Algorithms for linear time reconstruction by discrete tomography

Algorithms for linear time reconstruction by discrete tomography

We present an algorithm that for any given rectangular grid A∈Z2 and set of directions D computes in linear time the values of any function f:A→R outside the convex hull of the union of the switching domains from its line sums in the directions of D. Moreover, the algorithm reconstructs f completely...

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Veröffentlicht in:Discrete Applied Mathematics 2019-12, Vol.271, p.152-170
Hauptverfasser: Pagani, Silvia M.C., Tijdeman, Rob
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Computational geometry
Convexity
Discrete tomography
Domains
Hulls
Lattice direction
Reconstruction algorithm
Region of uniqueness
Sums
Switching
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Zusammenfassung:We present an algorithm that for any given rectangular grid A∈Z2 and set of directions D computes in linear time the values of any function f:A→R outside the convex hull of the union of the switching domains from its line sums in the directions of D. Moreover, the algorithm reconstructs f completely if there are no switching domains. We present a simpler algorithm in case the directions satisfy some monotonicity condition. Finally, for given A we propose how to choose the set D so that only a small number of directions is needed to reconstruct any f from its line sums in the directions of D.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2019.07.012