Of course, I found the answer shortly after posting the question.
Affine3d transform;
AngleAxisd aa(transform.rotation());
Naturally this discards any translation component in the original affine transformation.
Question
How can this be done using Eigen 3?
#include <Eigen/Geometry>
Affine3d transform;
AngleAxisd aa = ...;
Solution
Of course, I found the answer shortly after posting the question.
Affine3d transform;
AngleAxisd aa(transform.rotation());
Naturally this discards any translation component in the original affine transformation.