A Statistical Approach to Monte Carlo Denoising

Information

• Publication Type: Conference Paper
• Workgroup(s)/Project(s):
  • Toward Optimal Path Guiding for Photorealistic Rendering
• Date: December 2024
• ISBN: 979-8-4007-1131-2
• Publisher: Association for Computing Machinery
• Open Access: yes
• Location: Tokyo
• Lecturer: Hiroyuki Sakai
• Event: SA '24: SIGGRAPH Asia 2024
• DOI: 10.1145/3680528.3687591
• Booktitle: SA '24: SIGGRAPH Asia 2024 Conference Papers
• Article Number: 68
• Pages: 11
• Conference date: 3. December 2024 – 6. December 2024
• Keywords: Monte Carlo rendering, path tracing, denoising, image filtering, statistics

Abstract

The stochastic nature of modern Monte Carlo (MC) rendering methods inevitably produces noise in rendered images for a practical number of samples per pixel. The problem of denoising these images has been widely studied, with most recent methods relying on data-driven, pretrained neural networks. In contrast, in this paper we propose a statistical approach to the denoising problem, treating each pixel as a random variable and reasoning about its distribution. Considering a pixel of the noisy rendered image, we formulate fast pair-wise statistical tests—based on online estimators—to decide which of the nearby pixels to exclude from the denoising filter. We show that for symmetric pixel weights and normally distributed samples, the classical Welch t-test is optimal in terms of mean squared error. We then show how to extend this result to handle non-normal distributions, using more recent confidence-interval formulations in combination with the Box-Cox transformation. Our results show that our statistical denoising approach matches the performance of state-of-the-art neural image denoising without having to resort to any computation-intensive pretraining. Furthermore, our approach easily generalizes to other quantities besides pixel intensity, which we demonstrate by showing additional applications to Russian roulette path termination and multiple importance sampling.

Additional Files and Images

Weblinks

• Project Page
• Entry in reposiTUm (TU Wien Publication Database)
• DOI: 10.1145/3680528.3687591

BibTeX

@inproceedings{sakai-2024-asa,
  title =      "A Statistical Approach to Monte Carlo Denoising",
  author =     "Hiroyuki Sakai and Christian Freude and Thomas Auzinger and
               David Hahn and Michael Wimmer",
  year =       "2024",
  abstract =   "The stochastic nature of modern Monte Carlo (MC) rendering
               methods inevitably produces noise in rendered images for a
               practical number of samples per pixel. The problem of
               denoising these images has been widely studied, with most
               recent methods relying on data-driven, pretrained neural
               networks. In contrast, in this paper we propose a
               statistical approach to the denoising problem, treating each
               pixel as a random variable and reasoning about its
               distribution. Considering a pixel of the noisy rendered
               image, we formulate fast pair-wise statistical tests—based
               on online estimators—to decide which of the nearby pixels
               to exclude from the denoising filter. We show that for
               symmetric pixel weights and normally distributed samples,
               the classical Welch t-test is optimal in terms of mean
               squared error. We then show how to extend this result to
               handle non-normal distributions, using more recent
               confidence-interval formulations in combination with the
               Box-Cox transformation. Our results show that our
               statistical denoising approach matches the performance of
               state-of-the-art neural image denoising without having to
               resort to any computation-intensive pretraining.
               Furthermore, our approach easily generalizes to other
               quantities besides pixel intensity, which we demonstrate by
               showing additional applications to Russian roulette path
               termination and multiple importance sampling.",
  month =      dec,
  isbn =       "979-8-4007-1131-2",
  publisher =  "Association for Computing Machinery",
  location =   "Tokyo",
  event =      "SA '24: SIGGRAPH Asia 2024",
  doi =        "10.1145/3680528.3687591",
  booktitle =  "SA '24: SIGGRAPH Asia 2024 Conference Papers",
  articleno =  "68",
  pages =      "11",
  keywords =   "Monte Carlo rendering, path tracing, denoising, image
               filtering, statistics",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/",
}