Minkowski tensor-based shape analysis methods on the sphere
  Recently, Minkowski Tensors (MT) have gained popularity for morphological
analysis tasks. As opposed to the scalar Minkowski functionals (MF; in 2D given
by area, perimeter and Euler characteristic), MT can characterize symmetry and
orientation of a body. This has been used for a variety of tasks, e.g. to
detect interstellar bubbles by tracing back the origins of filaments in
HII-regions, or to search for alignment of structures in the CMB. I present a
marching-square-based method for calculating MT and MF on the sphere for maps
in the Healpix format. MT are calculated for a local neighborhood and can then
be summed up/averaged over a larger region, using their additivity property.
This provides the possibility of localized analyses looking for CMB
anisotropies and non-Gaussianities at varying scales.
