Computational geometry: an introduction
Computational geometry: an introduction
Partitioning a polygonal region into trapezoids
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Recovering a polygon from noisy data
Computer Vision and Image Understanding
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Decomposing a polygon into its convex parts
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Topological Equivalence between a 3D Object and the Reconstruction of Its Digital Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the min DSS problem of closed discrete curves
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
3D noisy discrete objects: Segmentation and application to smoothing
Pattern Recognition
Digitization scheme that assures faithful reconstruction of plane figures
Pattern Recognition
Computing upper and lower bounds of rotation angles from digital images
Pattern Recognition
Some theoretical challenges in digital geometry: A perspective
Discrete Applied Mathematics
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In this paper we propose a method for obtaining a faithful digitization of certain broad classes of plane figures, so that the original continuous object and its digitization feature analogous geometric properties. The approach is based on an appropriate scaling of a given figure so that the obtained one admits digitization satisfying some desirable conditions. Informally speaking, we show that from certain point on, a continuous object and its digitization are in a sense equivalent. In terms of computational complexity, the scaling factor is easily computable. As a corollary of the presented theory we prove the strong NP-hardness of the problem of obtaining a polyhedron reconstruction in which the facets are trapezoids or triangles.