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Followup: Finding an accurate "distance" between colors

Followup: Finding an accurate "distance" between colors

"Original Question

I am looking for a function that attempts to quantify how ""distant"" (or distinct) two colors are. This question is really in two parts:

What color space best represents human vision?
What distance metric in that space best represents human vision (euclidean?)"

Asked by: Guest | Views: 42
Total answers/comments: 4
Guest [Entry]

"Convert to La*b* (aka just plain ""Lab"", and you'll also see reference to ""CIELAB""). A good quick measaure of color difference is

(L1-L2)^2 + (a1-a2)^2 + (b1-b2)^2

Color scientists have other more refined measures, which may not be worth the bother, depending on accuracy needed for what you're doing.

The a and b values represent opposing colors in a way similar to how cones work, and may be negative or positive. Neutral colors - white, grays are a=0,b=0. The L is brightness defined in a particular way, from zero (pure darkness) up to whatever.

Crude explanation :>> Given a color, our eyes distinguish between two broad ranges of wavelength - blue vs longer wavelengths. and then, thanks to a more recent genetic mutation, the longer wavelength cones bifurcated into two, distinguishing for us red vs. green.

By the way, it'll be great for your career to rise above your color caveman collegues who know of only ""RGB"" or ""CMYK"" which are great for devices but suck for serious perception work. I've worked for imaging scientists who didn't know a thing about this stuff!

For more fun reading on color difference theory, try:

http://white.stanford.edu/~brian/scielab/introduction.html and info
and links on color theory in general, websurf starting with http://www.efg2.com/Lab/Library/Color/ and
http://www.poynton.com/Poynton-color.html

More detail on Lab at http://en.kioskea.net/video/cie-lab.php3 I can't at this time find a non-ugly page that actually had the conversion formulas but I'm sure someone will edit this answer to include one."
Guest [Entry]

"as cmetric.htm link above failed for me, as well as many other implementations for color distance I found (after a very long jurney..) how to calculate the best color distance, and .. most scientifically accurate one: deltaE and from 2 RGB (!) values using OpenCV:

This required 3 color space conversions + some code conversion from javascript (http://svn.int64.org/viewvc/int64/colors/colors.js) to C++

And finally the code (seems to work right out of the box, hope no one finds a serious bug there ... but it seems fine after a number of tests)

#include <opencv2/core/core.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/photo/photo.hpp>
#include <math.h>

using namespace cv;
using namespace std;

#define REF_X 95.047; // Observer= 2°, Illuminant= D65
#define REF_Y 100.000;
#define REF_Z 108.883;

void bgr2xyz( const Vec3b& BGR, Vec3d& XYZ );
void xyz2lab( const Vec3d& XYZ, Vec3d& Lab );
void lab2lch( const Vec3d& Lab, Vec3d& LCH );
double deltaE2000( const Vec3b& bgr1, const Vec3b& bgr2 );
double deltaE2000( const Vec3d& lch1, const Vec3d& lch2 );

void bgr2xyz( const Vec3b& BGR, Vec3d& XYZ )
{
double r = (double)BGR[2] / 255.0;
double g = (double)BGR[1] / 255.0;
double b = (double)BGR[0] / 255.0;
if( r > 0.04045 )
r = pow( ( r + 0.055 ) / 1.055, 2.4 );
else
r = r / 12.92;
if( g > 0.04045 )
g = pow( ( g + 0.055 ) / 1.055, 2.4 );
else
g = g / 12.92;
if( b > 0.04045 )
b = pow( ( b + 0.055 ) / 1.055, 2.4 );
else
b = b / 12.92;
r *= 100.0;
g *= 100.0;
b *= 100.0;
XYZ[0] = r * 0.4124 + g * 0.3576 + b * 0.1805;
XYZ[1] = r * 0.2126 + g * 0.7152 + b * 0.0722;
XYZ[2] = r * 0.0193 + g * 0.1192 + b * 0.9505;
}

void xyz2lab( const Vec3d& XYZ, Vec3d& Lab )
{
double x = XYZ[0] / REF_X;
double y = XYZ[1] / REF_X;
double z = XYZ[2] / REF_X;
if( x > 0.008856 )
x = pow( x , .3333333333 );
else
x = ( 7.787 * x ) + ( 16.0 / 116.0 );
if( y > 0.008856 )
y = pow( y , .3333333333 );
else
y = ( 7.787 * y ) + ( 16.0 / 116.0 );
if( z > 0.008856 )
z = pow( z , .3333333333 );
else
z = ( 7.787 * z ) + ( 16.0 / 116.0 );
Lab[0] = ( 116.0 * y ) - 16.0;
Lab[1] = 500.0 * ( x - y );
Lab[2] = 200.0 * ( y - z );
}

void lab2lch( const Vec3d& Lab, Vec3d& LCH )
{
LCH[0] = Lab[0];
LCH[1] = sqrt( ( Lab[1] * Lab[1] ) + ( Lab[2] * Lab[2] ) );
LCH[2] = atan2( Lab[2], Lab[1] );
}

double deltaE2000( const Vec3b& bgr1, const Vec3b& bgr2 )
{
Vec3d xyz1, xyz2, lab1, lab2, lch1, lch2;
bgr2xyz( bgr1, xyz1 );
bgr2xyz( bgr2, xyz2 );
xyz2lab( xyz1, lab1 );
xyz2lab( xyz2, lab2 );
lab2lch( lab1, lch1 );
lab2lch( lab2, lch2 );
return deltaE2000( lch1, lch2 );
}

double deltaE2000( const Vec3d& lch1, const Vec3d& lch2 )
{
double avg_L = ( lch1[0] + lch2[0] ) * 0.5;
double delta_L = lch2[0] - lch1[0];
double avg_C = ( lch1[1] + lch2[1] ) * 0.5;
double delta_C = lch1[1] - lch2[1];
double avg_H = ( lch1[2] + lch2[2] ) * 0.5;
if( fabs( lch1[2] - lch2[2] ) > CV_PI )
avg_H += CV_PI;
double delta_H = lch2[2] - lch1[2];
if( fabs( delta_H ) > CV_PI )
{
if( lch2[2] <= lch1[2] )
delta_H += CV_PI * 2.0;
else
delta_H -= CV_PI * 2.0;
}

delta_H = sqrt( lch1[1] * lch2[1] ) * sin( delta_H ) * 2.0;
double T = 1.0 -
0.17 * cos( avg_H - CV_PI / 6.0 ) +
0.24 * cos( avg_H * 2.0 ) +
0.32 * cos( avg_H * 3.0 + CV_PI / 30.0 ) -
0.20 * cos( avg_H * 4.0 - CV_PI * 7.0 / 20.0 );
double SL = avg_L - 50.0;
SL *= SL;
SL = SL * 0.015 / sqrt( SL + 20.0 ) + 1.0;
double SC = avg_C * 0.045 + 1.0;
double SH = avg_C * T * 0.015 + 1.0;
double delta_Theta = avg_H / 25.0 - CV_PI * 11.0 / 180.0;
delta_Theta = exp( delta_Theta * -delta_Theta ) * ( CV_PI / 6.0 );
double RT = pow( avg_C, 7.0 );
RT = sqrt( RT / ( RT + 6103515625.0 ) ) * sin( delta_Theta ) * -2.0; // 6103515625 = 25^7
delta_L /= SL;
delta_C /= SC;
delta_H /= SH;
return sqrt( delta_L * delta_L + delta_C * delta_C + delta_H * delta_H + RT * delta_C * delta_H );
}

Hope it helps someone :)"
Guest [Entry]

"HSL and HSV are better for human color perception. According to Wikipedia:

It is sometimes preferable in working with art materials, digitized images, or other media, to use the HSV or HSL color model over alternative models such as RGB or CMYK, because of differences in the ways the models emulate how humans perceive color. RGB and CMYK are additive and subtractive models, respectively, modelling the way that primary color lights or pigments (respectively) combine to form new colors when mixed."
Guest [Entry]

The Wikipedia article on color differences lists a number of color spaces and distance metrics designed to agree with human perception of color distances.