This doesn't answer your question at all but it's still kind of neat. It transforms your example input into the example output by removing repeated lines, vertically and horizontally. It also removes "empty" lines from the edges.

$image = <<IMAGE;
0000000000000000000000
0000000001111100000000
0000000001111100000000
0000000001111100000000
0000000001111100000000
0000011111111111110000
0000011111111111110000
0000011111111111110000
0000011111111111110000
0000000001111100000000
0000000001111100000000
0000000001111100000000
0000000001111100000000
0000000000000000000000
IMAGE

$result =
    transpose(
        trim( vertical_squish( transpose(
            trim( vertical_squish( $image ) ) ) ) ) );

$result eq <<EXPECT or die "Failed.\n$result\n";
010
111
010
EXPECT

sub trim {
    local $_ = shift;

    s/\A(?:^0+[\r\n]+)+//m;
    s/(?:^0+[\r\n]+)+\z//m;

    return $_;
}

sub vertical_squish {
    local $_ = shift;

    s/(^[^\r\n]+[\r\n]+)\1+/$1/gm;

    return $_;
}

use Algorithm::Loops 'MapCarU';
sub transpose {
    local $_ = shift;

    return
        join( "",
              &MapCarU(
                  sub { join( "", @_ ) . "\n" },
                  map( [ split // ],
                       split( /[\r\n]+/ ) ) ) );
}
[download]

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