  The morphology of galaxy clusters is quantified using Minkowski functionals,
especially the vector-valued ones, which contain directional information and
are related to curvature centroids. The asymmetry of clusters and the amount of
their substructure can be characterized in a unique way using these measures.
-- We briefly introduce vector-valued Minkowski functionals (also known as
Querma\ss vectors) and suggest their application to cluster data in terms of a
morphological characterization of excursion sets. Furthermore, we develop
robust structure functions which describe the dynamical state of a cluster and
study the evolution of clusters using numerical simulations.
