The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Curve reconstruction: connecting dots with good reason
Computational Geometry: Theory and Applications
Reconstructing a collection of curves with corners and endpoints
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Traveling Salesman-Based Curve Reconstruction in Polynomial Time
SIAM Journal on Computing
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Reconstructing curves with sharp corners
Computational Geometry: Theory and Applications
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Robust reconstruction of 2D curves from scattered noisy point data
Computer-Aided Design
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We present an algorithm to reconstruct a collection of disjoint smooth closed curves from n noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation of each point in the normal direction with a magnitude smaller than the minimum local feature size. The reconstruction is faithful with a probability that approaches 1 as n increases.We expect that our approach can lead to provable algorithms under less restrictive noise models and for handling non-smooth features.