Optimization and reconstruction of hv-convex (0, 1)-matrices

Authors:
Geir Dahl;Truls Flatberg
Affiliations:
Centre of Mathematics for Applications, University of Oslo, Blindern, Oslo, Norway;Centre of Mathematics for Applications, University of Oslo, Blindern, Oslo, Norway
Venue:
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Year:
2005

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Abstract

We consider a variant of the NP-hard problem of reconstructing hv-convex (0, 1)-matrices from known row and column sums. Instead of requiring the ones to occur consecutively in each row and column, we maximize the number of neighboring ones. This is reformulated as an integer programming problem. A solution method based on variable splitting is proposed and tested with good results on moderately sized test problems.