An algorithm for the reconstruction of discrete sets from two projections in presence of absorption

Authors:
Elena Barcucci;Andrea Frosini;Simone Rinaldi
Affiliations:
Dipartimento di Sistemi e Informatica, Universití degli Studi di Firenze, Via Lombroso 6/17, 50134 Firenze, Italy;Dipartimento di Scienze Matematiche ed Informatiche "Roberto Magari", Universití degli Studi di Siena Pian dei Mantellini 44, 53100 Siena, Italy;Dipartimento di Scienze Matematiche ed Informatiche "Roberto Magari", Universití degli Studi di Siena Pian dei Mantellini 44, 53100 Siena, Italy
Venue:
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Year:
2005

Citing 1
Cited 1

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Abstract

In this paper we consider the problem of reconstructing a binary matrix from absorbed projections, as introduced in [Kuba and Nivat, Linear Algebra Appl. 339 (2001) 171-194]. In particular we prove that two left and right horizontal absorbed projections along a single direction uniquely determine a row of a binary matrix for a specific absorption coefficient. Moreover, we give a linear time algorithm which reconstructs such a row and we analyze its performances by determining the worst case complexity. Finally, we study the same problems in the presence of different absorption coefficients.