Symmetric Masks for In-fill Pixel Interpolation on Discrete p

q Lattices

Matthew Ceko, Arnaud Guinard, Imants Svalbe

Research output: Contribution to journalArticleResearchpeer-review

Abstract

A 2D p:q lattice contains image intensity entries at pixels located at regular, staggered intervals that are spaced p rows and q columns apart. Zero values appear at all other intermediate grid locations. We consider here the construction, for any given p:q, of convolution masks to smoothly and uniformly interpolate values across all of the intermediate grid positions. The conventional pixel-filling approach is to allocate intensities proportional to the fractional area that each grid pixel occupies inside the boundaries formed by the p:q lines. However, these area-based masks have asymmetric boundaries, flat interior values and may be odd or even in size. Where edges, lines or points are in-filled, area-based p:q masks imprint intensity patterns that recall p:q because the shape of those masks is asymmetric and depends on p:q. We aim to remove these “memory” artefacts by building symmetric p:q masks. We show here that smoother, symmetric versions of such convolution masks exist. The coefficients of the masks constructed here have simple integer values whose distribution is derived purely from symmetry considerations. We have application for these symmetric interpolation masks as part of a precise image rotation algorithm which disguises the rotation angle, as well as to smooth back-projected values when performing discrete tomographic image reconstruction.

Original languageEnglish
Pages (from-to)304-312
Number of pages9
JournalJournal of Mathematical Imaging and Vision
Volume60
Issue number3
DOIs
Publication statusPublished - Mar 2018

Keywords

  • Discrete Haar interpolation
  • Mojette discrete back-projection
  • Rational angle rotation
  • Symmetric convolution masks

Cite this

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abstract = "A 2D p:q lattice contains image intensity entries at pixels located at regular, staggered intervals that are spaced p rows and q columns apart. Zero values appear at all other intermediate grid locations. We consider here the construction, for any given p:q, of convolution masks to smoothly and uniformly interpolate values across all of the intermediate grid positions. The conventional pixel-filling approach is to allocate intensities proportional to the fractional area that each grid pixel occupies inside the boundaries formed by the p:q lines. However, these area-based masks have asymmetric boundaries, flat interior values and may be odd or even in size. Where edges, lines or points are in-filled, area-based p:q masks imprint intensity patterns that recall p:q because the shape of those masks is asymmetric and depends on p:q. We aim to remove these “memory” artefacts by building symmetric p:q masks. We show here that smoother, symmetric versions of such convolution masks exist. The coefficients of the masks constructed here have simple integer values whose distribution is derived purely from symmetry considerations. We have application for these symmetric interpolation masks as part of a precise image rotation algorithm which disguises the rotation angle, as well as to smooth back-projected values when performing discrete tomographic image reconstruction.",
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Symmetric Masks for In-fill Pixel Interpolation on Discrete p : q Lattices. / Ceko, Matthew; Guinard, Arnaud; Svalbe, Imants.

In: Journal of Mathematical Imaging and Vision, Vol. 60, No. 3, 03.2018, p. 304-312.

Research output: Contribution to journalArticleResearchpeer-review

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