In the pattern matching approach to imaging science, the process of ``metamorphosis is template matching with dynamical templates. Here, we recast the metamorphosis equations of into the Euler-Poincare variational framework of and show that the metam
orphosis equations contain the equations for a perfect complex fluid cite{Ho2002}. This result connects the ideas underlying the process of metamorphosis in image matching to the physical concept of order parameter in the theory of complex fluids. After developing the general theory, we reinterpret various examples, including point set, image and density metamorphosis. We finally discuss the issue of matching measures with metamorphosis, for which we provide existence theorems for the initial and boundary value problems.
