Stereology of tensors

Eva B. Vedel Jensen (Aarhus)

Abstract: 

Minkowski tensors are an important morphometric tool in the analysis of shape and orientation of spatial structures. They have been used with success, mainly in material science, but there are also examples of applications from the biosciences. In the imaging literature, Minkowski tensors are often called moments. In relation to particle analysis, tensors can be used to describe particle shape and orientation in terms of an approximating ellipsoid associated to each particle.

Common to the above-mentioned applications is that the structure can be studied directly. But in some cases, the structure is only available via sections or projections.

In the present talk, I will give an informal introduction to the field of Minkowski tensors and show how these tensors can be estimated, using a new rotational Crofton formula for Minkowski tensors. This formula concerns integrals of Minkowski tensors on sections passing through fixed points with respect to the rotation invariant measure on such sections.

Joint work with Johanna F. Ziegel.