Boundary Ghosts for Discrete Tomography

Matthew Ceko, Timothy Petersen, Imants Svalbe, Rob Tijdeman

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

Discrete tomography reconstructs an image of an object on a grid from its discrete projections along relatively few directions. When the resulting system of linear equations is under-determined, the reconstructed image is not unique. Ghosts are arrays of signed pixels that have zero sum projections along these directions; they define the image pixel locations that have non-unique solutions. In general, the discrete projection directions are chosen to define a ghost that has minimal impact on the reconstructed image. Here we construct binary boundary ghosts, which only affect a thin string of pixels distant from the object centre. This means that a large portion of the object around its centre can be uniquely reconstructed. We construct these boundary ghosts from maximal primitive ghosts, configurations of 2 N connected binary (± 1) points over N directions. Maximal ghosts obfuscate image reconstruction and find application in secure storage of digital data.

Original languageEnglish
Pages (from-to)428–440
Number of pages13
JournalJournal of Mathematical Imaging and Vision
Volume63
Issue number3
DOIs
Publication statusPublished - Mar 2021

Keywords

  • Bad configuration
  • Discrete tomography
  • Lattice tiling
  • Mojette transform
  • Projection ghost

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