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.
Comment: Contribution to the 2022 Cosmology session of the 56th Rencontres de Moriond