Fast filling operations used in the reconstruction of convex lattice sets

Sara Brunetti, Alain Daurat, A. Kuba

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Filling operations are procedures which are used in Discrete Tomography for the reconstruction of lattice sets having some convexity constraints. In [1], an algorithm which performs four of these filling operations has a time complexity of O(N2 log N), where N is the size of projections, and leads to a reconstruction algorithm for convex polyominoes running in O(N 6 log N)-time. In this paper we first improve the implementation of these four filling operations to a time complexity of O(N2), and additionally we provide an implementation of a fifth filling operation (introduced in [2]) in O(N2 log N) that permits to decrease the overall time-complexity of the reconstruction algorithm to O(N4 log N). More generally, the reconstruction of Q-convex sets and convex lattice sets (intersection of a convex polygon with ℤ2) can be done in O(N4 log N)-time.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages98-109
Number of pages12
Volume4245 LNCS
ISBN (Print)3540476512, 9783540476511
Publication statusPublished - 2006
Event13th International Conference on Discrete Geometry for Computer Imagery, DGCI 2006 - Szeged, Hungary
Duration: Oct 25 2006Oct 27 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4245 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other13th International Conference on Discrete Geometry for Computer Imagery, DGCI 2006
CountryHungary
CitySzeged
Period10/25/0610/27/06

Fingerprint

Time Complexity
Reconstruction Algorithm
Discrete Tomography
Intersection of sets
Polyominoes
Convex polygon
Convex Sets
Tomography
Convexity
Projection
Decrease

Keywords

  • Convexity
  • Discrete tomography
  • Filling operations

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Brunetti, S., Daurat, A., & Kuba, A. (2006). Fast filling operations used in the reconstruction of convex lattice sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4245 LNCS, pp. 98-109). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4245 LNCS). Springer Verlag.

Fast filling operations used in the reconstruction of convex lattice sets. / Brunetti, Sara; Daurat, Alain; Kuba, A.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4245 LNCS Springer Verlag, 2006. p. 98-109 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4245 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Brunetti, S, Daurat, A & Kuba, A 2006, Fast filling operations used in the reconstruction of convex lattice sets. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4245 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4245 LNCS, Springer Verlag, pp. 98-109, 13th International Conference on Discrete Geometry for Computer Imagery, DGCI 2006, Szeged, Hungary, 10/25/06.
Brunetti S, Daurat A, Kuba A. Fast filling operations used in the reconstruction of convex lattice sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4245 LNCS. Springer Verlag. 2006. p. 98-109. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Brunetti, Sara ; Daurat, Alain ; Kuba, A. / Fast filling operations used in the reconstruction of convex lattice sets. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4245 LNCS Springer Verlag, 2006. pp. 98-109 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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