Curve Reconstruction from Noisy Samples

Siu-Wing Cheng, Stefan Funke, Mordecai Golin, Piyush Kumar, Sheung-Hung Poon and Edgar Ramos
Most recent version of the associated paper Abstract We present an algorithm to reconstruct a collection of disjoint smooth closed curves from noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation in the normal directions. Our reconstruction is faithful with probability approaching 1 as the sampling density increases. We expect that our approach can lead to provable algorithms under less restrictive noise models and for handling non-smooth features. Recently we have also implemented a variant of the algorithm we develop in our paper. The implementation currently handles only one closed curve for now. Here are some outputs (Click on the figures for enlarging them) :-

Siu-Wing Cheng, Stefan Funke, Mordecai Golin,
Piyush Kumar, Sheung-Hung Poon and Edgar Ramos

Most recent version of the associated paper

Abstract

We present an algorithm to reconstruct a collection of disjoint smooth closed curves from noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation in the normal directions. Our reconstruction is faithful with probability approaching 1 as the sampling density increases. We expect that our approach can lead to provable algorithms under less restrictive noise models and for handling non-smooth features.

Recently we have also implemented a variant of the algorithm we develop in our paper. The implementation currently handles only one closed curve for now. Here are some outputs (Click on the figures for enlarging them) :-