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

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Advances in Visual Computing (ISVC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9474))

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Abstract

We introduce CINAPACT-splines, a class of \(C^\infty \), accurate and compactly supported splines. The integer translates of a CINAPACT-spline form a 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 an infinitely smooth and compactly supported bump function that has been properly normalized so that it fulfills the partition of unity criterion. We use our construction to design two CINAPACT-splines, and explore their properties in the context of rendering volumetric data sampled on Cartesian grids. Our results show that CINAPACT-splines, while being infinitely smooth, are capable of providing similar reconstruction accuracy compared to some well-established filters of similar cost.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Calgary, Calgary AB, Canada

    Bita Akram, Usman R. Alim & Faramarz F. Samavati

Authors
  1. Bita Akram
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  2. Usman R. Alim
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  3. Faramarz F. Samavati
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Corresponding author

Correspondence to Usman R. Alim .

Editor information

Editors and Affiliations

  1. University of Nevada, Reno, Nevada, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, California, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, California, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, Nevada, USA

    Darko Koracin

  5. University of Houston, Houston, Texas, USA

    Ioannis Pavlidis

  6. IBM T.J. Watson Research Center, Yorktown Heights, New York, USA

    Rogerio Feris

  7. Purdue University, West Lafayette, Indiana, USA

    Tim McGraw

  8. Side Effects Software, Santa Monica, California, USA

    Mark Elendt

  9. The DiVE, Durham, North Carolina, USA

    Regis Kopper

  10. Texas A&M University, College Station, Texas, USA

    Eric Ragan

  11. Kent State University, Kent, Ohio, USA

    Zhao Ye

  12. Lawrence Berkeley National Laboratory, Berkeley, California, USA

    Gunther Weber

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© 2015 Springer International Publishing Switzerland

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Akram, B., Alim, U.R., Samavati, F.F. (2015). CINAPACT-Splines: A Family of Infinitely Smooth, Accurate and Compactly Supported Splines. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2015. Lecture Notes in Computer Science(), vol 9474. Springer, Cham. https://doi.org/10.1007/978-3-319-27857-5_73

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  • DOI: https://doi.org/10.1007/978-3-319-27857-5_73

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27856-8

  • Online ISBN: 978-3-319-27857-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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