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Rotational integral geometry of tensor valuations

By Jérémy Auneau-Cognacq, Johanna Ziegel and Eva B. Vedel Jensen
CSGB Research Reports
No. 02, March 2012
Abstract:

We derive a new rotational Crofton formula for Minkowski tensors. In special cases, this formula gives (1) the rotational average of Minkowski tensors defined on linear subspaces and (2) the functional defined on linear subspaces with rotational average equal to a Minkowski tensor. Earlier results obtained for intrinsic volumes appear now as special cases.

Keywords: Crofton formula; local stereology; Minkowski tensors; rotational integral geometry; tensor valuations

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