Integral estimation from point cloud in d-dimensional space: a geometric view

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...

• Type: Conference
• Year: 2009
• Where: COMPGEOM
• Authors: Chuanjiang Luo, Jian Sun, Yusu Wang
• Keywords: COMPGEOM 2009, Discrete Geometry, Integral, Principal Eigenvector Scheme, Theoretical Guarantee