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Color Processing

TV Space Color

YUV

It's the basic encoding for analog TV. It is used in the NTSC and PAL. The luminance Y is compute as:

Y = 0. 299 ⋅ R + 0. 587 ⋅ G + 0. 114 ⋅ B

The components U and V are the difference between red or blue and the luminance weighted by a fator.

U = 0. 492 ⋅ ( B - Y ) et V = 0. 877 ⋅ ( R - Y )

We can also write this conversion in the following way:

( Y U V ) = ( 0. 299 0. 587 0. 114 - 0. 147 - 0. 289 0. 436 0. 615 - 0. 515 - 0. 1 ) ⋅ ( R G B )

The inverse transformation YUV to RGB is compute as:

( R G B ) = ( 1 0 1. 14 1 - 0. 395 - 0. 581 1 2. 032 0 ) ⋅ ( Y U V )

The Matlab program :

% conversion RGB --> YUV
%normalisation des couleurs
Y = 0.299*R + 0.587*G + 0.114*B  ;
U = 0.492*(B-Y);
V = 0.877*(R-Y);
Rp= Y + 1.140*V;
Gp= Y - 0.395*U -0.581*V;
Bp= Y + 2.032*U ;
figure(  'Name','RGB --> YUV',...
            'NumberTitle','off',...
            'color',[0.3137 0.3137 0.5098]);
vide=zeros(ligne,colonne);
subplot(331)
imshow(uint8(cat(3,R,vide,vide)))
title('Image R origine')
subplot(334)
imshow(uint8(cat(3,vide,G,vide)))
title('Image G origine')
subplot(337)
imshow(uint8(cat(3,vide,vide,B)))
title('Image B origine')
subplot(332)
imagesc(Y,[min(min(Y)) max(max(Y))])
colormap(gray)
axis image
title('Image Y')
subplot(335)
imagesc(U,[min(min(U)) max(max(U))])
colormap(gray)
axis image
title('Image U')
subplot(338)
imagesc(V,[min(min(V)) max(max(V))])
colormap(gray)
axis image
title('Image V')
subplot(333)
imshow(uint8(cat(3,Rp,vide,vide)))
title('Image R reconstruit')
subplot(336)
imshow(uint8(cat(3,vide,Gp,vide)))
title('Image G reconstruit')
subplot(339)
imshow(uint8(cat(3,vide,vide,Bp)))
title('Image B reconstruit')

An example:
rgbyuv

YIQ

It's the original NTSC system. The luminance Y is the same as for th YUV. I represent the inphase and Q the quadrature. U and V are rotated and mirrored thanks to the angle b. Here is the equations:

I = - sin ( b ) ⋅ U + cos ( b ) ⋅ V

et

Q = cos ( b ) ⋅ U + sin ( b ) ⋅ V

the angle b is equal to 0.576 or 33°.

We can also compute this transformation as:

( Y I Q ) = ( 0. 299 0. 587 0. 114 0. 596 - 0. 274 - 0. 322 0. 211 - 0. 523 0. 312 ) ⋅ ( R G B )

The inverse transformation is made with:

( R G B ) = ( 1 0. 956 0. 621 1 - 0. 272 - 0. 647 1 - 1. 106 1. 703 ) ⋅ ( Y I Q )

The Matlab program:

Y = 0.299*R + 0.587*G + 0.114*B  ;
U = 0.492*(B-Y);
V = 0.877*(R-Y);
b=0.576;
I = -sin(b)*U + cos(b)*V ;
Q = cos(b)*U + sin(b)*V ;
Rp= Y +  0.956*I +  0.621*Q;
Gp= Y -  0.272 *I - 0.647*Q;
Bp= Y -  1.106*I + 1.703*Q;

figure(  'Name','RGB --> YIQ',...
            'NumberTitle','off',...
            'color',[0.3137 0.3137 0.5098]);
vide=zeros(ligne,colonne);
subplot(331)
imshow(uint8(cat(3,R,vide,vide)))
title('Image R')
subplot(334)
imshow(uint8(cat(3,vide,G,vide)))
title('Image G')
subplot(337)
imshow(uint8(cat(3,vide,vide,B)))
title('Image G')
 subplot(332)
imagesc(Y,[min(min(Y)) max(max(Y))])
colormap(gray)
axis image
title('Image Y')
subplot(335)
imagesc(I,[min(min(I)) max(max(I))])
colormap(gray)
axis image
title('Image I')
subplot(338)
imagesc(Q,[min(min(Q)) max(max(Q))])
colormap(gray)
axis image
title('Image Q')
subplot(333)
imshow(uint8(cat(3,Rp,vide,vide)))
title('Image R reconstruit')
subplot(336)
imshow(uint8(cat(3,vide,Gp,vide)))
title('Image G reconstruit')
subplot(339)
imshow(uint8(cat(3,vide,vide,Bp)))
title('Image B  reconstruit')

An example:
rgbyiq

YCbCr

This color scale is a international standard of YUV. It is used in the digital TV and in compression (JPEG). We have for the RGB to YCbCr transformation:

Y = w r ⋅ R + w g ⋅ G + w b ⋅ B
C b = 0. 5 1 - w b ⋅ ( B - Y )
C r = 0. 5 1 - w r ⋅ ( R - Y )

where wr = 0.299, wb = 0.114 and Wc = 1 - wb - wr.
The inverse transformation YCbCr to RGB is made thanks to:

R = Y + 1 - w r 0. 5 ⋅ C r
G = Y + w b ⋅ ( 1 - w b ) ⋅ C b - w r ⋅ ( 1 - w r ) ⋅ C r 0. 5 ⋅ ( w g )
B = Y + 1 - w b 0. 5 ⋅ C b

This transfomartion can also be made with the folowing matrix:

( Y C b C r ) = ( 0. 299 0. 587 0. 114 - 0. 169 - 0. 331 0. 5 0. 5 - 0. 419 - 0. 081 ) ⋅ ( R G B )
( R G B ) = ( 1 0 1. 403 1 - 0. 344 - 0. 714 1 1. 773 0 ) ⋅ ( Y Cb Cr )

The Matlab program:

% conversion RGB --> YCbCr
%normalisation des couleurs
Wr=0.299;Wb=0.114; Wg=1-Wr-Wb;
Y = Wr*R + Wg*G + Wb*B  ;
Cb= ( 0.5 / ( 1-Wb) ) * (B-Y);
Cr= ( 0.5 / ( 1-Wr) ) * (R-Y);
Rp= Y + ((1 - Wr)/0.5)*Cr;
Gp= Y + (Wb*(1-Wb)*Cb - Wr*(1-Wr)*Cr)/(0.5*(1-Wb-Wr));
Bp= Y + ((1 - Wb)/0.5) * Cb;

figure(  'Name','RGB --> YCbCr',...
            'NumberTitle','off',...
            'color',[0.3137 0.3137 0.5098]);
vide=zeros(ligne,colonne);
subplot(331)
imshow(uint8(cat(3,R,vide,vide)))
title('Image R origine')
subplot(334)
imshow(uint8(cat(3,vide,G,vide)))
title('Image G origine')
subplot(337)
imshow(uint8(cat(3,vide,vide,B)))
title('Image B  origine')
 subplot(332)
imagesc(Y,[min(min(Y)) max(max(Y))])
colormap(gray)
axis image
title('Image Y')
subplot(335)
imagesc(Cb,[min(min(Cb)) max(max(Cb))])
colormap(gray)
axis image
title('Image Cb')
subplot(338)
imagesc(Cr,[min(min(Cr)) max(max(Cr))])
colormap(gray)
axis image
title('Image Cr')
subplot(333)
imshow(uint8(cat(3,Rp,vide,vide)))
title('Image R reconstruit')
subplot(336)
imshow(uint8(cat(3,vide,Gp,vide)))
title('Image G reconstruit')
subplot(339)
imshow(uint8(cat(3,vide,vide,Bp)))
title('Image B  reconstruit')

An example:
rgbycbcr

Complete 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);
Imax = max(max(img));

 
% conversion RGB --> YUV
Y = 0.299*R + 0.587*G + 0.114*B  ;
U = 0.492*(B-Y);
V = 0.877*(R-Y);
Rp= Y + 1.140*V;
Gp= Y - 0.395*U -0.581*V;
Bp= Y + 2.032*U ;
figure(  'Name','RGB --> YUV',...
            'NumberTitle','off',...
            'color',[0.3137 0.3137 0.5098]);
vide=zeros(ligne,colonne);
subplot(331)
imshow(uint8(cat(3,R,vide,vide)))
title('Image R origine')
subplot(334)
imshow(uint8(cat(3,vide,G,vide)))
title('Image G origine')
subplot(337)
imshow(uint8(cat(3,vide,vide,B)))
title('Image B origine')
subplot(332)
imagesc(Y,[min(min(Y)) max(max(Y))])
colormap(gray)
axis image
title('Image Y')
subplot(335)
imagesc(U,[min(min(U)) max(max(U))])
colormap(gray)
axis image
title('Image U')
subplot(338)
imagesc(V,[min(min(V)) max(max(V))])
colormap(gray)
axis image
title('Image V')
subplot(333)
imshow(uint8(cat(3,Rp,vide,vide)))
title('Image R reconstruit')
subplot(336)
imshow(uint8(cat(3,vide,Gp,vide)))
title('Image G reconstruit')
subplot(339)
imshow(uint8(cat(3,vide,vide,Bp)))
title('Image B reconstruit')
% conversion RGB --> YIQ
Y = 0.299*R + 0.587*G + 0.114*B  ;
U = 0.492*(B-Y);
V = 0.877*(R-Y);
b=0.576;
I = -sin(b)*U + cos(b)*V ;
Q = cos(b)*U + sin(b)*V ;
Rp= Y +  0.956*I +  0.621*Q;
Gp= Y -  0.272 *I - 0.647*Q;
Bp= Y -  1.106*I + 1.703*Q;

figure(  'Name','RGB --> YIQ',...
            'NumberTitle','off',...
            'color',[0.3137 0.3137 0.5098]);
vide=zeros(ligne,colonne);
subplot(331)
imshow(uint8(cat(3,R,vide,vide)))
title('Image R')
subplot(334)
imshow(uint8(cat(3,vide,G,vide)))
title('Image G')
subplot(337)
imshow(uint8(cat(3,vide,vide,B)))
title('Image G')
 subplot(332)
imagesc(Y,[min(min(Y)) max(max(Y))])
colormap(gray)
axis image
title('Image Y')
subplot(335)
imagesc(I,[min(min(I)) max(max(I))])
colormap(gray)
axis image
title('Image I')
subplot(338)
imagesc(Q,[min(min(Q)) max(max(Q))])
colormap(gray)
axis image
title('Image Q')
subplot(333)
imshow(uint8(cat(3,Rp,vide,vide)))
title('Image R reconstruit')
subplot(336)
imshow(uint8(cat(3,vide,Gp,vide)))
title('Image G reconstruit')
subplot(339)
imshow(uint8(cat(3,vide,vide,Bp)))
title('Image B  reconstruit')

% conversion RGB --> YCbCr
Wr=0.299;Wb=0.114; Wg=1-Wr-Wb;
Y = Wr*R + Wg*G + Wb*B  ;
Cb= ( 0.5 / ( 1-Wb) ) * (B-Y);
Cr= ( 0.5 / ( 1-Wr) ) * (R-Y);
Rp= Y + ((1 - Wr)/0.5)*Cr;
Gp= Y + (Wb*(1-Wb)*Cb - Wr*(1-Wr)*Cr)/(0.5*(1-Wb-Wr));
Bp= Y + ((1 - Wb)/0.5) * Cb;

figure(  'Name','RGB --> YCbCr',...
            'NumberTitle','off',...
            'color',[0.3137 0.3137 0.5098]);
vide=zeros(ligne,colonne);
subplot(331)
imshow(uint8(cat(3,R,vide,vide)))
title('Image R origine')
subplot(334)
imshow(uint8(cat(3,vide,G,vide)))
title('Image G origine')
subplot(337)
imshow(uint8(cat(3,vide,vide,B)))
title('Image B  origine')
 subplot(332)
imagesc(Y,[min(min(Y)) max(max(Y))])
colormap(gray)
axis image
title('Image Y')
subplot(335)
imagesc(Cb,[min(min(Cb)) max(max(Cb))])
colormap(gray)
axis image
title('Image Cb')
subplot(338)
imagesc(Cr,[min(min(Cr)) max(max(Cr))])
colormap(gray)
axis image
title('Image Cr')
subplot(333)
imshow(uint8(cat(3,Rp,vide,vide)))
title('Image R reconstruit')
subplot(336)
imshow(uint8(cat(3,vide,Gp,vide)))
title('Image G reconstruit')
subplot(339)
imshow(uint8(cat(3,vide,vide,Bp)))
title('Image B  reconstruit')

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