Morphometry of Spatial Patterns
  Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape and connectivity. Here we point out, that these scalar descriptors can be complemented by vector-valued curvature measures also known as Quermass vectors. Using examples of galaxy clusters, we demonstrate that the Quermass vectors provide additional morphological information on directional features and symmetries displayed by spatial data. 
C. Beisbart (LMU Munich), T. Buchert (National Astronomical   Observatory Tokyo), H. Wagner (LMU Munich)