Shape dimension and intrinsic metric from samples of manifolds

Discrete and Computational Geometry

Volumn 32, Issue 2, 2004, Pages 245-267

  Giesen, Joachim ^a   Wagner, Uli ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344564994     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-004-1120-8     Document Type: Conference Paper

References (19)

1. A.D. Aleksandrov and Y.G. Reshetnyak, General Theory of Irregular Curves. Kluwer Academic, Dordrecht (1989).
2. N. Amenta and M. Bern. Surface reconstruction by Voronoi filtering. Discrete Comput. Geom., 22 (1999), 481-504.
3. N. Amenta, S. Choi, T.K. Dey, and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. In Proc. 16th. ACM Sympos. Comput. Geom., pp. 213-222 (2000).
4. N. Amenta, S. Choi, and R.K. Kolluri. The power crust, unions of balls, and the medial axis transform. Comp. Geom. Theory Appl., 19(2-3) (2001), 127-153.
5. S. Arya, T. Malamatos, and D.M. Mount. Space-efficient approximate Voronoi diagrams. In Proc. 34th ACM Sympos. Theory Comput., pp. 721-730 (2002).
6. D. Attali, J.-D. Boissonnat, and A. Lieutier. Complexity of the Delaunay triangulation of points on surfaces: the smooth case. In Proc. 19th ACM Sympos. Comput. Geom., pp. 201-210 (2003).
7. M. Bern et al. Emerging Challenges in Computational Topology. NSF report (1999).
8. M. Bernstein, V. de Silva, J.C. Langford and J. Tenenbaum. Graph approximations to geodesies on embedded manifolds. Manuscript (2000).
9. C. Bregler and S.M. Omohundro. Nonlinear manifold learning for visual speech recognition. In Proc. Int. Conf. Comput. Vision, pp. 494-499 (1995).
10. C. Bregler and S.M. Omohundro. Nonlinear image interpolation using manifold learning. In G. Tesauro, O.S. Touretzky, and T.K. Leen (eds.), Advances in Neural Information Processing Systems, vol. 7. MIT Press, Cambridge, MA, pp. 973-980 (1995).
11. T.K. Dey and J. Giesen. Detecting undersampling in surface reconstruction. In Proc. 17th. ACM Sympos. Comput. Geom., pp. 257-263 (2001).
12. T.K. Dey, J. Giesen, S. Goswami and W. Zhao. Shape dimension and approximation from samples. In Proc. 13th ACM-SIAM Sympos. Discrete Algorithms, pp. 772-780 (2002).
13. J. Erickson. Dense point sets have sparse Delaunay triangulations. Discrete Comput. Geom., to appear.
14. S. Funke and E. Ramos. Smooth-surface reconstruction in near-linear time. In P roc. 13th ACM-SIAM Sympos. Discrete Algorithms, pp. 781-790 (2002).
15. S. Har-Peled and K. Varadarajan. Projective clustering in high dimensions using core-sets. In Proc. 18th Sympos. Comp. Geom., pp. 312-318 (2002).
16. J. Jost. Differential geometrie und Minimalfiächen. Springer-Verlag, Berlin (1991).
17. T. Martinetz and K. Schulten. Topology representing networks. Neural Networks, 7 (1994), 507-522.
18. E. Schmidt. Über das Extremum der Bogenlänge einer Raumkurve bei vorgeschriebenen Einschränkungen ihrer Krümmung. Sitzungsber. Preuss. Akad. Wiss. Berlin Phys. Math. Kl., 25 (1925), 485-490.
19. J. Tenenbaum, V. de Silva and J.C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290 (2000), 2319-2322.