Color difference algorithm – part 2

September 8, 2009 • Php, Tutorials by Emanuele Feronato • 11 Comments

It’s time to see how to calculate difference between two colors.

I am using the CIE1994 formula because it’s quite accurate and not that complex to calculate.

Here it is, assuming I have two colors in Lab format

where

(thanx to Bruce Lindbloom)

First, I am turning the scripts explained at Color difference algorithm into functions, this way:

function rgb_to_xyz($rgb){

$red = $rgb[0];

$green = $rgb[1];

$blue = $rgb[2];

$_red = $red/255;

$_green = $green/255;

$_blue = $blue/255;

if($_red>0.04045){

$_red = ($_red+0.055)/1.055;

$_red = pow($_red,2.4);

}

else{

$_red = $_red/12.92;

}

if($_green>0.04045){

$_green = ($_green+0.055)/1.055;

$_green = pow($_green,2.4);

}

else{

$_green = $_green/12.92;

}

if($_blue>0.04045){

$_blue = ($_blue+0.055)/1.055;

$_blue = pow($_blue,2.4);

}

else{

$_blue = $_blue/12.92;

}

$_red *= 100;

$_green *= 100;

$_blue *= 100;

$x = $_red * 0.4124 + $_green * 0.3576 + $_blue * 0.1805;

$y = $_red * 0.2126 + $_green * 0.7152 + $_blue * 0.0722;

$z = $_red * 0.0193 + $_green * 0.1192 + $_blue * 0.9505;

return(array($x,$y,$z));

}

and…

function xyz_to_lab($xyz){

$x = $xyz[0];

$y = $xyz[1];

$z = $xyz[2];

$_x = $x/95.047;

$_y = $y/100;

$_z = $z/108.883;

if($_x>0.008856){

$_x = pow($_x,1/3);

}

else{

$_x = 7.787*$_x + 16/116;

}

if($_y>0.008856){

$_y = pow($_y,1/3);

}

else{

$_y = (7.787*$_y) + (16/116);

}

if($_z>0.008856){

$_z = pow($_z,1/3);

}

else{

$_z = 7.787*$_z + 16/116;

}

$l= 116*$_y -16;

$a= 500*($_x-$_y);

$b= 200*($_y-$_z);

return(array($l,$a,$b));

}

Now, it’s time to determine color difference, using the above formula:

function de_1994($lab1,$lab2){

$c1 = sqrt($lab1[1]*$lab1[1]+$lab1[2]*$lab1[2]);

$c2 = sqrt($lab2[1]*$lab2[1]+$lab2[2]*$lab2[2]);

$dc = $c1-$c2;

$dl = $lab1[0]-$lab2[0];

$da = $lab1[1]-$lab2[1];

$db = $lab1[2]-$lab2[2];

$dh = sqrt(($da*$da)+($db*$db)-($dc*$dc));

$first = $dl;

$second = $dc/(1+0.045*$c1);

$third = $dh/(1+0.015*$c1);

return(sqrt($first*$first+$second*$second+$third*$third));

}

And you’ll find the difference between colors.

Next time, a real application using all this boring theory… (you will be surprised…)

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This post has 11 comments

dim

on September 9, 2009 at 12:40 am

great snippet … i will love to see a function that can generate lighter or darker color by a given color value through parameter

this will be very handy when we want to auto generate color themes bye given color value by user
How to Choose Colours Procedurally (Algorithms) » devmag.org.za

on July 30, 2012 at 10:49 am

[...] http://www.emanueleferonato.com/2009/09/08/color-difference-algorithm-part-2/ [...]
Eduardo

on October 27, 2012 at 10:06 pm

I trying to transfer this code to pascal. I don’t understan the following operation:
$_red *= 100;
$_green *= 100;
$_blue *= 100;
Could you explain to me?
kpodenphant

on November 12, 2012 at 1:12 am

This is frickin’ awesome.I ported it to Actionscript.
I tried the RGB distance method which worked ok, but had some errors. Then i tried converting to HSB which worked well for the RGB errors but has some other error.
This algorithm is sweet!
anonyMouse

on December 28, 2012 at 3:33 pm

Eduardo it means that the variable is set to its current value times 100;

i.e. red=2;
red*=100; (red is now 200, all further code that uses the variable “red” will now use 200 rather than 2);
Radek

on February 16, 2013 at 9:04 pm

Thanks for great snippet Emanuele !
Just one point – shouldn’t be used abs(…) for all delta computations in de_1994() ?
Thanks anyway !
Igor

on March 9, 2013 at 12:11 pm

Thanks for explaining this stuff, and for your snippets of code )

I’d like to use those snippets in our project, but in your post you don’t mention it anywhere, so can I ask you if it’s okay to reuse them? And if so, can you please put a license note on them, so they will be legally accessible?
Emanuele Feronato

on March 11, 2013 at 5:37 pm

Hello Igor,

use it as you want, there’s no restriction, ok?
Dylan

on May 5, 2013 at 9:10 pm

Thanks for this, it saved me A LOT of time.

I had to change Line 8 of de_1994 to $dh = sqrt(abs(($da*$da)+($db*$db)-($dc*$dc)));
Dylan

on May 6, 2013 at 1:29 am

Change line 8 of de_1994 to:
$dh = sqrt(($da*$da)+($db*$db)+($dc*$dc));
Dylan

on May 6, 2013 at 4:21 pm

You are going to kill me!!! Ignore the nonsense I posted earlier…

Change line 8 of de_1994 to:
$dh = ($da * $da) + ($db * $db) – ($dc * $dc);
if ($dh < 0) { $dh = 0; } else { $dh = sqrt($dh); }

I guess the problem is an excessively large delta C resulting in a sqrt of a negative number. This was causing NaN on many comparisons.

Emanuele Feronato

italian geek and PROgrammer

Color difference algorithm – part 2

This post has 11 comments

dim

How to Choose Colours Procedurally (Algorithms) » devmag.org.za

Eduardo

kpodenphant

anonyMouse

Radek

Igor

Emanuele Feronato

Dylan

Dylan

Dylan