Bounds on the difference between reconstructions in binary tomography

Authors:
K. Joost Batenburg;Wagner Fortes;Lajos Hajdu;Robert Tijdeman
Affiliations:
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands and Vision Lab, University of Antwerp, Belgium;Centrum Wiskunde & Informatica, Amsterdam, The Netherlands and Mathematical Institute, Leiden University, The Netherlands;Institute of Mathematics, University of Debrecen, Hungary and Number Theory Research Group of the Hungarian Academy of Sciences, Debrecen, Hungary;Mathematical Institute, Leiden University, The Netherlands
Venue:
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Year:
2011

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Abstract

Tomography is concerned with the reconstruction of images fromtheir projections. In this paper, we consider the reconstruction problem for a class of tomography problems, where the images are restricted to binary grey levels. For any given set of projections, we derive an upper bound on the di??erence between any two binary images having these projections, and a bound on the di??erence between a particular binary image and any binary image having the given projections. Both bounds are evaluated experimentally for different geometrical settings, based on simulated projection data for a range of images.