Minkowski tensor-based shape analysis methods on the sphere

2022/02/16 by Collischon, Caroline, Klatt, Michael, Räth, Christoph +1
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Instrumentation and Methods for Astrophysics (astro-ph.IM)

paper · doi:10.48550/arxiv.2202.08976

Abstract

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.

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