Manifold Fitting under Unbounded Noise

Curvature measures

Herbert Federer · 1959

Earlier work this paper cites.

Principal curves

Trevor Hastie and Werner Stuetzle · 1989

Earlier work this paper cites.

Ice floe identification in satellite images using mathematical morphology and clustering about principal curves

Jeffrey D Banfield and Adrian E Raftery · 1992

Earlier work this paper cites.

On eigenvalue optimization

Alexander Shapiro and Michael Fan · 1995

Earlier work this paper cites.

Columbia object image library (coil-20)

Sameer A Nene, Shree K Nayar, Hiroshi Murase, et al · 1996

Earlier work this paper cites.

Finding curvilinear features in spatial point patterns: principal curve clustering with noise

Derek C Stanford and Adrian E Raftery · 2000

Earlier work this paper cites.

From few to many: Illumination cone models for face recognition under variable lighting and pose

Athinodoros S. Georghiades, Peter N. Belhumeur, and David Kriegman · 2001

Earlier work this paper cites.

Vector analysis, linear algebra, and differential forms: A unified approach

John Hubbard and Barbara Hubbard · 2001

Earlier work this paper cites.

A k-segments algorithm for finding principal curves

Jakob J Verbeek, Nikos Vlassis, and B Kröse · 2002

Earlier work this paper cites.

Finding the homology of submanifolds with high confidence from random samples

Partha Niyogi, Stephen Smale, and Shmuel Weinberger · 2008

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Dian Gong, Fei Sha, and Gérard Medioni · 2010

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A video database of human faces under near infra-red illumination for human computer interaction applications

SL Happy, Anirban Dasgupta, Anjith George, and Aurobinda Routray · 2012

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Charles Fefferman, Sergei Ivanov, Yaroslav Kurylev, Matti Lassas, and Hariharan Narayanan · 2018

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