CINAPACT-Splines: A Family of Infnite Smooth, Accurate and Compactly Supported Splines

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atmire.migration.oldid3455
dc.contributor.advisorAlim, Usman
dc.contributor.advisorSamavati, Faramarz
dc.contributor.authorAkram, Bita
dc.date.accessioned2015-09-01T16:50:24Z
dc.date.available2015-11-20T08:00:37Z
dc.date.issued2015-09-01
dc.date.submitted2015en
dc.description.abstractWe introduce a class of compactly supported C infinite kernels (CINAPACT-splines) whose integer translates form a shift-invariant reconstruction space that can be tuned to achieve any order of accuracy. CINAPACT-splines resemble traditional B-splines in that higher orders of accuracy are achieved by successive convolutions with a B-spline of degree zero. Unlike B-splines however, the starting point for CINAPACT-splines is a compactly supported bump function that has been properly normalized so that it fulfills the partition of unity criterion. We explore the properties of CINAPACT-splines in reconstructing volumetric data sampled on regular grids. We show that CINAPACT-splines provide similar reconstruction quality and cost compared to some well-established filters, while being infinitely smooth. We further explore the advantages of our filter by implementing a curvature-based transfer function using second derivatives of the filter to demonstrate feature lines of a function. We apply the same technique using filters of smaller support and less cost.en_US
dc.identifier.citationAkram, B. (2015). CINAPACT-Splines: A Family of Infnite Smooth, Accurate and Compactly Supported Splines (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25328en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/25328
dc.identifier.urihttp://hdl.handle.net/11023/2418
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. 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.
dc.subjectComputer Science
dc.subject.classificationReconstruction Filteren_US
dc.subject.classificationPartition of Unity parametricsen_US
dc.subject.classificationInfinitely smoothen_US
dc.subject.classificationAccurateen_US
dc.subject.classificationCompactly Supporteden_US
dc.titleCINAPACT-Splines: A Family of Infnite Smooth, Accurate and Compactly Supported Splines
dc.typemaster thesis
thesis.degree.disciplineComputer Science
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.item.requestcopytrue
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