ReSTIRについて

ReSTIRについての私的まとめ資料。
間違い等があれば，修正例と共にご指摘頂けると大変助かります。
資料は随時更新します。

Transcript

1. ～Reservoir Spatio-Temporal Importance Resampling～
2. https://www.youtube.com/watch?v=AQXRiP6XQdo
3. https://www.youtube.com/watch?v=Tk7Zbzd-6fs
4. https://dl.acm.org/doi/10.1145/3478512.3488613
5. • •
6. • •
7. • •
8. • •
9. • •
10. •
11. • • Big Wave
13. • 𝐼 𝐼 𝜀 • 𝜖 𝔼 𝐼 − 𝐼 = 𝜀
14. 𝐿𝑜 𝑥, 𝜔 = 𝐿𝑒 𝑥, 𝜔 + න Ω 𝑓𝑟 𝑥, 𝜔′, 𝜔 𝐿𝑖 𝑥, 𝜔 cos 𝜃 𝑑𝜔 Emissive BSDF =BRDF+BTDF Light 解析解が無い（答えが一意に定まらない）。 再帰的に書きなおすことが出来る。
15. • • • 𝐼 = 1 𝑁 ෍ 𝑖=1 𝑁 𝑓 𝑥𝑖 𝜌 𝑥𝑖 𝑓 𝑥𝑖 ：被積分関数 𝜌 𝑥𝑖 ：確率密度関数 𝑁：サンプル数
16. • • Importance Sampling • Stratified Sampling ( ) • Multiple Importance Sampling • Quasi Monte Carlo Method ( ) •
17. • • 𝑓 𝑥 𝜌 𝑥 𝑃 𝑋 ≤ 𝑥 𝑃 𝑥 𝑃−1 𝑢 𝑓 𝑥 ※レンダリングにおける具体的な例は[Pocol 2021]を参照。
18. • • • 𝑥 𝑓 𝑥 𝑎 𝑏 strata 0
23. • • • • • •
24. • • • • • 𝑤𝐵𝑆𝐷𝐹 𝑥 = 𝑝𝐵𝑆𝐷𝐹 𝑥 𝑝𝐵𝑆𝐷𝐹 𝑥 + 𝑝𝑙𝑖𝑔ℎ𝑡 𝑥 𝑤𝑙𝑖𝑔ℎ𝑡 𝑥 = 𝑝𝑙𝑖𝑔ℎ𝑡 𝑥 𝑝𝐵𝑆𝐷𝐹 𝑥 + 𝑝𝑙𝑖𝑔ℎ𝑡 𝑥
27. • • 𝑝 𝑀 𝑀 ≥ 1 𝐗 = 𝑋1 , ⋯ , 𝑋𝑀 𝑤𝑗 3. 𝐗 𝑤1 , ⋯ , 𝑤𝑀 𝑌 𝑤𝑗 = ො 𝑝 𝑋𝑗 𝑝 𝑋𝑗 を 𝑌 Ƹ 𝑝
28. • • 𝐼 = 1 𝑁 ෍ 𝑖=1 𝑁 𝑓 𝑌𝑖 Ƹ 𝑝 𝑌𝑖 ∙ 1 𝑀 ෍ 𝑗=1 𝑀 Ƹ 𝑝 𝑋𝑖𝑗 𝑝 𝑋𝑖𝑗 • 𝑓が Ƹ 𝑝 𝑝 • 𝑀 𝑁 補正項がくっついている
33. 𝑀
34. 𝑓 = 𝐹𝑟 𝐺 𝑉 𝐿𝑒 Ƹ 𝑝 = 𝐹𝑟 𝐺 𝐿𝑒 𝐹𝑟 𝐺 𝑉 𝐿𝑒 • • • 比較的軽量な候補サンプルが生成できる!!
36. • • • 𝑀 •
37. • • • • •
39. • 𝑀 • 𝑥1 , 𝑥2 , ⋯ , 𝑥𝑀 • 𝑀 • 𝑥1
40. • 𝑥1 𝑚 𝑥𝑚 • 𝑥𝑖 • 𝑥𝑖 𝑥𝑚+1 𝑤 𝑥𝑖 σ 𝑗=1 𝑚 𝑤 𝑥𝑗 𝑤 𝑥𝑚+1 σ 𝑗=1 𝑚+1 𝑤 𝑥𝑗
41. • 𝑥𝑚+1 𝑥𝑖 𝑤 𝑥𝑖 σ 𝑗=1 𝑚 𝑤 𝑥𝑗 1 − 𝑤 𝑥𝑚+1 σ 𝑗=1 𝑚+1 𝑤 𝑥𝑗 = 𝑤 𝑥𝑖 σ 𝑗=1 𝑚+1 𝑤 𝑥𝑗 𝒎 𝒎 + 𝟏
43. • •
52. • • •
53. •
55. 𝑝 𝑥𝑖 𝑤𝑖 𝑀 = 32
56. • 𝑀 Ƹ 𝑝 • 𝑓 𝑀
64. • •
65. •
73. • • • • • • •
74. • 𝐿 𝑟𝑖𝑠 1,𝑀 = 𝑓(𝑦) Ƹ 𝑝(𝑦) ∙ 1 𝑀 ෍ 𝑗=1 𝑀 𝑤 𝑥𝑗 = 𝑓 𝑦 ∙ 1 Ƹ 𝑝 𝑦 1 𝑀 ෍ 𝑗=1 𝑀 𝑤 𝑥𝑗 = 𝑓 𝑦 𝑊 𝐱, 𝑧 𝑊 𝐱, 𝑧 = 1 Ƹ 𝑝 𝑥𝑧 1 𝑀 ෍ 𝑖=1 𝑀 𝑤𝑖 𝑥𝑖
75. • 𝑊 𝐱, 𝑧 Τ 1 𝑝 𝑦 • 𝑊 𝐱, 𝑧 𝔼 𝑊 𝐱, 𝑧 = 1 𝑝 𝑦 𝑍 𝑦 𝑀 𝑍 𝑦 = 𝑖 | 1 ≤ 𝑖 ≤ 𝑀 and 𝑝𝑖 𝑦 > 0 𝑝𝑖 𝑦 > 0 𝑦 𝑖 𝑝𝑖 𝑦 = 0の 𝑦
76. • 𝔼 𝑀 𝑍 𝑦 𝑊 𝐱, 𝑧 = 1 𝑝 𝑦 𝐼 = 1 𝑁 ෍ 𝑖=1 𝑁 𝑓 𝑌𝑖 Ƹ 𝑝 𝑌𝑖 ∙ 1 𝑍 𝑌𝑖 ෍ 𝑗=1 𝑀 Ƹ 𝑝 𝑋𝑖𝑗 𝑝 𝑋𝑖𝑗
77. • 𝑍 • 𝑍 • • • if 𝑝 𝜔 > 0 when 𝑓 𝜔 > 0 if Ƹ 𝑝 𝜔 > 0 and 𝑞𝑗 𝜔 > 0 when 𝑓 𝜔 > 0 if Ƹ 𝑝𝑖 𝜔 > 0 and 𝑞𝑗 𝜔 > 0 when 𝑓 𝜔 > 0 𝑍 𝜔 𝑀
78. • Ƹ 𝑝 Ƹ 𝑝 Ƹ 𝑝𝐴 𝑎 > 0 but Ƹ 𝑝𝐵 𝑎 = 0 Ƹ 𝑝𝐴 𝑑 = 0 Ƹ 𝑝𝐵 𝑎 = 0
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123. • • • • • • •
124. 𝑋𝑖 𝑓 Ω 𝑝 𝑝𝑖 𝑋 𝑚𝑖 𝑋𝑖 𝑊𝑖 Τ 1 𝑝𝑖 𝑋𝑖 Ω𝑖 𝑋𝑖 𝑝𝑖 𝑓 𝑓 𝑌 𝑊𝑌
125. • 𝑋𝑖 Ω𝑖 𝑊𝑖 ∈ ℝ Τ 1 𝑝𝑖 𝑋𝑖 • 𝑓 Ω 𝑇𝑠 : Ω𝑠 → Ω 𝑋𝑠 ∈ Ω𝑠 Ω • Τ 𝜕𝑇𝑖 𝜕𝑥 • 𝑇𝑖 𝑤𝑖 = 𝑚𝑖 𝑇𝑖 𝑋𝑖 Ƹ 𝑝 𝑇𝑖 𝑋𝑖 𝑊𝑖 ∙ 𝜕𝑇𝑖 𝜕𝑋𝑖
126. • • • •
127. • • • •
129. • • • 𝐱𝑖 , 𝐱𝑖+1 𝐲𝑖 𝐲𝑖+1 = 𝐱𝑖+1 •
130. • • 𝐲𝑖+1
131. • • 𝐲𝑖+1 •
132. • 𝑦𝑖+1 •
133. • • •
136. • • • • •
137. 𝐱3 𝐱4 𝐱4 𝐱1 𝐱2 𝐲1 𝐲2 𝐲3 𝐱4 𝐲1 𝐱2 𝐲1 ↔ 𝐱2 ↔ 𝐱3
138. • • • 𝐱𝑖+1 − 𝐱𝑖 ≥ 𝑑𝑚𝑎𝑥 𝐱𝑖 , 𝐱𝑖+1 , 𝐲𝑖 𝑦𝑖+1 𝑥𝑖+1 𝑥𝑖+1 − 𝑦𝑖 ≥ 𝑑𝑚𝑎𝑥
143. • 𝑖 𝑋𝑖 𝑡 𝑊 𝑋𝑖 𝑡 𝑌𝑖 𝑡−1 𝑋𝑖 𝑡 𝑍𝑖 𝑗 𝑍𝑖 𝑍𝑗 𝑌𝑖 𝑡 𝑍𝑖 ≔ 𝑌𝑖 𝑡 𝐼𝑖 𝑡 ≈ 𝑓𝑖 𝑌𝑖 𝑡 𝑊 𝑌𝑖 𝑡 ※𝑌𝑖 𝑡−1を 𝑡 − 1 𝑖
145. • 𝑀𝑟 𝑀𝑐 • • 𝑀𝑟
147. •
154. • • • •
155. • • • • • •
156. • LightingPasses::RenderDirectLighting() • ExecuteRayTracingPass(…, …, “GenerateInitialSamples”, …, …); • ExecuteRayTracingPass(…, …, “TemporalResampling”, …, …); • ExecuteRayTracingPass(…, …, “SpatialResampling”, …, …); • ExecuteRayTracingPass(…, …, “ShadeSamples”, …, …);
157. • LightingPasses::RenderBrdfRays() • ExecuteRayTracingPass(…, …, “BrdfRayTracingPass”, …, …); • ExecuteRayTracingPass(…, …, “ShadeSecondarySurfaces”, …, …); • ExecuteRayTracingPass(…, …, “GITemporalResampling”, …, …); • ExecuteRayTracingPass(…, …, “GISpatialResampling”, …, …); • ExecuteRayTracingPass(…, …, “GIFinalShading”, …, …);
158. • •
159. •
160. • ReSTIRPT/Source/RenderPasses/ReSTIRPTPass • C++ ReSTIRPTPass.cpp • Slang • Shift.slang
162. • [Talbot 2005] Justin F. Talbot, Davit Cline, Parris Egbert, “Importance Resampling fo Global Illumination”, ESGR’05, pp.139-146, 2005 • [Bitterli 2020] Benedikt Bitterli, Chris Wyman, Matt Pharr, Peter Shirley, Aaron Lefohon, Wojciech Jarosz, “Spatiotemporal reservoir resampling for real-time ray tracing with dynamic direct lighting”, ACM Transactions on Graphics, Vol.39, No.4, 2020. • [Wyman 2021] Chris Wyman, Alexey Panteleev, “Rearchitecting Spatiotemporal Resampling for Production”, High-Performance Graphics 2021. • [Ouyang 2021] Y.Ouyang, S.Liu, M.Kettunen, M.Pharr, J.Pataleoni, “ReSTIR GI: Path Resampling for Real-Time Path Tracing”, High- Performance Graphics 2021. • [Lin 2022] Daqi Lin, Markus Kettunen, Benedikt Bitterli, Jacopo Pantaleoni, Cem Yukesel, Chris Wyman, “Generalized Resampled Importance Sampling”, SIGGRAPH 2022. • [Veach 1997] Eric Veach, “Robust Monte Carlo Methods for Light Transport Simulation”, Ph.D. dissertation, Standford University, 1997. • [Shocker 2022] Shocker, “ (Path Tracing)”, memoRANDOM, https://rayspace.xyz/CG/contents/path_tracing/, 2022. • [Pocol 2021] Pocol, “Direct3D 12 ”, , 2021. • [KiNaNkomoti 2022] KiNaNkomoti, “Pathtracing Caustics ”, 8 , 2022. • [Hirai 2022] , , “ 7 ”, CEDEC KUSYU 2022 • [NVIDIA 2023] NVIDIA, “ 2077 4 11 ”, https://www.nvidia.com/ja-jp/geforce/news/cyberpunk-2077-ray-tracing-overdrive-update-launches-april-11/, 2023. • [Capcom 2019] Capcom, “Devil May Cry5 Special Edition”, https://www.devilmaycry.com/5se/jp/, 2019. • [EmbarkStudios 2023] EmbarkStudios, “kajiya”, https://github.com/EmbarkStudios/kajiya, 2023. • [Halen 2021] Henrik Halen, Andres Brinck, Kyle Hayward, Xiangshun Bei, “Global Illumination Based on Surfels”, SIGGRAPH 2021 Advances in Real-Time Rendering in Games course, 2021. • [Boksansky 2021] Jakub Boksansky, Paula Jukarainen, Chris Wyman, “Rendering Many Lights With Grid-Based Reservoirs”, Ray Tracing Gems 2, Chapter 23, pp.351-365, 2021.