One Step Further Beyond Trilinear Interpolation and Central Differences: Triquadratic Reconstruction and its Analytic Derivatives at the Cost of One Additional Texture Fetch

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dc.contributor.authorCsébfalvi, Balázsen_US
dc.contributor.editorMyszkowski, Karolen_US
dc.contributor.editorNiessner, Matthiasen_US
dc.date.accessioned2023-05-03T06:10:04Z
dc.date.available2023-05-03T06:10:04Z
dc.date.issued2023
dc.description.abstractRecently, it has been shown that the quality of GPU-based trilinear volume resampling can be significantly improved if the six additional trilinear samples evaluated for the gradient estimation also contribute to the reconstruction of the underlying function [Csé19]. Although this improvement increases the approximation order from two to three without any extra cost, the continuity order remains C0. In this paper, we go one step further showing that a C1 continuous triquadratic B-spline reconstruction and its analytic partial derivatives can be evaluated by taking only one more trilinear sample into account. Thus, our method is the first volume-resampling technique that is nearly as fast as trilinear interpolation combined with on-thefly central differencing, but provides a higher-quality reconstruction together with a consistent analytic gradient calculation. Furthermore, we show that our fast evaluation scheme can also be adapted to the Mitchell-Netravali [MN88] notch filter, for which a fast GPU implementation has not been known so far.en_US
dc.description.number2
dc.description.sectionheadersReconstruction and Remeshing
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume42
dc.identifier.doi10.1111/cgf.14753
dc.identifier.issn1467-8659
dc.identifier.pages191-200
dc.identifier.pages10 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14753
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14753
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectCCS Concepts: Computing methodologies -> Volumetric models; Image processing; Texturing
dc.subjectComputing methodologies
dc.subjectVolumetric models
dc.subjectImage processing
dc.subjectTexturing
dc.titleOne Step Further Beyond Trilinear Interpolation and Central Differences: Triquadratic Reconstruction and its Analytic Derivatives at the Cost of One Additional Texture Fetchen_US
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