Non uniform projections of surfaces in $\P^3$

Consider the projection of a smooth irreducible surface in $\P^3$ from a point.The uniform position principle implies that the monodromy group of such a projection from a general point in $\P^3$ is the whole symmetric group. We will call such points uniform. Inspired by a result of Pirola and Schlesinger for the case of curves, we proved that the locus of non-uniform points of $\P^3$ is at most finite