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COMPGEOM

2009

ACM

2009

ACM

Integration over a domain, such as a Euclidean space or a Riemannian manifold, is a fundamental problem across scientiﬁc ﬁelds. Many times, the underlying domain is only accessible through a discrete approximation, such as a set of points sampled from it, and it is crucial to be able to estimate integral in such discrete settings. In this paper, we study the problem of estimating the integral of a function deﬁned over a k-submanifold embedded in IRd , from its function values at a set of sample points. Previously, such estimation is usually obtained in a statistical setting, where input data is typically assumed to be drawn from certain probabilistic distribution. Our paper is the ﬁrst to consider this important problem of estimating integral from point clouds data (PCD) under the more general non-statistical setting, and provide certain theoretical guarantees. Our approaches consider the problem from a geometric point of view. Speciﬁcally, we estimate the integral by comput...

Related Content

Added |
28 May 2010 |

Updated |
28 May 2010 |

Type |
Conference |

Year |
2009 |

Where |
COMPGEOM |

Authors |
Chuanjiang Luo, Jian Sun, Yusu Wang |

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