Estimation of surface area

We study the problem of estimating surface area boundary ∂S a sufficiently smooth set S⊂Rd when available information is only finite subset Xn⊂S. propose two estimators. The first makes use Devroye–Wise support estimator and based on Crofton’s formula, which, roughly speaking, states that (d−1)-dimensional enough mean number intersections randomly chosen lines. For purpose, we an such lines with second α-convex hull Xn, which denoted by Cα(Xn). More precisely, it Cα(Xn), as |Cα(Xn)|d−1, proven to converge ∂S. Moreover, |Cα(Xn)|d−1 can be computed using formula. Our results depend Hausdorff distance between S Xn for estimator, ∂Cα(Xn) estimator.