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

TL;DR

This paper presents a new estimator for curvature in point clouds, linking the number of points needed to the probability of having sufficient local data, enabling accurate curvature estimation for curves and surfaces.

Contribution

It introduces a novel algorithm for curvature estimation from point clouds, with a method to determine the minimum number of points required for accuracy.

Findings

The estimator effectively computes curvature from finite samples.

The relation between point count and local density ensures reliable estimation.

The method extends to Gaussian curvature of surfaces.

Abstract

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.