The Reconstruction of Polyominoes from Horizontal and Vertical Projections and Morphological Skeleton is NP-complete

Authors:
Norbert Hantos;Pé/ter Balá/zs
Affiliations:
Department of Image Processing and Computer Graphics, University of Szeged, Á/rpá/d té/r 2. H-6720, Szeged, Hungary. nhantos@inf.u-szeged.hu/ pbalazs@inf.u-szeged.hu;Department of Image Processing and Computer Graphics, University of Szeged, Á/rpá/d té/r 2. H-6720, Szeged, Hungary. nhantos@inf.u-szeged.hu/ pbalazs@inf.u-szeged.hu
Venue:
Fundamenta Informaticae - Strategies for Tomography
Year:
2013

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Abstract

Reconstruction of binary images from their projections is one of the main tasks in many image processing areas, therefore determining the computational complexity of those problems is essential. The reconstruction complexity is highly dependent on the requirements of the image. In this paper, we will show that the reconstruction is NP-complete if the horizontal and vertical projections and the morphological skeleton of the image are given, and it is supposed that the image is 4-connected.