Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
Proceedings of the nineteenth annual symposium on Computational geometry
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Provably good moving least squares
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Dimension detection via slivers
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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We present simple algorithms for detecting the dimension k of a smooth manifold M ⊂ Rd from a set P of point samples, provided that P satisfies a standard sampling condition as in previous results. The best running time so far is O(d2O(k7 log k)) worst-case by Giesen and Wagner after the adaptive neighborhood graph is constructed in O(d|P|2) worst-case time. Given the adaptive neighborhood graph, for any l ≥ 1, our algorithm outputs the true dimension with probability at least 1-2-l in O(2O(k)kd(k + l log d)) expected time. Our experimental results validate the effectiveness of our approach in computing the dimension. A further advantage is that both the algorithm and its analysis can be generalized to the noisy case, in which outliers and a small perturbation of the samples are allowed.