RGB2Lab.m

function [L,a,b] = RGB2Lab(color_image)
% function [L, a, b] = RGB2Lab(R, G, B)
% RGB2Lab takes matrices corresponding to Red, Green, and Blue, and 
% transforms them into CIELab.  This transform is based on ITU-R 
% Recommendation  BT.709 using the D65 white point reference.
% The error in transforming RGB -> Lab -> RGB is approximately
% 10^-5.  RGB values can be either between 0 and 1 or between 0 and 255.  
% By Mark Ruzon from C code by Yossi Rubner, 23 September 1997.
% Updated for MATLAB 5 28 January 1998.

% commented out grayscale case
% if (nargin == 1)
%   B = double(R(:,:,3));
%   G = double(R(:,:,2));
%   R = double(R(:,:,1));
% end

% commented out error checking, jhhays
% if ((max(max(R)) > 1.0) | (max(max(G)) > 1.0) | (max(max(B)) > 1.0))
%   R = R/255;
%   G = G/255;
%   B = B/255;
% end

M = size(color_image,1);
N = size(color_image,2);
s = M*N;

% Set a threshold
T = 0.008856;

RGB = [reshape(color_image(:,:,1),1,s); ...
       reshape(color_image(:,:,2),1,s); ...
       reshape(color_image(:,:,3),1,s)];

% RGB to XYZ
MAT = [0.412453 0.357580 0.180423;
       0.212671 0.715160 0.072169;
       0.019334 0.119193 0.950227];
XYZ = MAT * RGB;

X = XYZ(1,:) / 0.950456;
Y = XYZ(2,:);
Z = XYZ(3,:) / 1.088754;

XT = X > T;
YT = Y > T;
ZT = Z > T;

fX = XT .* X.^(1/3) + (~XT) .* (7.787 .* X + 16/116);

% Compute L
Y3 = Y.^(1/3); 
fY = YT .* Y3 + (~YT) .* (7.787 .* Y + 16/116);
L  = YT .* (116 * Y3 - 16.0) + (~YT) .* (903.3 * Y);

fZ = ZT .* Z.^(1/3) + (~ZT) .* (7.787 .* Z + 16/116);

% Compute a and b
a = 500 * (fX - fY);
b = 200 * (fY - fZ);

L = reshape(L, M, N);
a = reshape(a, M, N);
b = reshape(b, M, N);

if ((nargout == 1) | (nargout == 0))
  L = cat(3,L,a,b);
end