  Reference frame optimization is a generic framework to calculate a
spatially-varying observer field that views an unsteady fluid flow in a
reference frame that is as-steady-as-possible. In this paper, we show that the
optimized vector field is objective, i.e., it is independent of the initial
Euclidean transformation of the observer. To check objectivity, the optimized
velocity vectors and the coordinates in which they are defined must both be
connected by an Euclidean transformation. In this paper we show that a recent
publication [1] applied this definition incorrectly, falsely concluding that
reference frame optimizations are not objective. Further, we prove the
objectivity of the variational formulation of the reference frame optimization
proposed in [1], and discuss how the variational formulation relates to recent
local and global optimization approaches to unsteadiness minimization.
