Abstract
Inspired by recent developments in stereology, rotational versions of the Crofton formula are derived. The first version involves rotation averages of Minkowski functionals. It is shown that for the special case where the Minkowski functional is surface area, the rotation average can be expressed in terms of hypergeometric functions. The second rotational version of the Crofton formula solves the ‘opposite’ problem of finding functions with rotation averages equal to the Minkowski functionals. For the case of surface area, hypergeometric functions appear again. The second type of rotational Crofton formula has applications in local stereology. As a by-product, a formula involving mixed volumes is found.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Bibliography;Mathematical Foundations of Image Processing and Analysis 2;2014-07-22
2. Bibliography;Mathematical Foundations of Image Processing and Analysis 1;2014-07-08
3. A rotational integral formula for intrinsic volumes;Advances in Applied Mathematics;2008-10
4. The distribution of volume reductions induced by isotropic random projections;Advances in Applied Probability;1999-12
5. The distribution of volume reductions induced by isotropic random projections;Advances in Applied Probability;1999-12