Greetings,

Running parallel is possible for both examples. The latter makes use of relay (for orderly) and gather capabilities in MCE.

First Example

use strict;
use warnings;
use GD::Simple;
use MCE::Map;

my $png = GD::Image->newFromPng('test.png');
my ($width,$height) = $png->getBounds;

MCE::Map->init( max_workers => 4 );

my @sw = mce_map {
    my ($y,$str) = ($_,'');
    for my $x (0..$width - 1) {
        $str .= getPixel($x,$y);
    }
    $str;
} 0..$height - 1;

MCE::Map->finish();

# print $_, "\n" for @sw;

sub getPixel {
    my ($index)   = $png->getPixel($_[0],$_[1]);
    my ($r,$g,$b) = $png->rgb($index);
    my $p = ($b > 128 || $r > 128) ? 0 : 1;
    return $p;
}
[download]

Second Example

use strict;
use warnings;
use GD::Simple;
use MCE;

my $png = GD::Image->newFromPng('test.png');
my ($bx,$by) = $png->getBounds;
my @col;                         # foreground colors

for (0..$png->colorsTotal) {
    my ($r,$g,$b) = $png->rgb($_);
    push (@col,$_) unless ($b>128 || $r>128);
}

my $pdata = '';

MCE->new(
    max_workers => 4,
    chunk_size  => 1,
    input_data  => \@col,
    init_relay  => 1,  # loads MCE::Relay

    gather => sub {
        # this runs inside the parent
        $pdata |= $_[0];
    },

    user_func => sub {
        # run parallel
        my $val = ~$png->wbmp($_);

        # send the val to the parent process
        # relay makes it run serially and orderly
        MCE::relay {
            MCE->gather($val);
        };
    }
)->run();

our $zlen = int(($bx + 7) / 8);  # number of Bytes per line
my $pos = 6; my $y = 0;          # position after Header of WBMP
my @sw;

while ($pos < length($pdata)) {
    $sw[$y] = '';
    for (1..$zlen) {
        # convert binary data into string
        $sw[$y] .= sprintf("%08b",ord(substr($pdata,$pos++,1)));
    }
    # print $sw[$y], "\n";
    $y++;
}
[download]

The examples run well. Output matches the OP's non-parallel demonstrations.

Regards, Mario