Reconstruction of convex 2D discrete sets in polynomial time

Attila Kuba, Emese Balogh

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

The reconstruction problem is considered in those classes of discrete sets where the reconstruction can be performed from two projections in polynomial time. The reconstruction algorithms and complexity results are summarized in the case of hv-convex sets, hv-convex 8-connected sets, hv-convex polyominoes, and directed h-convex sets. As new results some properties of the feet and spines of the hv-convex 8-connected sets are proven and it is shown that the spine of such a set can be determined from the projections in linear time. Two algorithms are given to reconstruct hv-convex 8-connected sets. Finally, it is shown that the directed h-convex sets are uniquely reconstructible with respect to their row and column sum vectors.

Original languageEnglish
Pages (from-to)223-242
Number of pages20
JournalTheoretical Computer Science
Volume283
Issue number1
DOIs
Publication statusPublished - Jun 11 2002

Keywords

  • Convex discrete set
  • Discrete tomography
  • Reconstruction from projections

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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