Try this. Supply an image name on the command line and it will produce an image (junk.jpg) the same size as the original that looks roughly like this:

     _____
    |\___/|
    | | | |
    | | | |
    | |_| |
    |/___\|
[download]

where each of the 3 walls, the floor and ceilng are the original image "perspectivated" to fit.

You'll probably have to prefix the filename in the system command with your local favorite image viewer if your on *nix.

#! perl -slw
use strict;
use GD;

my $img = GD::Image->new( $ARGV[ 0 ] );
my( $ox, $oy ) = $img->getBounds();
my $im2 = GD::Image->new( $ox, $oy, 1 );

$im2->copyResampled( 
    $img, 
    $ox/4, $oy/4,    ## dstXY
    0, 0,             ## srcXY
    $ox/2, $oy/2,     ## dstWH
    $ox, $oy        ## srcWH
);

my( $ys, $ye, $dy ) = ( 0, $oy, $oy/$ox );
for my $x ( 0 .. $ox/4 ) {
    $im2->copyResampled( 
        $img, 
        $x,     $ys+=$dy, 
        $x*4,     0, 
        1,         $ye-=($dy*2),
        4,         $oy
    );
}

( $ys, $ye, $dy ) = (  $oy/4, $oy/2, $oy/$ox );
for my $x ( 0 .. $ox/4 ) {
    $im2->copyResampled( 
        $img, 
        $ox*3/4+$x, $ys-=$dy, 
        $x*4,         0, 
        1,             $ye+=$dy*2,
        4,             $oy
    );
}


my( $xs, $xe, $dx ) = (  0, $ox, $ox/$oy );
for my $y ( 0 .. $oy/4 ) {
    $im2->copyResampled( 
        $img, 
        $xs+=$dx,    $y, 
        0,             $y*4, 
        $xe-=$dx*2, 1,
        $ox,         4,
    );
}

( $xs, $xe, $dx ) = (  $ox/4, $ox/2, $ox/$oy );
for my $y ( 0 .. $oy/4 ) {
    $im2->copyResampled( 
        $img, 
        $xs-=$dx,    $oy*3/4+$y, 
        0,             $y*4, 
        $xe+=$dx*2, 1,
        $ox,         4,
    );
}

open IMG, '>:raw', 'junk.jpg' or die $!;
print IMG $im2->jpeg;
close IMG;

system 'junk.jpg';
[download]

See Imager::Matrix2d.

I believe that the transformation he wants is not an affine one. The pseudo-3D effect is not the same as skew, and as such I'm not surprised it is not present out of the box. There may have to be some "manual" pixel-mangling, and I think one of the earlier posts explains the formulas behind it. Gimp::Fu may also be useful, as stated earlier.