Abstract
Rendering photorealistic visuals of virtual scenes requires tractable models for the simulation of light. The rendering equation describes one such model using an integral equation, the crux of which is a continuous integral operator. A majority of rendering algorithms aim to approximate the effect of this light transport operator via discretization (using rays, particles, patches, etc.). Research spanning four decades has uncovered interesting properties and intuition surrounding this operator. In this paper we analyze compactness, a key property that is independent of its discretization and which characterizes the ability to approximate the operator uniformly by a sequence of finite rank operators. We conclusively prove lingering suspicions that this operator is not compact and therefore that any discretization that relies on a finite-rank or nonadaptive finite-bases is susceptible to unbounded error over arbitrary light distributions. Our result justifies the expectation for rendering algorithms to be evaluated using a variety of scenes and illumination conditions. We also discover that its lower dimensional counterpart (over purely diffuse scenes) is not compact except in special cases, and uncover connections with it being noninvertible and acting as a low-pass filter. We explain the relevance of our results in the context of previous work. We believe that our theoretical results will inform future rendering algorithms regarding practical choices.
Original language | English |
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Title of host publication | ACM SIGGRAPH 2022 Conference Proceedings |
Editors | Munkhtsetseg Nandigjav, Niloy J. Mitra, Aaron Hertzmann |
Publisher | ACM |
Number of pages | 9 |
ISBN (Electronic) | 9781450393379 |
DOIs | |
Publication status | Published - 5 Aug 2022 |
Event | SIGGRAPH 2022 - Vancouver, Canada Duration: 8 Aug 2022 → 11 Aug 2022 https://s2022.siggraph.org/ |
Conference
Conference | SIGGRAPH 2022 |
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Abbreviated title | SIGGRAPH 2022 |
Country/Territory | Canada |
City | Vancouver |
Period | 8/08/22 → 11/08/22 |
Internet address |
Keywords
- Light Transport Operator
- Compactness
- Fredholm Equations