  Four classic criteria used to the classification of complex flows are
discussed here. These criteria are useful to identify regions of the flow
related to shear, elongation or rigid-body motion. These usual criteria, namely
$Q$, $\Delta$, $\lambda_{2}$ and $\lambda_{cr}/\lambda_{ci}$, use the fluid's
rate-of-rotation tensor, which is known to vary with respect to a reference
frame. The advantages of using objective (invariant with respect to a general
transformation on the reference frame) criteria are discussed in the present
work. In this connection, we construct versions of classic criteria replacing
standard vorticity, a non-objective quantity, by effective vorticity, a rate of
rotation tensor with respect to the angular velocity of the eigenvectors of the
strain rate tensor. The classic criteria and their corresponding objective
versions are applied to classify two complex flows: the transient ABC flow and
the flow through the abrupt 4:1 contraction. It is shown that the objective
versions of the criteria provide richer information on the kinematics of the
flow
