Boundary Ghosts for Discrete Tomography

• Published in: Journal of mathematical imaging and vision Vol. 63; no. 3; pp. 428 - 440
• Main Authors: Ceko, Matthew, Petersen, Timothy, Svalbe, Imants, Tijdeman, Rob
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Computer Science; Digital data; Digital imaging; Ghosts; Image Processing and Computer Vision; Image reconstruction; Linear equations; Mathematical Methods in Physics; Pixels; Signal,Image and Speech Processing; Tomography; Uniqueness; Discrete tomography; Bad configuration; Mojette transform; Projection ghost; Lattice tiling
• ISSN: 0924-9907; 1573-7683
• DOI: 10.1007/s10851-020-01010-2

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.