Strategies for polyhedral surface decomposition: an experimental study
Proceedings of the eleventh annual symposium on Computational geometry
Discrete analytical hyperplanes
Graphical Models and Image Processing
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Introduction to Algorithms
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
On the min DSS problem of closed discrete curves
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Discrete Applied Mathematics
Reversible vectorisation of 3D digital planar curves and applications
Image and Vision Computing
Some theoretical challenges in digital geometry: A perspective
Discrete Applied Mathematics
Maximal planes and multiscale tangential cover of 3D digital objects
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
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This paper deals with the complexity of the decomposition of a digital surface into digital plane segments (DPSs for short). We prove that the decision problem (does there exist a decomposition with less than @l DPSs?) is NP-complete, and thus that the optimization problem (finding the minimum number of DPSs) 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.