How to compute the Cumulative Distribution Function of an image in MATLAB

Question

I need to compute the Cumulative Distribution Function of an image. I normalized the values using the following code:

im = imread('cameraman.tif');
im_hist = imhist(im);
tf = cumsum(im_hist); %transformation function
tf_norm = tf / max(tf);
plot(tf_norm), axis tight

Also, when the CDF function is plotted, does the plot have to be somewhat a straight line which ideally should be a straight line to represent equal representation for pixel intensities?

Answer 1

You can obtain a CDF very easily by:

A = imread('cameraman.tif');    
[histIM, bins] = imhist(A);
cdf = cumsum(counts) / sum(counts);
plot(cdf); % If you want to be more precise on the X axis plot it against bins

For the famous cameraman.tif it results in:

As for your second question. When the histogram is perfectly equalized (i.e. when at each intensity correspond roughly the same number of pixels) your CDF will look like a straight 45° line.

EDIT: Strictly speaking cumsum alone is not a proper CDF as a CDF describe a probability, hence it must obey probability axioms. In particular the first axiom of probability tell us that a probability value should lie in the range [0 ... 1] and cumsum alone does not guarantee that.