a path is redistributed, this may result in a feature consisting of only a single path causing a one-pixel sized speckle. In the original ERPT paper, consecutive sample filtering is used to solve this problem. The consecutive sample filter prevents a mutation chain from getting stuck to long at the same pixel. If it has been stuck at the same pixel for some fixed number of consecutive mutations, the mutation chain will stop contributing energy until it has moved away from the pixel. This filter reduces speckles, but makes the sampling method irreversibly biased. We use a simple post-processing filter to remove speckles. We compute an unbiased (progressive) ERPT image, and remove speckles if necessary. For each pixel, the filter works on a region of nearby pixels 2 . First, we compute the color intensity average and variance within the region. If the distance between the pixel’s intensity and the region’s average is at least twice the region’s variance, the pixel belongs to a speckle and is ignored. Instead, the region’s average color is used. 9.3 GPU ERPT 9.3.1 Overview In this section, we start with a short overview of our GPU ERPT implementation. The ERPT implementation is an extension of the TPPT implementation from chapter 7. Besides path tracing, an ERPT sampler also performs energy redistribution. Whenever a sampler finds a light transport path during path tracing, its energy is redistributed using a multiple of 32 mutation chains running in parallel. ERPT samplers are run in groups of 32 samplers. Each group maps to one GPU warp. During path tracing, each thread runs its own sampler, similar to the TPPT implementation. However, during energy redistribution, all threads in a warp work together on a single sampler from the sampler group, all other samplers in the group are temporarily suspended until energy redistribution for the one sampler is complete. 2 The region size depends on the maximum speckle size we want to remove. We used a region of 3 × 3 pixels around each pixel. 103
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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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Hybrid Tracer 6.3 Results 6.3.2 Hyb
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Hybrid Tracer 6.3 Results 6.3.3 Con
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Page 89 and 90: Streaming BiDirectional Path Tracer
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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
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Page 159 and 160: Appendix B Sample probability When
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Page 165 and 166: Appendix D PT Algorithm This append
Page 167 and 168: PT Algorithm D.3 Algorithm are used
Page 169 and 170: Appendix E BDPT Algorithm This appe
Page 171 and 172: 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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