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Consequently, emission spectra and surface albedos need to be known at each wavelength. It is practical to store dense samples for emission spectra but for albedo textures, the memory requirements of this approach are unreasonable. Prior works that approximate dense spectra from tristimulus data introduce strong errors under illuminants with sharp peaks and in indirect illumination. We represent spectra by an arbitrary number of Fourier coefficients. However, we do not use a common truncated Fourier series because its ringing could lead to albedos below zero or above one. Instead, we present a novel approach for reconstruction of bounded densities based on the theory of moments. The core of our technique is our bounded maximum entropy spectral estimate. It uses an efficient closed form to compute a smooth signal between zero and one that matches the given Fourier coefficients exactly. Still, a ground truth that localizes all of its mass around a few wavelengths can be reconstructed adequately. Therefore, our representation covers the full gamut of valid reflectances. The resulting textures are compact because each coefficient can be stored in 10 bits. For compatibility with existing tristimulus assets, we implement a mapping from tristimulus color spaces to three Fourier coefficients. Using three coefficients, our technique gives state of the art results without some of the drawbacks of related work. With four to eight coefficients, our representation is superior to all existing representations. Our focus is on offline rendering but we also demonstrate that the technique is fast enough for real-time rendering.<\/jats:p>","DOI":"10.1145\/3306346.3322964","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T19:04:08Z","timestamp":1562958248000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Using moments to represent bounded signals for spectral rendering"],"prefix":"10.1145","volume":"38","author":[{"given":"Christoph","family":"Peters","sequence":"first","affiliation":[{"name":"Karlsruhe Institute of Technology, Germany"}]},{"given":"Sebastian","family":"Merzbach","sequence":"additional","affiliation":[{"name":"University of Bonn, Germany"}]},{"given":"Johannes","family":"Hanika","sequence":"additional","affiliation":[{"name":"Karlsruhe Institute of Technology and Weta Digital, Germany"}]},{"given":"Carsten","family":"Dachsbacher","sequence":"additional","affiliation":[{"name":"Karlsruhe Institute of Technology, Germany"}]}],"member":"320","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"2017 IEEE International Conference on Computer Vision Workshops (ICCVW). 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