Manifold Path Guiding for Importance Sampling Specular Chains

Zhimin Fan*, Pengpei Hong*, Jie Guo, Changqing Zou, Yanwen Guo, and Ling-Qi Yan
ACM Transactions on Graphics (Proceedings of SIGGRAPH ASIA 2023)
[Paper] [Supplementary] [Code]

Abstract

Complex visual effects such as caustics are often produced by light paths containing multiple consecutive specular vertices (dubbed specular chains), which pose a challenge to unbiased estimation in Monte Carlo rendering. In this work:

We analyze light transport behavior within sub-paths containing specular chains and non-specular separators.
We leverage specular manifolds to reconstruct continuous energy distributions from historical/coherent sub-paths.
We propose manifold path guiding, a progressive pipeline to importance sample paths with long specular chains via seed chain generation and manifold walks.

Our method achieves up to 40× variance reduction compared to state-of-the-art unbiased methods, particularly in scenes with long specular chains and complex visibility.

The Challenge of Specular Chains

Several common scenes still lack effective sampling strategies for handling light paths with multiple consecutive specular/near-specular scattering events (e.g., curved metals, water, glass). These paths cause severe convergence issues in physically-based rendering due to:

The difficulty of finding valid path samples that satisfy physical constraints at specular vertices.
High dimensionality and discrete nature of admissible specular chain spaces.

Limitations of Existing Approaches

Method	Shortcomings
MLT-based	Struggles with SDS paths despite specialized mutations.
Fitted Distributions	Fail for pure specular cases (e.g., near point lights).
Specular Manifold Sampling (SMS)	Performance degrades for long chains; ignores energy distributions.

Our Solution: Manifold Path Guiding

Importance sample seed chains in a continuous space, then refine via manifold walks to converge to admissible chains.
Exploit coherence in specular manifolds for dimensionality reduction.
Use converged distributions for efficient sampling.

Key figures

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Citation


xxxxxxxxxx
@article{Fan23MPG,
  title     = {Manifold Path Guiding for Importance Sampling Specular Chains},
  author    = {Fan, Zhimin and Hong, Pengpei and Guo, Jie and Zou, Changqing and Guo, Yanwen and Yan, Ling-Qi},
  journal   = {ACM Trans. Graph.},
  volume    = {42},
  number    = {6},
  year      = {2023},
  month     = {Dec},
  issue_date= {December 2023},
  articleno = {257},
  numpages  = {14}
}