To a pair of normal functions on a complex manifold $U$ one can associate a canonically metrized line bundle ($B$, $h$).If $U$ is Zariski open in a complex manifold $S$ one can ask two natural questions:

a) Is there a canonical choice of extension of $B$ to a line bundle on $S$?

b) Does the metric $h$ extend to a metric on $S$?

For normal functions which are admissible in the sense of M. Saito, in joint work with P. Brosnan, we give a positive answer to (a) and determine an obstruction to (b) which can be expressed as a pairing on intersection cohomology.