### 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 language | English |
---|---|

Pages (from-to) | 304-312 |

Number of pages | 9 |

Journal | Journal of Mathematical Imaging and Vision |

Volume | 60 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2018 |

### Keywords

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

### Cite this

*p*:

*q*Lattices.

*Journal of Mathematical Imaging and Vision*,

*60*(3), 304-312. https://doi.org/10.1007/s10851-017-0760-2

}

*p*:

*q*Lattices',

*Journal of Mathematical Imaging and Vision*, vol. 60, no. 3, pp. 304-312. https://doi.org/10.1007/s10851-017-0760-2

**Symmetric Masks for In-fill Pixel Interpolation on Discrete p : q Lattices.** / Ceko, Matthew; Guinard, Arnaud; Svalbe, Imants.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Symmetric Masks for In-fill Pixel Interpolation on Discrete p

T2 - q Lattices

AU - Ceko, Matthew

AU - Guinard, Arnaud

AU - Svalbe, Imants

PY - 2018/3

Y1 - 2018/3

N2 - 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.

AB - 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.

KW - Discrete Haar interpolation

KW - Mojette discrete back-projection

KW - Rational angle rotation

KW - Symmetric convolution masks

UR - http://www.scopus.com/inward/record.url?scp=85029593687&partnerID=8YFLogxK

U2 - 10.1007/s10851-017-0760-2

DO - 10.1007/s10851-017-0760-2

M3 - Article

VL - 60

SP - 304

EP - 312

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

SN - 0924-9907

IS - 3

ER -

*p*:

*q*Lattices. Journal of Mathematical Imaging and Vision. 2018 Mar;60(3):304-312. https://doi.org/10.1007/s10851-017-0760-2