Abstract

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.

Keywords: Curve; surface; curvature; manifold.

MSC: 53C21, 53C23, 62D05

DOI: 10.57016/MV-ONvQ1063

Pages:  1--11