Aarhus University Seal / Aarhus Universitets segl

Rotational integral geometry and local stereology - with a view to image analysis

Publikation: Bidrag til bog/antologi/rapport/proceedingBidrag til bog/antologiForskningpeer review


This chapter contains an introduction to rotational integral geometry that is the key tool in local stereological procedures for estimating quantitative properties of spatial structures. In rotational integral geometry, focus is on integrals of geometric functionals with respect to rotation invariant measures. Rotational integrals of intrinsic volumes are studied. The opposite problem of expressing intrinsic volumes as rotational integrals is also considered. It is shown how to express intrinsic volumes as integrals with respect to geometric functionals defined on lower dimensional linear subspaces. Rotational integral geometry of Minkowski tensors is shortly discussed as well as a principal rotational formula. These tools are then applied in local stereology leading to unbiased stereological estimators of mean intrinsic volumes for isotropic random sets. At the end of the chapter, emphasis is put on how these procedures can be implemented when automatic image analysis is available. Computational procedures play an increasingly important role in the stereological analysis of spatial structures and a new sub-discipline, computational stereology, is emerging.

TitelStochastic Geometry, Spatial Statistics and Random Fields : Models and Algorithms
RedaktørerVolker Schmidt
Antal sider23
ForlagSpringer Publishing Company
ISBN (trykt)978-3-319-10063-0
ISBN (Elektronisk)978-3-319-10064-7
StatusUdgivet - 2014
SerietitelLecture Notes in Mathematics

Se relationer på Aarhus Universitet Citationsformater

ID: 98033427