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- Title
Morphometry on the sphere: Cartesian and irreducible Minkowski tensors explained and implemented.
- Authors
Collischon, Caroline; Klatt, Michael A.; Banday, Anthony J.; Sasaki, Manami; Räth, Christoph
- Abstract
Minkowski tensors are comprehensive shape descriptors that robustly capture n-point information in complex random geometries and that have already been extensively applied in the Euclidean plane. Here, we devise a framework for Minkowski tensors on the sphere. We first advance the theory by introducing irreducible Minkowski tensors, which avoid the redundancies of previous representations. We, moreover, generalize Minkowski sky maps to the sphere. These maps are a concept of local anisotropy, which easily adjusts to masked data. We demonstrate the power of our new procedure by applying it to simulations and real data of the Cosmic Microwave Background, finding an anomalous region close to the well-known Cold Spot. The accompanying open-source software, litchi, used to generate these maps from data in the HEALPix-format is made publicly available to facilitate broader integration of Minkowski maps in other fields, such as fluid demixing, porous structures, or geosciences more generally. Image data located on spherical surfaces pose unique analytic challenges. In this paper the authors extend the definition of irreducible Minkowski Tensors, powerful additive shape descriptors, to the surface of the sphere and provide an open-source toolset to facilitate their use.
- Subjects
COSMIC background radiation; MORPHOMETRICS; STAR maps (Astronomy); CONCEPT mapping
- Publication
Communications Physics, 2024, Vol 7, Issue 1, p1
- ISSN
2399-3650
- Publication type
Article
- DOI
10.1038/s42005-024-01751-1