Computing canonical forms from orbit partitions

Suppose we know the orbit partition of the vertices of a graph (due to the action of its automorphism group). Is it easy (as in "polynomial time") to generate a canonical form (aka "canonical labeling") for that graph using its orbit partition? A quick Google search did not reveal any material that looked like it contains an answer. Wikipedia was not helpful either.
I found some interesting work done by McKay and Piperno using "equitable" partitions (I'm currently reading Practical Graph Isomorphism II), but so far that appears mostly heuristic over a potentially large search space and may be I'm too dumb to make a connection to orbit partitions. (I know that every orbit partition is equitable but the reverse in general is not true.)

• What is a canonical form for a graph? – Gerry Myerson Jul 24 '16 at 4:51
• Gerry Myerson: I edited the question. By canonical form I meant canonical labeling of a graph. – J Reed Jul 24 '16 at 15:53