rgb to ycbcr conversion in matlab

Question

I am trying to write a function in Matlab that takes an RGB image of class unit8 and double and converts it to a YCBCR image. The transformation formula is below.

I would be really thankful for any help of any kind.

Answer 1

There's an Image Processing Toolbox function for that, if you have access to it: RGB2YCBCR

If you don't have access to it, here's how you can do the conversion yourself:

rgbImage = imread('peppers.png');  %# A sample RGB image
A = [65.481 -37.797 112; ...       %# A 3-by-3 matrix of scale factors
     128.553 -74.203 -93.786; ...
     24.966 112 -18.214];

%# First convert the RGB image to double precision, scale its values to the
%#   range 0 to 1, reshape it to an N-by-3 matrix, and multiply by A:
ycbcrImage = reshape(double(rgbImage)./255,[],3)*A;

%# Shift each color plane (stored in each column of the N-by-3 matrix):
ycbcrImage(:,1) = ycbcrImage(:,1)+16;
ycbcrImage(:,2) = ycbcrImage(:,2)+128;
ycbcrImage(:,3) = ycbcrImage(:,3)+128;

%# Convert back to type uint8 and reshape to its original size:
ycbcrImage = reshape(uint8(ycbcrImage),size(rgbImage));

And here's the image you get when you display ycbcrImage:

Answer 2

"rgb2ycbcr" function (image processing toolbox):

Path :

MATLAB\R2013a\toolbox\images\colorspaces\rgb2ycbcr.m

Code :

function ycbcr = rgb2ycbcr(varargin)
rgb = parse_inputs(varargin{:});
isColormap = false;

if (ndims(rgb) == 2)
 isColormap=true;
 colors = size(rgb,1);
 rgb = reshape(rgb, [colors 1 3]);
end

origT = [65.481 128.553 24.966;-37.797 -74.203 112; 112 -93.786 -18.214];
origOffset = [16;128;128];


scaleFactor.double.T = 1/255;      
scaleFactor.double.offset = 1/255; 
scaleFactor.uint8.T = 1/255;       
scaleFactor.uint8.offset = 1;      
scaleFactor.uint16.T = 257/65535;  
scaleFactor.uint16.offset = 257;   

classIn = class(rgb);
T = scaleFactor.(classIn).T * origT;
offset = scaleFactor.(classIn).offset * origOffset;


ycbcr = zeros(size(rgb),classIn);

for p = 1:3
 ycbcr(:,:,p) = imlincomb(T(p,1),rgb(:,:,1),T(p,2),rgb(:,:,2), T(p,3),rgb(:,:,3),offset(p));
end  

if isColormap
 ycbcr = reshape(ycbcr, [colors 3 1]);
end