Assuming there's no performance pressure, I think a straightforward search would be sufficient.

Here's an untested code outline:

use strict;

# Build grid array
my @grid;
foreach ( <DATA> ) {
  s/^\s*\b// or next;
  push @grid, [ split ' ', $_ ],
}

# Assign arbitrary regions
my @region;
foreach my $x ( 0 .. $#grid ) {
  foreach my $y ( 0 .. $#{ $grid[0] } ) {
    $region[$x][$y] = "$x.$y";
  }
}

# Merge neighboring regions
foreach my $x ( 0 .. $#grid ) {
  foreach my $y ( 0 .. $#{ $grid[0] } ) {
    my @neighbors = ( [ $x-1, $y ], [$x, $y-1] );
    foreach my $coord ( @neighbors ) {
      my ( $nx, $ny ) = @$coord;
      next if ( $nx < 0 or $ny < 0 );
      if ( $grid[$x][$y] eq $grid[ $nx ][ $ny ] and
         $region[$x][$y] ne $region[ $nx ][ $ny ] ) {
        # Cell is the same color as its neighbor, join it
        merge_regions( $x, $y, $nx, $ny )
      }
    }
  }
}

sub merge_regions {
  my ( $tx, $ty, $nx, $ny ) = @_;
  my $tr = $region[$tx][$ty];
  my $nr = $region[$nx][$ny];
  foreach my $x ( 0 .. $#grid ) {
    foreach my $y ( 0 .. $#{ $grid[0] } ) {
      if ( $region[$x][$y] eq $tr ) {
        $region[$x][$y] = $nr
      }
    }
  }
}

my $count = 0;
my %regions;
foreach my $x ( 0 .. $#grid ) {
  foreach my $y ( 0 .. $#{ $grid[0] } ) {
    my $num = ( $regions{ $region[$x][$y] } ||= ++ $count );
    print $num . " ";
  }
  print "\n"
}

__DATA__

  P P B R B
  
  P R B B B
  
  B R R R B
  
  B R R R B
  
  B G G B B
[download]

The output needs to be adjusted to your application; for now it just prints a grid of contiguous regions:

1 1 2 3 2 
1 4 2 2 2 
5 4 4 4 2 
5 4 4 4 2 
5 6 6 2 2 

P.S. I've only seen "Moore Neighbourhood" used to refer to the immediate lateral and diagonal neighbors of a cell, but perhaps there's more than one meaning? Do you want to allow diagonal connections between neighbors, or only lateral ones?

Update: Looking at kvale's solution, I noticed that I implicitly assumed that the OP was looking for "contiguous regions" rather than "boundaries" -- it works out to the same thing, but influenced my choice of approach.