How to decompose a binary matrix into three hv-convex polyominoes

Authors:
Andrea Frosini;Christophe Picouleau
Affiliations:
Dipartimento di Sistemi e Informatica, Universitá di Firenze, Firenze, Italy;Laboratoire CEDRIC, CNAM, Paris, France
Venue:
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Year:
2013

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Abstract

Given a binary matrix, deciding wether it can be decomposed into three hv-convex matrices is an $\cal NP$-complete problem, whereas its decomposition into two hv-convex matrices or two hv-polyominoes can be performed in polynomial time. In this paper we give a polynomial time algorithm that decomposes a binary matrix into three hv-polyominoes, if such a decomposition exists. These problems are motivated by the Intensity Modulated Radiation Therapy (IMRT).