  We describe a family of new algorithms for finding the canonical image of a
set of points under the action of a permutation group. This family of
algorithms makes use of the orbit structure of the group, and a chain of
subgroups of the group, to efficiently reduce the amount of search which must
be performed to find a canonical image.
  We present both a formal proof of correctness of our algorithms and
experiments on different permutation groups, which compare our algorithms with
the previous state of the art.
