  We introduce the non-commutative $f$-divergence functional
$\Theta(\widetilde{A},\widetilde{B}):=\int_TB_t^{\frac{1}{2}}f\left(B_t^{-\frac{1}{2}}
A_tB_t^{-\frac{1}{2}}\right)B_t^{\frac{1}{2}}d\mu(t)$ for an operator convex
function $f$, where $\widetilde{A}=(A_t)_{t\in T}$ and
$\widetilde{B}=(B_t)_{t\in T}$ are continuous fields of Hilbert space operators
and study its properties. We establish some relations between the perspective
of an operator convex function $f$ and the non-commutative $f$-divergence
functional. In particular, an operator extension of Csisz\'{a}r's result
regarding $f$-divergence functional is presented. As some applications, we
establish a refinement of the Choi--Davis--Jensen operator inequality, obtain
some unitarily invariant norm inequalities and give some results related to the
Kullback--Leibler distance.
