Task as stated looks pretty much as case for interpolation to me. One trick pony, etc., but I even found my answer (Re: which function in PDL can do the same thing as matlab pcolor?) through SS for "Delaunay", see links in last paragraph there, especially ugly formulae for barycentric weights (didn't find ready-made solution on CPAN). Code is adjusted version of what I did a few years ago for some image hacking, unrelated to feature recognition.

No idea what data pryrt used for a sample (same "red-blue" terms used here), and whether they are supposed to represent a trivial demo, or, indeed, an "interesting" non-affine distortion was applied. Anyway, results below seem to match well with his, even if it's just a hack -- X and Y of target are treated as separate functions to interpolate, with, furthermore, simple linear interpolation.

use strict;
use warnings;
use feature qw/ say /;

use POSIX qw/ round /;      # use 5.022;
use List::Util qw/ sum /;

use Math::Geometry::Delaunay qw/ TRI_CONSTRAINED /;

use constant EPSILON_NEGATIVE => -1e-6;

sub key { pack 'II', @{ $_[ 0 ]}}

my @red_in  = ( [58,48], [108,155], [186,80], [255,191], [331,48] );
my @red_out = ( [471,15], [531,141], [603,90], [682,227], [747,107] );

my %mapped  = map { key( $red_in[ $_ ]), $red_out[ $_ ]} 0 .. $#red_in
+;

my $tri = Math::Geometry::Delaunay-> new( TRI_CONSTRAINED );
$tri-> addPoints( \@red_in );
$tri-> triangulate;

my @blue_in = ( [125,73], [197,158], [282,94] );

BLUE: for my $blue ( @blue_in ) {
    TRI: for my $elem ( @{ $tri-> elements }) {
        my $y23 = $elem-> [ 1 ][ 1 ] -
                  $elem-> [ 2 ][ 1 ];
        my $x32 = $elem-> [ 2 ][ 0 ] -
                  $elem-> [ 1 ][ 0 ];
        my $x13 = $elem-> [ 0 ][ 0 ] -
                  $elem-> [ 2 ][ 0 ];
        my $y13 = $elem-> [ 0 ][ 1 ] -
                  $elem-> [ 2 ][ 1 ];
        
        my $denominator = $y23 * $x13 + $x32 * $y13;
        
        my $xx3 = $blue-> [ 0 ] - $elem-> [ 2 ][ 0 ];
        my $yy3 = $blue-> [ 1 ] - $elem-> [ 2 ][ 1 ];

        my @weights;
        next TRI if EPSILON_NEGATIVE > ( $weights[ 0 ] =
            ( $y23 * $xx3 + $x32 * $yy3 ) / $denominator );
        next TRI if EPSILON_NEGATIVE > ( $weights[ 1 ] =
            ( -$y13 * $xx3 + $x13 * $yy3 ) / $denominator );
        next TRI if EPSILON_NEGATIVE > ( $weights[ 2 ] =
            1 - $weights[ 0 ] - $weights[ 1 ]);

        printf "[%3d,%3d] => [%3d,%3d]\n", 
            @$blue,
            map {
                my $coord = $_;
                round sum map {
                    $weights[ $_ ] * $mapped{ key $elem-> [ $_ ]}[ $co
+ord ]
                } 0 .. 2    # 3 vertices
            } 0, 1;         # x, y
        next BLUE
    }
    die "point @$blue outside convex hull"
}

__END__

[125, 73] => [541, 63]
[197,158] => [621,174]
[282, 94] => [701,137]
[download]

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