The Geometry of Nonparametric Filament Estimation

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We consider the problem of estimating filamentary structure from planar point process data.

• We make some connections with computational geometry and we develop nonparametric methods for estimating the filaments.
• We show that, under weak conditions, the filaments have a simple geometric representation as the medial axis of the data distribution's support.
• Our methods convert an estimator of the support's boundary into an estimator of the filaments.