Invariance Properties of Generalized Polarization Tensors and Design of   Shape Descriptors in Three Dimensions
  We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be used as shape descriptors for dictionary matching. 
Habib Ammari, Daewon Chung, Hyeonbae Kang, and Han Wang
math.AP math.NA