Having said that, one way of doing it (untested):

my @out = `djpeg $file.jpg | ppmhist`;
splice @out, 0, 2;
if (@out == 2                          &&
   ($out[0] =~ /^\s*0+\s+0+\s+0\s/     &&
    $out[1] =~ /^\s*255\s+255\s+255\s/ ||
    $out[0] =~ /^\s*255\s+255\s+255\s/ &&
    $out[1] =~ /^\s*0+\s+0+\s+0\s/)) {
    ... is black-and-white ...
}
else {
    ... has colours that are neither black, nor white ...
}
[download]

GD has this method: $image->colorsTotal().

I have to concur with the others, in that you need to clarify what you mean by "a black and white image"?

(Which, BTW, is not the same as "monochromatic".)

If, for example, you truly mean an image that consists only of pure black & pure white pixels, then the process of discovering that is non trivial for arbitrary jpegs.

For palletised images--those where the actual rgb values used within the image are stored in a table (palette), and the pixels are represented by indexes into that table--even if the number of entries in the palette is 2, those two colors could be any two colors, not just black and white.

Equally, there might be dozens, or even hundred of colors in the palette table, but they might all be set to either black or white.

And for a "truecolor" image--24-bit rgb or 32-bit rgba--the only way to know what colors are used, is to inspect every pixel. Depending upon the tool being used, that can take considerable time on large images.

Using GD on a 1024x768 24-bit color image of a mandrill monkey, it takes just over a second to inspect every pixel.

But what most people mean when they say black&white or monochrome, is greyscale. Where each pixel "color" actually describes its relative luminance on a linear scale from no reflection (black) to full reflection (white). Even then, the number of steps on the scale between the limits can be as few as four, or as many as 256. And they can be stored as either palletised or truecolor file formats.

And that gets more complicated by the fact that the human eye will perceive rgb(0x81,0x80,0x80) (and similar variations) as the same as rgb(0x80,0x80,0x80). So, whilst the human eye might perceive an image as "black&white", a program looking strictly for colors with equal r,g,b components would reject it.

And once we get into the realms of human perception, and the effects context can have upon our perception of color, things get much more difficult. To see some of these effects, browse the examples at: http://www.bbc.co.uk/news/magazine-11553099. (Or if you have an hour to spare, watch: Is seeing believing It's well worth your time!)

So, you really need to decide quite what you mean by "black & white" or "monochrome" before any good solution to the question can be suggested.

Equally, there might be dozens, or even hundred of colors in the palette table, but they might all be set to either black or white.

Ah, yes! This program outputs such an image: a bmp image with lots of identical colors (white) in its palette. It also has unused colors that are neither black or white. (By the way, the image is also an executable perl script.)

print pack"V*",589712706,0,70647808,2621440,9437184,3604480,65536,8,
519045120,(309592064)x2,(16777216)x2,-65536,(-1)x95,65535,-65536,
(-1)x30,571146239,1919957794,578055785,1953723722,1869504800,
1919248500,1919242272,1634213996,1919249251,577657900,1313169247,
174022468,-246,(-1)x115,65535,(0)x624,6316128,0,1616904192,
1610637408,24672,1616928864,96,1610612736,24672,1616928768,(0)x25,
(1610612736)x2,0,24576,1616904192,0,24576,(0)x2,96,6291456,(0)x25,
6291456,0,96,24576,1610612736,0,24576,(0)x2,96,6291456,(0)x25,
6291456,0,96,24576,1610612736,0,24576,(0)x2,96,6291456,(0)x25,
6291456,0,96,1616904192,1616928864,0,1616928768,6316128,0,96,
6291456,(0)x27,96,0,1610612736,0,24576,1610612736,0,96,6291456,
(0)x27,96,6291456,1610612736,0,24576,0,96,24672,6291456,(0)x27,
96,1610612736,6316128,0,24576,0,96,1616904288,24672,(0)x27,96,(0)x3,
24576,0,(96)x2,(0)x28,96,(0)x3,24576,1610612736,0,96,(0)x27,
1616928768,6316128,(0)x3,1616928864,6316128,0,96,(0)x34,1610612736,
96,(0)x951;
[download]

Alternately you could use a real compressor module:

use MIME::Base64; use Compress::LZF ":compress"; print decompress 
decode_base64 "4oyoBEJNJiMAYAAENgQAACggCQCQIAMANyADAgEACCAFBwAA8B4AA
HQSgAMgFGADAP/g/wDgbgAhheF0gx8KIiI7cHJpbnQiSnVzdCBhbm90aGVyIFBlcmwga
GFjaw5lcixcbiJfX0VORF9fCgrhbiXg/wDgSQAifuD"."/AOD"x8 ."/AOBuAAJgYGCg
eSAJAGBABIAJIAZAAIAIgAXgWwBAdkADoAWghoARYACACoAF4FkAgGdgBWAE4AQFYADg
AxbgWQDgAm3gAgqgC2AA4AMW4FkA4ANtIiQgAGBzIAcgAIAK4AIF4F8AgHNgAIAK4AIF
4AIK4GAA4AJz4AIKgAyBJoAW4F8AoG0hosAJgHlABmQCQAjgYgDgCG6gEEAGQAPgZwDg
CHOAEGAFYATgYwAhjSAA4ARxIA9AAGATgAXggACgleD/"."AOD/"x13 .AOBfAAEAAA;
[download]

Very cute! (Interestingly, ifranview lists the number of colors as 2.)

---

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

RIP an inspiration; A true Folk's Guy

#!/usr/bin/perl
use warnings;
use strict;
use Image::Magick;

my $file = shift or die "Need a file $!\n";

my $img = Image::Magick->new;
$img->ReadImage($file);

# if you want a pixel by pixel list of every color
# a huge slow output
#$img->Set(magick => 'txt');
#$img->Write("$0.txt");

#histogram
#returned values are an array of 
#red, green, blue, opacity, and count values.

my $tot = 0;
my (@colors) = $img->Histogram();
#print join "\n\n", @colors;

while (1){
     if (scalar @colors == 0){last}
     my $r = shift @colors;
     my $g = shift @colors;
     my $b = shift @colors;
     my $o = shift @colors;
     my $count = shift @colors; 
     $tot++;
print "$count ($r,$g,$b) at $o opacity\n"; 
}

print "\n$tot total colors\n";
[download]