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Proceedings of the eleventh annual symposium on Computational geometry
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DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
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Pattern Recognition
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This paper deals with the complexity of the decomposition of a digital surface into digital plane segments (DPS for short) We prove that the decision problem (does there exist a decomposition with less than k DPS?) is NP-complete, and thus that the optimisation problem (finding the minimal number of DPS) is NP-hard The proof is based on a polynomial reduction of any instance of the well-known 3-SAT problem to an instance of the digital surface decomposition problem A geometric model for the 3-SAT problem is proposed.