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

2025/06/07 by Mirzaie, R.
#53C21 #53C23 #62D05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.06779

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.

Citations

• Robust Estimation of Surface Curvature Information from Point Cloud Data
• Estimating differential quantities using polynomial fitting of osculating jets

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