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Color Processing

Color Space RGB to XYZ

simple Method

The two transformation matrix RGB to XYZ and XYZ to RGB are:

T = ( 0. 412453 0. 357580 0. 180423 0. 212671 0. 715160 0. 072169 0. 019334 0. 119193 0. 950227 )
T - 1 = ( 3. 240479 - 1. 537150 - 0. 498535 - 0. 969256 1. 875992 0. 041556 0. 055648 - 0. 204043 1. 057311 )

then we applied the linear transformation on the RGB color space to convert.

( R G B ) = T ⋅ ( X Y Z ) and ( X Y Z ) = T - 1 ⋅ ( R G B )

Here the program

clear all;
close all;

[filename, pathname] = uigetfile({'*.jpg;*.tif;*.png;*.gif;*.bmp','All Image Files';...
          '*.*','All Files' },'mytitle',...
          'C:\Work\myfile.jpg');

img = imread(filename);
[ligne colonne dimension]=size(img);
img=double(img);
R=img(:,:,1);
G=img(:,:,2);
B=img(:,:,3);

% rgb to XYZ methode 1

X = 0.412453*R + 0.357580*G + 0.180423*B;
Y = 0.212671*R + 0.715160*G + 0.072169*B;
Z = 0.019334*R + 0.119193*G + 0.950227*B;


Rp =  3.240479*X - 1.537150*Y - 0.498535*Z;
Gp = -0.969256*X + 1.875992*Y + 0.041556*Z;
Bp =  0.055648*X - 0.204043*Y + 1.057311*Z;

figure(  'Name','RGB --> XYZ --> RGB methode 1',...
            'NumberTitle','off',...
            'color',[0.3137 0.3137 0.5098]);
vide=zeros(ligne,colonne);
subplot(421)
imshow(uint8(cat(3,R,G,B)))
title('Image origine')
subplot(423)
imshow(uint8(cat(3,R,vide,vide)))
title('Image R origine')
subplot(425)
imshow(uint8(cat(3,vide,G,vide)))
title('Image G origine')
subplot(427)
imshow(uint8(cat(3,vide,vide,B)))
title('Image B origine')
 subplot(422)
imshow(uint8(cat(3,Rp,Gp,Bp)))
title('Image reconstuite')
 subplot(424)
imshow(uint8(cat(3,Rp,vide,vide)))
title('Image R reconstuite')
subplot(426)
imshow(uint8(cat(3,vide,Gp,vide)))
title('Image G reconstuite')
subplot(428)
imshow(uint8(cat(3,vide,vide,Bp)))
title('Image B reconstuite')

and an example
rgbtoxyz1

Method with gamma correctio

In this case, we apply a gamma correction on the RGB color. This correction is performed thanks to:

R ' = f ( R ) , G ' = f ( G ) , B ' = f ( B )

with f ( x ) = { ( x + 0. 055 1. 055 ) 2. 4  if  x > s x 12. 92  if  x ≤ s }
where s=0.03928. After the gamma correction, we apply the RGB to XYZ conversion above. To reverse the transformation we reverse the gamma correction too. We use the next equations:
R = f ' ( R ' ) , G = f ' ( G ' ) , B = f ' ( B ' )

f ' ( x ) = { 1. 055 ⋅ x 1 / 2. 4 - 0. 055  if  x > s 12. 92 ⋅ x  if  x ≤ s }

Where s = 0.0031308.
Here the program:

% rgb to XYZ methode 2
Rn=R/255;
Gn=G/255;
Bn=B/255;
seuil = 0.03928;

Rp= (Rn>seuil)  .* (((Rn+0.055)./1.055).^2.4);
Rp= Rp + (Rn<=seuil) .* (Rn/12.92);
Gp= (Gn>seuil)  .* (((Gn+0.055)./1.055).^2.4);
Gp= Gp + (Gn<=seuil) .* (Gn/12.92);
Bp= (Bn>seuil)  .* (((Bn+0.055)./1.055).^2.4);
Bp= Bp + (Bn<=seuil) .* (Bn/12.92);

X = 0.412453*Rp + 0.357580*Gp + 0.180423*Bp;
Y = 0.212671*Rp + 0.715160*Gp + 0.072169*Bp;
Z = 0.019334*Rp + 0.119193*Gp + 0.950227*Bp;

Rpp =  3.240479*X - 1.537150*Y - 0.498535*Z;
Gpp = -0.969256*X + 1.875992*Y + 0.041556*Z;
Bpp =  0.055648*X - 0.204043*Y + 1.057311*Z;

seuil = 0.0031308;
Rr= (Rpp>seuil)  .* (1.055*Rpp.^(1/2.4)-0.055);
Rr= Rr + (Rpp<=seuil)  .* (Rpp*12.92);
Gr= (Gpp>seuil)  .* (1.055*Gpp.^(1/2.4)-0.055);
Gr= Gr + (Gpp<=seuil)  .* (Gpp*12.92);
Br= (Bpp>seuil)  .* (1.055*Bpp.^(1/2.4)-0.055);
Br= Br + (Bpp<=seuil)  .* (Bpp*12.92);
Rr=Rr*255;
Gr=Gr*255;
Br=Br*255;
figure(  'Name','RGB --> XYZ --> RGB methode 2',...
            'NumberTitle','off',...
            'color',[0.3137 0.3137 0.5098]);
vide=zeros(ligne,colonne);
subplot(4,5,1)
imshow(uint8(cat(3,R,G,B)))
title('Image origine')
subplot(4,5,6)
imshow(uint8(cat(3,R,vide,vide)))
title('Image R origine')
subplot(4,5,11)
imshow(uint8(cat(3,vide,G,vide)))
title('Image G origine')
subplot(4,5,16)
imshow(uint8(cat(3,vide,vide,B)))
title('Image B origine')

subplot(4,5,2)
imshow(uint8(cat(3,Rp,Gp,Bp)*255))
title('Image RGB linéarisé gamma correction')
subplot(4,5,7)
imshow(uint8(cat(3,Rp,vide,vide)*255))
title('Image R linéarisé gamma correction')
subplot(4,5,12)
imshow(uint8(cat(3,vide,Gp,vide)*255))
title('Image G linéarisé gamma correction')
subplot(4,5,17)
imshow(uint8(cat(3,vide,vide,Bp)*255))
title('Image B linéarisé gamma correction')


%subplot(4,5,3)
subplot(4,5,8)
imagesc(X,[min(min(X)) max(max(X))])
colormap('gray')
axis image
title('Image X')
subplot(4,5,13)
imagesc(Y,[min(min(Y)) max(max(Y))])
colormap('gray')
axis image
title('Image Y')
subplot(4,5,18)
imagesc(Z,[min(min(Z)) max(max(Z))])
colormap('gray')
axis image
title('Image Z')

subplot(4,5,4)
imshow(uint8(cat(3,Rpp,Gpp,Bpp)*255))
title('Image non linéarisé gamma correction')
subplot(4,5,9)
imshow(uint8(cat(3,Rpp,vide,vide)*255))
title('Image R reconstuite linéarisé gamma correction')
subplot(4,5,14)
imshow(uint8(cat(3,vide,Gpp,vide)*255))
title('Image G reconstuite linéarisé gamma correction')
subplot(4,5,19)
imshow(uint8(cat(3,vide,vide,Bpp)*255))
title('Image B reconstuite linéarisé gamma correction')

 subplot(4,5,5)
imshow(uint8(cat(3,Rr,Gr,Br)))
title('Image reconstuite non linéarisé gamma correction')
 subplot(4,5,10)
imshow(uint8(cat(3,Rr,vide,vide)))
title('Image R reconstuite non linéarisé gamma correction')
subplot(4,5,15)
imshow(uint8(cat(3,vide,Gr,vide)))
title('Image G reconstuite non linéarisé gamma correction')
subplot(4,5,20)
imshow(uint8(cat(3,vide,vide,Br)))
title('Image B reconstuite non linéarisé gamma correction')

 

An example
rgbtoxyz2

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