  A classification of SL$(n)$ contravariant, continuous function valued
valuations on convex bodies is established. Such valuations are natural
extensions of SL$(n)$ contravariant $L_p$ Minkowski valuations, the
classification of which characterized $L_p$ projection bodies, which are
fundamental in the $L_p$ Brunn-Minkowski theory, for $p \geq 1$. Hence our
result will help to better understand extensions of the $L_p$ Brunn-Minkowski
theory. In fact, our results characterize general projection functions which
extend $L_p$ projection functions ($p$-th powers of the support functions of
$L_p$ projection bodies) to projection functions in the $L_p$ Brunn-Minkowski
theory for $0< p < 1$ and in the Orlicz Brunn-Minkowski theory.
