A fast algorithm for reconstructing hv-convex 8-connected but not 4-connected discrete sets

Péter Balázs, Emese Balogh, Attila Kuba

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

One important class of discrete sets where the reconstruction from two given projections can be solved in polynomial time is the class of hv-convex 8-connected sets. The worst case complexity of the fastest algorithm known so far for solving the problem is of O(mn· min{m2,n2}) [2]. However, as it is shown, in the case of 8-connected but not 4-connected sets we can give an algorithm with worst case complexity of O(mn·min{m,n}) by identifying the so-called S4-components of the discrete set. Experimental results are also presented in order to investigate the average execution time of our algorithm.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsIngela Nystrom, Gabriella Sanniti di Baja, Stina Svensson
PublisherSpringer Verlag
Pages388-397
Number of pages10
ISBN (Electronic)3540204997, 9783540204992
DOIs
Publication statusPublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2886
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • Convex and connected discrete set
  • Discrete tomography
  • Reconstruction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Balázs, P., Balogh, E., & Kuba, A. (2003). A fast algorithm for reconstructing hv-convex 8-connected but not 4-connected discrete sets. In I. Nystrom, G. S. di Baja, & S. Svensson (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 388-397). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2886). Springer Verlag. https://doi.org/10.1007/978-3-540-39966-7_37