将 1mb 数据编码为可解码模拟图像的最佳方法是什么？

Question

1. The image generated will have to be space restricted, not too big.
2. By analog i mean, it should be printed out. Much like how a QR code works, except, storing much larger size!
3. B/w image
4. Can be compressed (obviously because its better, time taken to uncompress should not be much either, so compression can be minimal)
5. You can assume any lower print density, and bits per pixel would be directly related to the solution you propose. Please go ahead and assume:)

Answer 1

I'm not sure how you could exactly encode this to fit on paper... I think the best way is to convert your digital information into a more compact analog representation. To clarify... What has been proposed is to take the digital information and represent it (with bits) digitally on an analog medium. What I'm trying to say is take the digital info, convert it and represent it in an analog form on an analog medium. How to do this? I have no idea, but I have a lead for you.

Remember the Voyager Golden Records? They fit 116 (115?) images onto the disks, both simple B&W images and full size, color images with high(ish) resolution. They did it with an analog box of wavelengths representing digital bits over 512 (2^9) lines.

Not sure if that helps, but maybe it gives you (or someone else) an idea?

Answer 2

Assuming no overhead for error correction, and 1mm resolution, you're looking at a 1 x 1 meter image. This assumes no compression (how compressible your data is really depends) and no real encoding scheme. This is not practical.

I'd break up your data into ~5kb chunks, encode them as QR codes together with their sequence numbers, and use the collection of QR codes. Each image has built-in error correction. You'll end up with maybe two hundred 15*15cm images. At least you'll be able to use regular paper and printers for it.

The reason I suggest QR codes is that they have error correction built in, so you have more tolerance for smeared ink, wrinkled or torn paper, or a less than perfect camera/scanner. Plus, the overhead of the error correction isn't bad, and you're getting something like 90% use out of your paper. Assuming some maximum resolution that you're willing to use for a pixel, regardless of encoding scheme. Plus, they're fast to decode, hence their name.

Answer 3

How about encoding your 1 MB into an image and print is at high enough resolution and color depth , this is a simple straight forward approach.

Recovering of the data depends greatly on the capabilities of your scanner/camera or "analog" reader (optical resolution etc.)

No error correction in this example, redundancy can be included in the data itself.

Which is a container that store this image of 1.1 MB:

Images hosted on

Other approaches: store data on paper .

The Perl script to create the image is below (it makes use of convert from imageMagick):

#!/usr/bin/perl

# this script take any data and make an image with it (format .png)

# deps
#  convert from ImageMagick
our $dbug=0;
#--------------------------------
# -- Options parsing ...
#
my $if = undef;
my $of = undef;
while (@ARGV && $ARGV[0] =~ m/^-/)
{
  $_ = shift;
  #/^-(l|r|i|s)(\d+)/ && (eval "\$$1 = \$2", next);
  if (/^-v(?:erbose)?/) { $verbose= 1; }
  elsif (/^-?if?=?([\w.]+)?/) { $if= $1?$1:shift; }
  elsif (/^-?of?=?([\w.]+)?/) { $of= $1?$1:shift; }
  else                  { die "Unrecognized switch: $_\n"; }

}
#understand variable=value on the command line...
eval "\$$1='$2'"while $ARGV[0] =~ /^(\w+)=(.*)/ && shift;

my $data;
if (! defined $of) {
 if (@ARGV) { $of = pop @ARGV }
 else { $of = '-' }
}
if (defined $if) {
   local *IN; 
   local $/ = undef;
   open IN,'<',$if;
   $data = <IN>;
   close IN;
} else {
   if ($ARGV > 0) { $if = '<>'; }
     elsif ($#ARGV == 0) { $if = $ARGV[0]; }
     else { $if = '-'; }
   local $/ = undef;
   $data = <>;
   close STDIN;

}
my $size = length($data);

my $pi = atan2(0,-1);
#my $iratio = 4/3; # y/x
my $iratio = $pi; # x/y

my $xy = $size/3 * ($iratio);
my $x = sqrt($xy);
if ($verbose) {
   printf STDERR "if: %s\n",$if;
   printf STDERR "of: %s\n",$of;
   printf STDERR "size: %s\n",$size;
   printf STDERR "x: %.3f\n",$x;
   printf STDERR "y: %.3f\n",$x / $iratio;
}
my $y = int($x / $iratio + $iratio);
   $x = int( ( $size / 3 + $y - 1) / $y ); 
my $n = $x*$y*3;
my $delta = $n - $size;
if ($delta < 0) {
   $x++; 
   $n = $x*$y*3;
   $delta = $n - $size;
}
my $pad = "\x00" x $delta;
if ($verbose) {
   printf STDERR "playload: %sx%s = %s\n",$x,$y,$n;
   printf STDERR "delta: %s\n", $delta;
}

my $hdr = <<"EOS";
P6
$x $y
255
EOS

#my $fname = $file; $fname =~ s,.*/,,;
#my $bname = $fname; $bname =~ s/\.[^\.]*$//;
#printf STDERR "fname: %s\n",$fname;
#printf STDERR "fname: %s.png\n",$bname;

local *PPM; open PPM,"| convert -compress LZW -strip -quality 90 ppm:- png:$of";
print PPM $hdr;
binmode(PPM);
print PPM $data;
print PPM $pad;
close PPM;

exit $?;

1; # $Source: /my/perl/scripts/dat2png.pl$