Algorithm to measure images colourfulness, adapted from "Measuring colourfulness in natural images" (Hasler and Susstrunk, 2003) http://infoscience.epfl.ch/record/33994/files/HaslerS03.pdf

getColourfulness.m

function C = getColourfulness( im )
%
% C = getColourfulness( im )
%   
% MATLAB algorithm implementation of the 
% "Measuring colourfulness in natural images" 
% (Hasler and Susstrunk, 2003) 
%
%   Input:
%       im  - image in RGB
%
%   Output:
%       C   - colourfulness
%

    i = 1;
    [W, H, RGB] = size(im);
    
    for x=1:W
        for y=1:H
    
            % rg = R - G
            rg(i) = abs(double(im(x,y,1)) - double(im(x,y,2)));
            
            % yb = 1/2(R + G) - B
            yb(i) = abs(.5 * (double(im(x,y,1)) + double(im(x,y,2))) - double(im(x,y,3)));
            
            i = i+1;
        end
    end
    
    % standard deviation and the mean value of the pixel
    % cloud along direction, respectively
    stdRG = std(rg);
    meanRG = mean(rg);
    
    stdYB = std(yb);
    meanYB = mean(yb);
    
    stdRGYB = sqrt((stdRG)^2 + (stdYB)^2);
    meanRGYB = sqrt((meanRG)^2 + (meanYB)^2);
    
    C = stdRGYB + 0.3*meanRGYB; 
end

The two for loops

for x=1:W
        for y=1:H

are redundant and takes much time as can be done in a single step, as shown in https://gist.github.com/MohitLamba94/7d40393f2fc1a478c84a6c5a4faaafdb. The code presented here and in the link given have exactly the same output but does not iterate over each pixel in two for loops by taking advantage of code vectorization.

Anyways thanks for the code.