关于随机正态测度的凸集重构
On the reconstruction of convex sets from random normal measurements
摘要：
我们研究了只用有限个外法向量的测量值重建凸体的问题。更准确地说，我们假设法向量是在独立的随机位置上测量的，这些位置沿着我们的凸集的边界均匀分布。给定一个所需的豪斯多夫误差η，我们提供了一个上界的探测器的数量，一个必须执行，以获得一个高概率的这个凸集的η-近似。我们的结果依赖于与Minkowski定理相关的稳定性理论。
英文摘要：
We study the problem of reconstructing a convex body using only a finite number of measurements of outer normal vectors. More precisely, we suppose that the normal vectors are measured at independent random locations uniformly distributed along the boundary of our convex set. Given a desired Hausdorff error eta, we provide an upper bounds on the number of probes that one has to perform in order to obtain an eta-approximation of this convex set with high probability. Our result rely on the stability theory related to Minkowski's theorem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
