  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 novel 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,
i.e., 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.
