Use the <> (glob()) operator, documented in perlfunc. Older versions of Perl require that you have a shell installed that groks tildes. Recent perl versions have this feature built in. The File::KGlob module (available from CPAN) gives more portable glob functionality.
Within Perl, you may use this directly:
$filename =~ s{
^ ~ # find a leading tilde
( # save this in $1
[^/] # a non-slash character
* # repeated 0 or more times (0 means me)
)
}{
$1
? (getpwnam($1))[7]
: ( $ENV{HOME} || $ENV{LOGDIR} )
}ex;