How many points in a point cloud is sufficient for accurate estimation of the curvature

Fuente: arXiv
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Main Author: Mirzaie, R.
Format: Preprint
Published: 2025
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author Mirzaie, R.
author_facet Mirzaie, R.
contents We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the curvature in a given point of a curve. Then, we extend it to estimate the Gaussian curvature of the surfaces. In the proposed algorithms, we use a relation between the number of selected points in the point cloud and the probability that a given point has a suffcient number of nearby points. This relation allows us to control the required number of points in the point cloud.
format Preprint
id arxiv_https___arxiv_org_abs_2506_06779
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle How many points in a point cloud is sufficient for accurate estimation of the curvature
Mirzaie, R.
Differential Geometry
53C21, 53C23, 62D05
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the curvature in a given point of a curve. Then, we extend it to estimate the Gaussian curvature of the surfaces. In the proposed algorithms, we use a relation between the number of selected points in the point cloud and the probability that a given point has a suffcient number of nearby points. This relation allows us to control the required number of points in the point cloud.
title How many points in a point cloud is sufficient for accurate estimation of the curvature
topic Differential Geometry
53C21, 53C23, 62D05
url https://arxiv.org/abs/2506.06779