On the ambiguity of reconstructing hv-convex binary matrices with decomposable configurations

Balázs, Péter: On the ambiguity of reconstructing hv-convex binary matrices with decomposable configurations. In: Acta cybernetica, (18) 3. pp. 367-377. (2008)

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Abstract

Reconstructing binary matrices from their row, column, diagonal, and antidiagonal sums (also called projections) plays a central role in discrete tomography. One of the main difficulties in this task is that in certain cases the projections do not uniquely determine the binary matrix. This can yield an extremely large number of (sometimes very different) solutions. This ambiguity can be reduced by having some prior knowledge about the matrix to be reconstructed. The main challenge here is to find classes of binary matrices where ambiguity is drastically reduced or even completely eliminated. The goal of this paper is to study the class of hv-convex matrices which have decomposable configurations from the viewpoint of ambiguity. First, we give a negative result in the case of three projections. Then, we present a heuristic for the reconstruction using four projections and analyze its performance in quality and running time.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2008
Volume: 18
Number: 3
ISSN: 0324-721X
Page Range: pp. 367-377
Language: angol
Event Title: Conference for PhD Students in Computer Science, 5., 2006, Szeged
Uncontrolled Keywords: Természettudomány, Informatika
Additional Information: Bibliogr.: p. 376-377.; Abstract
Date Deposited: 2016. Oct. 15. 12:25
Last Modified: 2018. Jun. 05. 14:30
URI: http://acta.bibl.u-szeged.hu/id/eprint/12824

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