Robust Fitting of Parallax-Aware Mixtures for Path Guiding

Lukas Ruppert1, Sebastian Herholz1,2, Hendrik P. A. Lensch1
1University of Tübingen, 2Intel Corporation


Effective local light transport guiding demands for high quality guiding information, i.e., a precise representation of the directional incident radiance distribution at every point inside the scene. We introduce a parallax-aware distribution model based on parametric mixtures. By parallax-aware warping of the distribution, the local approximation of the 5D radiance field remains valid and precise across large spatial regions, even for close-by contributors. Our robust optimization scheme fits parametric mixtures to radiance samples collected in previous rendering passes. Robustness is achieved by splitting and merging of components refining the mixture. These splitting and merging decisions minimize and bound the expected variance of the local radiance estimator. In addition, we extend the fitting scheme to a robust, iterative update method, which allows for incremental training of our model using smaller sample batches. This results in more frequent training updates and, at the same time, significantly reduces the required sample memory footprint. The parametric representation of our model allows for the application of advanced importance sampling methods such as radiance-based, cosine-aware, and even product importance sampling. Our method further smoothly integrates next-event estimation (NEE) into path guiding, avoiding importance sampling of contributions better covered by NEE. The proposed robust fitting and update scheme, in combination with the parallax-aware representation, results in faster learning and lower variance compared to state-of-the-art path guiding approaches.


Paper [pdf] (updated on 21.07.2020, there was an error in eq. 27)
Supplementary Material [interactive viewer] [parallax comparison video] [zip]
Code [github]
Scenes [zip]


  author = {Ruppert, Lukas and Herholz, Sebastian and Lensch, Hendrik P. A.},
  title = {Robust Fitting of Parallax-Aware Mixtures for Path Guiding},
  year = {2020},
  issue_date = {July 2020},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  volume = {39},
  number = {4},
  issn = {0730-0301},
  url = {},
  doi = {10.1145/3386569.3392421},
  journal = {ACM Trans. Graph.},
  month = jul,
  articleno = {Article 147},
  numpages = {15},
  keywords = {global illumination, ray tracing, sampling and reconstruction, stochastic sampling}



Supported by the DFG Cluster of Excellence “Machine Learning – New Perspectives for Science”, EXC 2064/1, project no. 390727645 and the CRC 1233 "Robust Vision", project no. 276693517.

We would like to thank the anonymous reviewers for their many helpful comments, and for recommending the use of the harmonic mean.

Further thanks goes to the authors of the used scenes:
Bathroom by Mareck, Clocks by Hachisuka and Jensen,
Country-Kitchen by Jay-Artist, Glossy CBox by Müller et al.,
Jewelry by Alex Telford and Kitchen via Kaplanyan et al., Kitchenette by Martin Šik,
LivingRoom by Georgiev et al., Pool by Michal Timo and Ondřej Karlík,
Torus by Olesya Jakob, based on a scene by Cline et al..


© 2020 Copyright is held by the owner/author(s). Publication rights licensed to ACM.
This is the author's version of the work. It is posted here for your personal use. Not for redistribution.
The definitive version was published in ACM Trans. Graph. 39, 4,