  Quasisymmetric functions have recently been used in time series analysis as
polynomial features that are invariant under, so-called, dynamic time warping.
We extend this notion to data indexed by two parameters and thus provide
warping invariants for images. We show that two-parameter quasisymmetric
functions are complete in a certain sense, and provide a two-parameter
quasi-shuffle identity. A compatible coproduct is based on diagonal
concatenation of the input data, leading to a (weak) form of Chen's identity.
