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To achieve our goal, we iteratively build multiple, but sparse linear models. Each linear model has its prediction window, where the linear model predicts the unknown ground truth image that can be generated with an infinite number of samples. Our method recursively estimates prediction errors introduced by linear predictions performed with different prediction windows, and selects an optimal prediction window minimizing the error for each linear model. Since each linear model predicts multiple pixels within its optimal prediction interval, we can construct our linear models only at a sparse set of pixels in the image screen. Predicting multiple pixels with a single linear model poses technical challenges, related to deriving error analysis for regions rather than pixels, and has not been addressed in the field. We address these technical challenges, and our method with robust error analysis leads to a drastically reduced reconstruction time even with higher rendering quality, compared to state-of-the-art adaptive methods. We have demonstrated that our method outperforms previous methods numerically and visually with high performance ray tracing kernels such as OptiX and Embree.<\/jats:p>","DOI":"10.1145\/2766992","type":"journal-article","created":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T12:26:38Z","timestamp":1438086398000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":33,"title":["Adaptive rendering with linear predictions"],"prefix":"10.1145","volume":"34","author":[{"given":"Bochang","family":"Moon","sequence":"first","affiliation":[{"name":"Disney Research Z\u00fcrich"}]},{"given":"Jose A.","family":"Iglesias-Guitian","sequence":"additional","affiliation":[{"name":"Disney Research Z\u00fcrich"}]},{"given":"Sung-Eui","family":"Yoon","sequence":"additional","affiliation":[{"name":"KAIST"}]},{"given":"Kenny","family":"Mitchell","sequence":"additional","affiliation":[{"name":"Disney Research Z\u00fcrich"}]}],"member":"320","published-online":{"date-parts":[[2015,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1974.10489157"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01996.x"},{"key":"e_1_2_2_3_1","unstructured":"Dammertz H. Sewtz D. Hanika J. and Lensch H. P. A. 2010. Edge-avoiding A-Trous wavelet transform for fast global illumination filtering. In High Performance Graphics 67--75.   Dammertz H. Sewtz D. Hanika J. and Lensch H. P. A. 2010. Edge-avoiding A-Trous wavelet transform for fast global illumination filtering. In High Performance Graphics 67--75."},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2532708"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531399"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024214"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1944846.1944849"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360632"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/15886.15902"},{"key":"e_1_2_2_10_1","doi-asserted-by":"crossref","unstructured":"Kalantari N. K. and Sen P. 2013. Removing the noise in Monte Carlo rendering with general image denoising algorithms. Computer Graphics Forum 32 2pt1 93--102.  Kalantari N. K. and Sen P. 2013. Removing the noise in Monte Carlo rendering with general image denoising algorithms. Computer Graphics Forum 32 2pt1 93--102.","DOI":"10.1111\/cgf.12029"},{"key":"e_1_2_2_11_1","volume-title":"14th International Joint Conference on Artificial Intelligence, 1137--1143","author":"Kohavi R.","year":"1995","unstructured":"Kohavi , R. 1995 . A study of cross-validation and bootstrap for accuracy estimation and model selection . In 14th International Joint Conference on Artificial Intelligence, 1137--1143 . Kohavi, R. 1995. A study of cross-validation and bootstrap for accuracy estimation and model selection. 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