Toward High Quality Gradient Estimation on Regular Lattices

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dc.contributor.authorHossain, Zahid
dc.contributor.authorAlim, Usman R.
dc.contributor.authorMöller, Torsten
dc.date.accessioned2019-07-02T19:47:07Z
dc.date.available2019-07-02T19:47:07Z
dc.date.issued2011-04
dc.description.abstractIn this paper, we present two methods for accurate gradient estimation from scalar field data sampled on regular lattices. The first method is based on the multi-dimensional Taylor series expansion of the convolution sum and allows us to specify design criteria such as compactness and approximation power. The second method is based on a Hilbert space framework and provides a minimum error solution in the form of an orthogonal projection operating between two approximation spaces. Both methods lead to discrete filters which can be combined with continuous reconstruction kernels to yield highly accurate estimators as compared to the current state of the art. We demonstrate the advantages of our methods in the context of volume rendering of data sampled on Cartesian and Body-Centered Cubic lattices. Our results show significant qualitative and quantitative improvements for both synthetic and real data, while incurring a moderate pre-processing and storage overhead.
dc.identifier.citationHossain, Z., Alim, U. R., & Möller, T. (2011). Toward High-Quality Gradient Estimation on Regular Lattices. IEEE Transactions on Visualization and Computer Graphics, 17(4), 426–439. https://doi.org/10.1109/tvcg.2010.37
dc.identifier.doihttps://doi.org/10.1109/TVCG.2010.37
dc.identifier.issn1941-0506
dc.identifier.urihttp://hdl.handle.net/1880/110556
dc.language.isoenen
dc.language.isoeng
dc.publisherIEEE
dc.publisher.departmentComputer Science
dc.publisher.facultyScienceen
dc.publisher.facultyScience
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.institutionUniversity of Calgary
dc.publisher.policyhttps://journals.ieeeauthorcenter.ieee.org/become-an-ieee-journal-author/guidelines-and-policies/policy-posting-your-journal-article/
dc.rightsUnless otherwise indicated, this material is protected by copyright and has been made available with authorization from the copyright owner. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en
dc.subjectApproximation theory
dc.subjectbody-centered cubic lattice
dc.subjectbox splines
dc.subjectnormal reconstruction
dc.subjectorthogonal projection
dc.subjectTaylor series expansion
dc.titleToward High Quality Gradient Estimation on Regular Lattices
dc.typejournal articleen_US
dc.typeacceptedVersionen_US
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