SCIL - Symbolic Constraints in Integer Linear Programming
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Curve reconstruction from noisy samples
Proceedings of the nineteenth annual symposium on Computational geometry
Curve reconstruction from noisy samples
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Optimization-based approach for curve and surface reconstruction
Computer-Aided Design
Curve reconstruction from noisy samples
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
On the representation of a digital contour with an unordered point set for visual perception
Journal of Visual Communication and Image Representation
Robust reconstruction of 2D curves from scattered noisy point data
Computer-Aided Design
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An instance of the curve reconstruction problem is a finite sample set V of an unknown collection of curves $\gamma$. The task is to connect the points in V in the order in which they lie on $\gamma$. Giesen [Proceedings of the 15th Annual ACM Symposium on Computational Geometry (SCG '99), 1999, pp. 207--216] showed recently that the traveling salesman tour of V solves the reconstruction problem for single closed curves under otherwise weak assumptions on $\gamma$ and V; $\gamma$ must be a single closed curve. We extend his result along several directions: we weaken the assumptions on the sample; we show that traveling salesman-based reconstruction also works for single open curves (with and without specified endpoints) and for collections of closed curves; we give alternative proofs; and we show that in the context of curve reconstruction, the traveling salesman tour can be constructed in polynomial time.