A Comprehensive Theory and Variational Framework for Anti-aliasing Sampling Patterns

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dc.contributor.authorĂ–ztireli, A. Cengizen_US
dc.contributor.editorDachsbacher, Carsten and Pharr, Matten_US
dc.date.accessioned2020-06-28T15:24:22Z
dc.date.available2020-06-28T15:24:22Z
dc.date.issued2020
dc.description.abstractIn this paper, we provide a comprehensive theory of anti-aliasing sampling patterns that explains and revises known results, and introduce a variational optimization framework to generate point patterns with any desired power spectra and anti-aliasing properties. We start by deriving the exact spectral expression for expected error in reconstructing a function in terms of power spectra of sampling patterns, and analyzing how the shape of power spectra is related to anti-aliasing properties. Based on this analysis, we then formulate the problem of generating anti-aliasing sampling patterns as constrained variational optimization on power spectra. This allows us to not rely on any parametric form, and thus explore the whole space of realizable spectra. We show that the resulting optimized sampling patterns lead to reconstructions with less visible aliasing artifacts, while keeping low frequencies as clean as possible. Although we focus on image plane sampling, our theory and algorithms apply in any dimensions, and the variational optimization framework can be utilized in all problems where point pattern characteristics are given or optimized.en_US
dc.description.number4
dc.description.sectionheadersSampling
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume39
dc.identifier.doi10.1111/cgf.14059
dc.identifier.issn1467-8659
dc.identifier.pages133-148
dc.identifier.urihttps://doi.org/10.1111/cgf.14059
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14059
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectComputing methodologies
dc.subjectAntialiasing
dc.subjectRendering
dc.subjectImage processing
dc.titleA Comprehensive Theory and Variational Framework for Anti-aliasing Sampling Patternsen_US
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