Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications

We investigate identifying the boundary of a domain from sample points in domain. introduce new estimators for normal vector to boundary, distance point and test whether lies within strip. The can be efficiently computed are more accurate than ones present literature. provide rigorous error estimates estimators. Furthermore we use detected solve boundary-value problems PDE on clouds. prove Laplace eikonal equations Finally range numerical experiments illustrating performance our estimators, applications clouds, tests image data sets.