Symmetric masks for In-fill pixel interpolation on discrete p:q lattices

Imants Svalbe, Arnaud Guinard

Research output: Chapter in Book/Report/Conference proceedingConference PaperOtherpeer-review

2 Citations (Scopus)


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. We ask here if smoother, symmetric versions of such convolution masks exist and, if so, is their structure unique for each p:q lattice? The answer appears to be yes on both counts. 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, as well as to smooth back-projected values when performing discrete tomographic image reconstruction.

Original languageEnglish
Title of host publicationProceedings of 19th IAPR International Conference Discrete Geometry for Computer Imagery
Subtitle of host publicationDGCI 2016
EditorsNicolas Normand, Jeanpierre Guédon, Florent Autrusseau
Place of PublicationSwitzerland
PublisherSpringer-Verlag London Ltd.
Number of pages11
ISBN (Print)9783319323596
Publication statusPublished - 2016
EventInternational Conference on Discrete Geometry for Computer Imagery 2016 - La Cité Nantes Events Center, Nantes, France
Duration: 18 Apr 201620 Apr 2016
Conference number: 19th (Proceedings)

Publication series

NameLecture Notes in Computer Science
PublisherSpringer International Publishing
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Conference on Discrete Geometry for Computer Imagery 2016
Abbreviated titleDGCI 2016
OtherDiscrete Geometry for Computer Imagery
19th IAPR International Conference, DGCI 2016, Nantes, France, April 18-20, 2016. Proceedings
Internet address


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

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