Fitting 3D curves to unorganized data points using deformable curves
CG International '92 Proceedings of the 10th International Conference of the Computer Graphics Society on Visual computing : integrating computer graphics with computer vision: integrating computer graphics with computer vision
Implicit Simplicial Models for Adaptive Curve Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
The approximation power of moving least-squares
Mathematics of Computation
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Curve reconstruction from unorganized points
Computer Aided Geometric Design
Curve reconstruction: connecting dots with good reason
Computational Geometry: Theory and Applications
Grouping and parameterizing irregularly spaced points for curve fitting
ACM Transactions on Graphics (TOG)
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
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Reconstructing curves with sharp corners
Computational Geometry: Theory and Applications
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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We present an algorithm to reconstruct a collection of disjoint smooth closed curves from 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 in the normal directions. Our reconstruction is faithful with probability approaching 1 as the sampling density increases.