Computational geometry: an introduction
Computational geometry: an introduction
Partitioning a polygonal region into trapezoids
Journal of the ACM (JACM)
Computer Vision and Image Understanding
Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
Object discretizations in higher dimensions
Pattern Recognition Letters
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
Discrete linear objects in dimension n: the standard model
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
An elementary algorithm for digital arc segmentation
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
On the min DSS problem of closed discrete curves
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Topological Equivalence between a 3D Object and the Reconstruction of Its Digital Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Mathematical Imaging and Vision
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
Scan Conversion of Regions Bounded by Parabolic Splines
IEEE Computer Graphics and Applications
Descnrptive Contour Fill of Parly Degenerated Shapes
IEEE Computer Graphics and Applications
Algorithm for computer control of a digital plotter
IBM Systems Journal
Scaling of plane figures that assures faithful digitization
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Analysis and comparative evaluation of discrete tangent estimators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Some theoretical challenges in digital geometry: A perspective
Discrete Applied Mathematics
On the Convex Hull of the Integer Points in a Bi-circular Region
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Guarding a set of line segments in the plane
Theoretical Computer Science
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In the present extensive work, we propose a digitization scheme for a broad class of plane figures. It includes arbitrary polygons (possibly, non-convex and with holes) and plane sets whose boundary consists of smooth curves or straight segments. Our approach is based on an appropriate scaling of the original continuous real object so that the obtained magnified object and its (appropriately constructed) digitization feature analogous geometric properties. As a bi-product of the presented theory we prove the strong NP-hardness of the problem of obtaining an optimal (i.e., with a minimal number of facets) polyhedral reconstruction in which the facets are trapezoids or triangles. This result implies the strong NP-hardness of the general polyhedral reconstruction problem, which was a long-standing open problem. As another major result, we show that the proposed digitization scheme allows faithful reconstruction of plane figures from the considered general class. The reconstructed set features the basic properties of the original object, such as location of curve and straight segments and inflection points of its boundary.