How Many Points in a Point Cloud Is Sufficient for Accurate Estimation of the Curvature

We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from a probability distribution whose support lies on the curve or surface. First, we give a probabilistic procedure for estimating the curvature at a given point of a curve. Then, we extend it to estimate the Gaussian curvature of surfaces. In the proposed probabilistic procedures, we use a relation between the number of selected points in the point cloud and the probability that a given point has a sufficient number of nearby points. This relation allows us to control the required number of points in the point cloud.