A Statistical Approach to
Monte Carlo Denoising

Hiroyuki Sakai1, Christian Freude1, Thomas Auzinger2, David Hahn1, Michael Wimmer1
1TU Wien, 2Institute of Science and Technology Austria
SIGGRAPH Asia 2024 Conference Paper
Paper Supplementary Document DOI BibTeX
Code Results (PFM) Results (PNG)
A visual and quantitative comparison between a noisy input rendering of the Staircase scene and the corresponding denoised outputs from Moon CI, OptiX, OIDN, ProDen, and our method.

Our statistical denoising method, using online estimates of sample statistics, achieves image quality comparable to current state-of-the-art methods, without any computation-heavy prior training. We compare our denoiser to the approach by Moon et al. [2013] (“Moon CI”), NVIDIA OptiX AI-Accelerated Denoiser (“OptiX”), Intel Open Image Denoise (OIDN), and progressive denoising [Firmino et al. 2022] (“ProDen”). These results have been generated using 256 samples per pixel (SPP) with the following denoising times; Moon CI: 35.3 ms, OptiX: 85.5 ms, OIDN: 19.5 ms, ProDen: 1834.9 ms, ours: 28.0 ms.

TL;DR

We propose a novel statistical approach to denoising Monte Carlo renderings. Building on a closed-form optimal solution, our approach matches the performance of state-of-the-art neural denoising without any hallucinations and computation-intensive pretraining.

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.

Acknowledgments

We thank Lukas Lipp for fruitful discussions, Károly Zsolnai-Fehér and Jaroslav Křivánek for valuable contributions to early versions of this work, and Bernhard Kerbl for help with our CUDA implementation. Moreover, we thank the creators of the scenes we have used: Wig42 for “Wooden Staircase” (Fig. 1), “Grey and White Room” (Fig. S6), and “Modern Living Room” (Fig. S8); nacimus for “Bathroom” (Fig. 3, S5); NovaZeeke for “Japanese Classroom” (Fig. 4, 6); Beeple for “Zero-Day” (Fig. 8); Jay-Artist for “White Room” (Fig. S7); Mareck for “Contemporary Bathroom” (Fig. 2); Christian Freude for “Glass Caustics” (Fig. S10); and Benedikt Bitterli for “Veach Ajar” (Fig. 7, S2), “Veach MIS” (Fig. S4), and “Fur Ball” (Fig. S11). This work has received funding from the Vienna Science and Technology Fund (WWTF) project ICT22-028 (“Toward Optimal Path Guiding for Photorealistic Rendering”) and the Austrian Science Fund (FWF) project F 77 (SFB “Advanced Computational Design”).

Changelog

We provide an updated version of our paper on this page, incorporating the following corrections to errors found in the publisher's version: