  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 metamorphosis 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.
