r-regular shape reconstruction from unorganized points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Crust and anti-crust: a one-step boundary and skeleton extraction algorithm
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Curve reconstruction: connecting dots with good reason
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Curve reconstruction, the traveling salesman problem and Menger's theorem on length
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
TSP-based curve reconstruction in polynomial time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Reconstructing a collection of curves with corners and endpoints
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
VICUR: A human-vision-based algorithm for curve reconstruction
Robotics and Computer-Integrated Manufacturing
Interpolating an unorganized 2D point cloud with a single closed shape
Computer-Aided Design
Constructing 3D motions from curvature and torsion profiles
Computer-Aided Design
EXPERIMENTAL APPROACH TO CURVE RECONSTRUCTION BASED ON HUMAN VISUAL PERCEPTION
Journal of Integrated Design & Process Science
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In this paper, a simple, efficient, and parameter free algorithm, DISCUR, is proposed to reconstruct curves from unorganized sample points. The proposed algorithm can reconstruct multiple simple curves that may be open, closed, and/or with sharp corners. The criteria for the curve reconstruction are based on two observations we have made concerning the human visual system: (1) two closest neighbors tend to be connected, and (2) sampling points tend to be connected into a smooth curve. To simulate these two observations, we use the neighborhood feature to connect the nearest neighbors and we present a statistical criterion to determine when two sample points should not be connected even if they are the nearest neighbors. Finally, a necessary and sufficient condition is proposed for the sampling of curves so that they can be reconstructed by using the present algorithm. Numerous examples show that this algorithm is effective.