The Minkowski tensors contain information about both the preferred direction and the amplitude of the anisotropy. The latter can be conveniently extracted by **scalar anisotropy indices**.

Here, we present some common indices in both 2D and 3D.

*q*

_{s}The shape indices are defined as

for closed polygons.

is the quadrupole component of the normal density

can detect anisotropy in a three-fold symmetric system (e.g. suitable for detecting equilateral triangles)

can detect anisotropy in a four-fold symmetric system (e.g. suitable for detecting rectangles)

…

**Morphometric distance**

A morphometric distance of a polygon to a reference structure can be quantified by considering the pseudo distance function

*β*

equal to 0 indicates a „flat“ body .

equal to 1 indicates an „isotropic“ body , in the sense that it has a statistically identical mass distribution in any set of three orthogonal directions; this includes the sphere, but also regular polyhedra and the FCC, BCC and HCP Voronoi cells.

*Q*

In 2D:

In 3D: