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All these contributions combine to a robust denoising pipeline that does not require any pretraining and can run efficiently on current GPU hardware. Our results show distinct advantages over previous denoising methods, especially in the range of a few hundred samples per pixel, which is of high practical relevance. Finally, we demonstrate good convergence behavior as the number of samples increases, providing predictable results with low bias that are free of hallucinated neural artifacts. In summary, our statistics-based algorithms for adaptive sampling and denoising deliver fast, consistent, low-bias variance and radiance estimates.", "authors_et_al": false, "substitute": null, "main_image": { "description": "“Veach, Bidir Room” scene by Benedikt Bitterli, dedicated to the public domain under CC0 1.0 Universal (https://benedikt-bitterli.me/resources/).", "filetitle": "Representative Image", "main_file": false, "use_in_gallery": false, "access": "public", "image_width": 1500, "image_height": 1000, "name": "sakai-2025-stater-Representative Image.png", "type": "image/png", "size": 711915, "path": "Publication:sakai-2025-stater", "url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/sakai-2025-stater-Representative Image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/sakai-2025-stater-Representative Image:thumb{{size}}.png" }, "sync_repositum_override": null, "repositum_presentation_id": null, "authors": [ 1129, 1128, 193, 1946 ], "booktitle": "Proceedings of the SIGGRAPH Asia 2025 Conference Papers", "date_from": "2025-12-15", "date_to": "2025-12-18", "doi": "10.1145/3757377.3763995", "event": "SIGGRAPH Asia 2025 Conference", "isbn": "979-8-4007-2137-3", "lecturer": [ 1129 ], "location": "Hong Kong", "open_access": "yes", "pages": "12", "pages_from": "1", "pages_to": "12", "publisher": "ACM", "research_areas": [ "Rendering" ], "keywords": [ "Monte Carlo rendering", "path tracing", "denoising", "image filtering", "statistics" ], "weblinks": [ { "href": "https://www.cg.tuwien.ac.at/StatER", "caption": "Project Page", "description": null, "main_file": 1 } ], "files": { "0": { "description": null, "filetitle": "paper", "main_file": true, "use_in_gallery": true, "access": "public", "name": "sakai-2025-stater-paper.pdf", "type": "application/pdf", "size": 10120331, "path": "Publication:sakai-2025-stater", "url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/sakai-2025-stater-paper.pdf", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/sakai-2025-stater-paper:thumb{{size}}.png" }, "1": { "description": "“Veach, Bidir Room” scene by Benedikt Bitterli, dedicated to the public domain under CC0 1.0 Universal (https://benedikt-bitterli.me/resources/).", "filetitle": "Representative Image", "main_file": false, "use_in_gallery": false, "access": "public", "image_width": 1500, "image_height": 1000, "name": "sakai-2025-stater-Representative Image.png", "type": "image/png", "size": 711915, "path": "Publication:sakai-2025-stater", "url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/sakai-2025-stater-Representative Image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/sakai-2025-stater-Representative Image:thumb{{size}}.png" }, "3": { "description": null, "filetitle": "Supplementary Document", "main_file": true, "use_in_gallery": false, "access": "public", "name": "sakai-2025-stater-Supplementary Document.pdf", "type": "application/pdf", "size": 29341520, "path": "Publication:sakai-2025-stater", "url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/sakai-2025-stater-Supplementary Document.pdf", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/sakai-2025-stater-Supplementary Document:thumb{{size}}.png" } }, "projects_workgroups": [ "d9259" ], "url": "https://www.cg.tuwien.ac.at/research/publications/2025/sakai-2025-stater/", "__class": "Publication" }, { "id": "sakai-2024-asa", "type_id": "inproceedings", "tu_id": null, "repositum_id": "20.500.12708/209940", "title": "A Statistical Approach to Monte Carlo Denoising", "date": "2024-12", "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.", "authors_et_al": false, "substitute": null, "main_image": { "description": "Image illustrating the proposed denoising method, created by the paper authors. The “Wooden Staircase” scene has been created by Wig42 (https://blendswap.com/profile/130393) under the CC BY 3.0 license.", "filetitle": "Representative Image", "main_file": false, "use_in_gallery": true, "access": "public", "image_width": 1980, "image_height": 1320, "name": "sakai-2024-asa-Representative Image.jpg", "type": "image/jpeg", "size": 3344845, "path": "Publication:sakai-2024-asa", "url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/sakai-2024-asa-Representative Image.jpg", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/sakai-2024-asa-Representative Image:thumb{{size}}.png" }, "sync_repositum_override": "date,articleno", "repositum_presentation_id": null, "authors": [ 1129, 1128, 808, 1946, 193 ], "articleno": "68", "booktitle": "SA '24: SIGGRAPH Asia 2024 Conference Papers", "date_from": "2024-12-03", "date_to": "2024-12-06", "doi": "10.1145/3680528.3687591", "event": "SA '24: SIGGRAPH Asia 2024", "isbn": "979-8-4007-1131-2", "lecturer": [ 1129 ], "location": "Tokyo", "open_access": "yes", "pages": "11", "publisher": "Association for Computing Machinery", "research_areas": [ "Rendering" ], "keywords": [ "Monte Carlo rendering", "path tracing", "denoising", "image filtering", "statistics" ], "weblinks": [ { "href": "https://www.cg.tuwien.ac.at/StatMC", "caption": "Project Page", "description": null, "main_file": 1 } ], "files": { "0": { "description": null, "filetitle": "paper", "main_file": true, "use_in_gallery": false, "access": "public", "name": "sakai-2024-asa-paper.pdf", "type": "application/pdf", "size": 11789710, "path": "Publication:sakai-2024-asa", "url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/sakai-2024-asa-paper.pdf", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/sakai-2024-asa-paper:thumb{{size}}.png" }, "1": { "description": "Image illustrating the proposed denoising method, created by the paper authors. The “Wooden Staircase” scene has been created by Wig42 (https://blendswap.com/profile/130393) under the CC BY 3.0 license.", "filetitle": "Representative Image", "main_file": false, "use_in_gallery": true, "access": "public", "image_width": 1980, "image_height": 1320, "name": "sakai-2024-asa-Representative Image.jpg", "type": "image/jpeg", "size": 3344845, "path": "Publication:sakai-2024-asa", "url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/sakai-2024-asa-Representative Image.jpg", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/sakai-2024-asa-Representative Image:thumb{{size}}.png" }, "3": { "description": null, "filetitle": "Supplementary Document", "main_file": true, "use_in_gallery": false, "access": "public", "name": "sakai-2024-asa-Supplementary Document.pdf", "type": "application/pdf", "size": 10739991, "path": "Publication:sakai-2024-asa", "url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/sakai-2024-asa-Supplementary Document.pdf", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/sakai-2024-asa-Supplementary Document:thumb{{size}}.png" } }, "projects_workgroups": [ "d9259" ], "url": "https://www.cg.tuwien.ac.at/research/publications/2024/sakai-2024-asa/", "__class": "Publication" }, { "id": "xmas-2023", "type_id": "xmascard", "tu_id": null, "repositum_id": null, "title": "X-Mas Card 2023", "date": "2023-12", "abstract": null, "authors_et_al": false, "substitute": null, "main_image": { "description": null, "filetitle": "image", "main_file": false, "use_in_gallery": true, "access": "public", "image_width": 2283, "image_height": 1615, "name": "xmas-2023-image.png", "type": "image/png", "size": 4679564, "path": "Publication:xmas-2023", "url": "https://www.cg.tuwien.ac.at/research/publications/2023/xmas-2023/xmas-2023-image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2023/xmas-2023/xmas-2023-image:thumb{{size}}.png" }, "sync_repositum_override": null, "repositum_presentation_id": null, "authors": [ 848, 1636, 1869, 1935, 1129, 193 ], "research_areas": [], "keywords": [ "Christmas", "Santa Edi", "Holy Michi", "Vulkan", "Auto-Vk-Toolkit", "Auto-Vk", "Tamashii", "Cyberpunk", "RTX. It's on.", "Christmas Tree" ], "weblinks": [], "files": [ { "description": "Christmas Card as PDF", "filetitle": "Card", "main_file": true, "use_in_gallery": false, "access": "public", "name": "xmas-2023-Card.pdf", "type": "application/pdf", "size": 1240736, "path": "Publication:xmas-2023", "url": "https://www.cg.tuwien.ac.at/research/publications/2023/xmas-2023/xmas-2023-Card.pdf", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2023/xmas-2023/xmas-2023-Card:thumb{{size}}.png" }, { "description": null, "filetitle": "image", "main_file": false, "use_in_gallery": true, "access": "public", "image_width": 2283, "image_height": 1615, "name": "xmas-2023-image.png", "type": "image/png", "size": 4679564, "path": "Publication:xmas-2023", "url": "https://www.cg.tuwien.ac.at/research/publications/2023/xmas-2023/xmas-2023-image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2023/xmas-2023/xmas-2023-image:thumb{{size}}.png" } ], "projects_workgroups": [ "xmas" ], "url": "https://www.cg.tuwien.ac.at/research/publications/2023/xmas-2023/", "__class": "Publication" }, { "id": "freude-2023-sem", "type_id": "inproceedings", "tu_id": null, "repositum_id": "20.500.12708/175763", "title": "Sampling-Distribution-Based Evaluation for Monte Carlo Rendering", "date": "2023", "abstract": "In this paper, we investigate the application of per-pixel difference metrics for evaluating Monte Carlo (MC) rendering techniques. In particular, we propose to take the sampling distribution of the mean (SDM) into account for this purpose. We establish the theoretical background and analyze other per-pixel difference metrics, such as the absolute deviation (AD) and the mean squared error (MSE) in relation to the SDM. Based on insights from this analysis, we propose a new, alternative, and particularly easy-to-use approach, which builds on the SDM and facilitates meaningful comparisons of MC rendering techniques on a per-pixel basis. In order to demonstrate the usefulness of our approach, we compare it to commonly used metrics based on a variety of images computed with different rendering techniques. Our evaluation reveals limitations of commonly used metrics, in particular regarding the detection of differences between renderings that might be difficult to detect otherwise—this circ umstance is particularly apparent in comparison to the MSE calculated for each pixel. Our results indicate the potential of SDM-based approaches to reveal differences between MC renderers that might be caused by conceptual or implementation-related issues. Thus, we understand our approach as a way to facilitate the development and evaluation of rendering techniques.", "authors_et_al": false, "substitute": null, "main_image": { "description": null, "filetitle": "image", "main_file": true, "use_in_gallery": false, "access": "public", "image_width": 1028, "image_height": 1028, "name": "freude-2023-sem-image.png", "type": "image/png", "size": 731748, "path": "Publication:freude-2023-sem", "url": "https://www.cg.tuwien.ac.at/research/publications/2023/freude-2023-sem/freude-2023-sem-image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2023/freude-2023-sem/freude-2023-sem-image:thumb{{size}}.png" }, "sync_repositum_override": null, "repositum_presentation_id": null, "authors": [ 1128, 1129, 1073, 193 ], "booktitle": "Proceedings of the 18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications", "date_from": "2023-02-19", "date_to": "2023-02-21", "doi": "10.5220/0011886300003417", "event": "18th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (GRAPP)", "isbn": "978-989-758-634-7", "lecturer": [ 1128 ], "location": "Lisbon, Portugal", "open_access": "yes", "pages": "12", "pages_from": "119", "pages_to": "130", "publisher": "Scitepress", "volume": "1", "research_areas": [ "Rendering" ], "keywords": [ "computer graphics", "Rendering", "Ray Tracing", "Evaluation", "Validation" ], "weblinks": [], "files": [ { "description": null, "filetitle": "image", "main_file": true, "use_in_gallery": false, "access": "public", "image_width": 1028, "image_height": 1028, "name": "freude-2023-sem-image.png", "type": "image/png", "size": 731748, "path": "Publication:freude-2023-sem", "url": "https://www.cg.tuwien.ac.at/research/publications/2023/freude-2023-sem/freude-2023-sem-image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2023/freude-2023-sem/freude-2023-sem-image:thumb{{size}}.png" }, { "description": null, "filetitle": "paper", "main_file": true, "use_in_gallery": false, "access": "public", "name": "freude-2023-sem-paper.pdf", "type": "application/pdf", "size": 8656300, "path": "Publication:freude-2023-sem", "url": "https://www.cg.tuwien.ac.at/research/publications/2023/freude-2023-sem/freude-2023-sem-paper.pdf", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2023/freude-2023-sem/freude-2023-sem-paper:thumb{{size}}.png" } ], "projects_workgroups": [ "OpenData", "d4314" ], "url": "https://www.cg.tuwien.ac.at/research/publications/2023/freude-2023-sem/", "__class": "Publication" }, { "id": "freude_2020_rs", "type_id": "techreport", "tu_id": null, "repositum_id": null, "title": "R-Score: A Novel Approach to Compare Monte Carlo Renderings", "date": "2020-08", "abstract": "In this paper, we propose a new approach for the comparison and analysis of Monte Carlo (MC) rendering algorithms. It is based on a novel similarity measure called render score (RS) that is specically designed for MC rendering, statistically motivated, and incorporates bias and variance. Additionally, we propose a comparison scheme that alleviates the need for practically converged reference images (RIs). Our approach can be used to compare and analyze dierent rendering methods by revealing detailed (per-pixel) dierences and subsequently potential conceptual or implementation-related issues, thereby offering a more informative and meaningful alternative to commonly used metrics.", "authors_et_al": false, "substitute": null, "main_image": { "description": null, "filetitle": "teaser-image", "main_file": false, "use_in_gallery": false, "access": "public", "image_width": 630, "image_height": 533, "name": "freude_2020_rs-teaser-image.png", "type": "image/png", "size": 89069, "path": "Publication:freude_2020_rs", "url": "https://www.cg.tuwien.ac.at/research/publications/2020/freude_2020_rs/freude_2020_rs-teaser-image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2020/freude_2020_rs/freude_2020_rs-teaser-image:thumb{{size}}.png" }, "sync_repositum_override": null, "repositum_presentation_id": null, "authors": [ 1128, 1129, 1073, 193 ], "number": "TR-193-02-2020-4", "open_access": "no", "research_areas": [ "Rendering" ], "keywords": [], "weblinks": [], "files": [ { "description": null, "filetitle": "teaser-image", "main_file": false, "use_in_gallery": false, "access": "public", "image_width": 630, "image_height": 533, "name": "freude_2020_rs-teaser-image.png", "type": "image/png", "size": 89069, "path": "Publication:freude_2020_rs", "url": "https://www.cg.tuwien.ac.at/research/publications/2020/freude_2020_rs/freude_2020_rs-teaser-image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2020/freude_2020_rs/freude_2020_rs-teaser-image:thumb{{size}}.png" }, { "description": null, "filetitle": "technical-report", "main_file": true, "use_in_gallery": false, "access": "public", "name": "freude_2020_rs-technical-report.pdf", "type": "application/pdf", "size": 1215341, "path": "Publication:freude_2020_rs", "url": "https://www.cg.tuwien.ac.at/research/publications/2020/freude_2020_rs/freude_2020_rs-technical-report.pdf", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2020/freude_2020_rs/freude_2020_rs-technical-report:thumb{{size}}.png" } ], "projects_workgroups": [ "OpenData" ], "url": "https://www.cg.tuwien.ac.at/research/publications/2020/freude_2020_rs/", "__class": "Publication" }, { "id": "CORNEL-2017-FRS", "type_id": "journalpaper", "tu_id": null, "repositum_id": null, "title": "Forced Random Sampling: fast generation of importance-guided blue-noise samples", "date": "2017-06", "abstract": "In computer graphics, stochastic sampling is frequently used to efficiently approximate complex functions and integrals. The error of approximation can be reduced by distributing samples according to an importance function, but cannot be eliminated completely. To avoid visible artifacts, sample distributions are sought to be random, but spatially uniform, which is called blue-noise sampling. The generation of unbiased, importance-guided blue-noise samples is expensive and not feasible for real-time applications. Sampling algorithms for these applications focus on runtime performance at the cost of having weak blue-noise properties. Blue-noise distributions have also been proposed for digital halftoning in the form of precomputed dither matrices. Ordered dithering with such matrices allows to distribute dots with blue-noise properties according to a grayscale image. By the nature of ordered dithering, this process can be parallelized easily. We introduce a novel sampling method called forced random sampling that is based on forced random dithering, a variant of ordered dithering with blue noise. By shifting the main computational effort into the generation of a precomputed dither matrix, our sampling method runs efficiently on GPUs and allows real-time importance sampling with blue noise for a finite number of samples. We demonstrate the quality of our method in two different rendering applications.", "authors_et_al": false, "substitute": null, "main_image": { "description": null, "filetitle": "image2", "main_file": false, "use_in_gallery": true, "access": "public", "image_width": 3206, "image_height": 1830, "name": "CORNEL-2017-FRS-image2.png", "type": "image/png", "size": 2261746, "path": "Publication:CORNEL-2017-FRS", "url": "https://www.cg.tuwien.ac.at/research/publications/2017/CORNEL-2017-FRS/CORNEL-2017-FRS-image2.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2017/CORNEL-2017-FRS/CORNEL-2017-FRS-image2:thumb{{size}}.png" }, "sync_repositum_override": null, "repositum_presentation_id": null, "authors": [ 877, 1129, 659, 193 ], "date_from": "2017-06-27", "date_to": "2017-06-30", "event": "Computer Graphics International 2017", "issn": "1432-2315", "journal": "The Visual Computer", "lecturer": [ 877 ], "location": "Yokohama, Japan", "number": "6", "pages_from": "833", "pages_to": "843", "volume": "33", "research_areas": [ "Rendering" ], "keywords": [ "blue-noise sampling", "importance sampling" ], "weblinks": [], "files": [ { "description": null, "filetitle": "image", "main_file": false, "use_in_gallery": true, "access": "public", "image_width": 1024, "image_height": 512, "name": "CORNEL-2017-FRS-image.png", "type": "image/png", "size": 345074, "path": "Publication:CORNEL-2017-FRS", "url": "https://www.cg.tuwien.ac.at/research/publications/2017/CORNEL-2017-FRS/CORNEL-2017-FRS-image.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2017/CORNEL-2017-FRS/CORNEL-2017-FRS-image:thumb{{size}}.png" }, { "description": null, "filetitle": "image2", "main_file": false, "use_in_gallery": true, "access": "public", "image_width": 3206, "image_height": 1830, "name": "CORNEL-2017-FRS-image2.png", "type": "image/png", "size": 2261746, "path": "Publication:CORNEL-2017-FRS", "url": "https://www.cg.tuwien.ac.at/research/publications/2017/CORNEL-2017-FRS/CORNEL-2017-FRS-image2.png", "thumb_image_sizes": [ 16, 64, 100, 175, 300, 600 ], "thumb_url": "https://www.cg.tuwien.ac.at/research/publications/2017/CORNEL-2017-FRS/CORNEL-2017-FRS-image2:thumb{{size}}.png" }, { "description": null, "filetitle": "paper", "main_file": true, "use_in_gallery": false, "access": "public", "name": "CORNEL-2017-FRS-paper.pdf", "type": "binary/octet-stream", "size": 4668674, "path": "Publication:CORNEL-2017-FRS", "url": "https://www.cg.tuwien.ac.at/research/publications/2017/CORNEL-2017-FRS/CORNEL-2017-FRS-paper.pdf", "thumb_image_sizes": [] } ], "projects_workgroups": [ "PathSpace", "VRVis" ], "url": "https://www.cg.tuwien.ac.at/research/publications/2017/CORNEL-2017-FRS/", "__class": "Publication" } ]