Binary image reconstruction from a small number of projections and the morphological skeleton

Norbert Hantos, Szabolcs Iván, Péter Balázs, Kálmán Palágyi

Research output: Contribution to journalArticle

Abstract

In binary tomography, the goal is to reconstruct binary images from a small set of their projections. This task can be underdetermined, meaning that several binary images can have the same projections, especially when only one or two projections are given. On the other hand, it is known that a binary image can be exactly reconstructed from its morphological skeleton when all skeletal labels are known. However, if only the skeletal points are given, different labellings yield different reconstructed images. In this paper, we consider a mixture of the above problems, reconstructing a binary image from few projections and the morphological skeleton. We show that the problem is NP-complete, yet a result with low projection and pixel error usually can be achieved, even if only a single projection is available. Three different variants of a method based on Simulated Annealing are developed and compared with respect to reconstruction time and error using artificial binary images.

Original languageEnglish
Pages (from-to)195-216
Number of pages22
JournalAnnals of Mathematics and Artificial Intelligence
Volume75
Issue number1-2
DOIs
Publication statusPublished - Nov 21 2014

Fingerprint

Binary images
Binary Image
Image Reconstruction
Image reconstruction
Skeleton
Projection
Simulated annealing
Tomography
Labels
Computational complexity
Simulated Annealing
Pixels
NP-complete problem
Pixel
Binary

Keywords

  • Binary tomography
  • Morphological skeleton
  • NP-completeness
  • Reconstruction
  • Simulated annealing

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

Cite this

Binary image reconstruction from a small number of projections and the morphological skeleton. / Hantos, Norbert; Iván, Szabolcs; Balázs, Péter; Palágyi, Kálmán.

In: Annals of Mathematics and Artificial Intelligence, Vol. 75, No. 1-2, 21.11.2014, p. 195-216.

Research output: Contribution to journalArticle

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