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

We 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.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Computer Science

Grantor dc:publisher.institution

Graduate Studies

Year dc:date.issued

2015

Author dc:creator

• Akram, Bita

Advisors dc:contributor.advisor

• Alim, Usman
• Samavati, Faramarz

• Computer Science

Statement dc:rights

• University 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.

Language dc:language.iso

eng

DOI

http://dx.doi.org/10.11575/PRISM/25328

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:11023/2418