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.
Pagani, S. M. C., Tijdeman, R., Algorithms for linear time reconstruction by discrete tomography, <<DISCRETE APPLIED MATHEMATICS>>, 2019; 271 (N/A): 152-170. [doi:10.1016/j.dam.2019.07.012] [http://hdl.handle.net/10807/144434]
Algorithms for linear time reconstruction by discrete tomography
Pagani, S. M. C.
;
2019
Abstract
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.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
