How about storing each line in a temporary variable, removing periods from that and then matching against the resulting string? e.g.

@matches=( qr/match1/,
           qr/match2/, ...);
open ($file,"<","/path/to/file") or die ("Horribly");

while (<$file>) {
  $temp=$_;
  $temp=~s/\.//g;
  for my $match (@matches) {
    if ($temp =~m/$match/) {
      do_something();
    }
  }
}
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If you're only going to match against one value you're probably better off adjusting that value (e.g.

), but if you have multiple matches(and possibly multiple ignorable characters) the first suggestion should work well for you.