title: Mean value of normalized pixel intensity histogram
body: <p>I'm following a paper (It's accessible <a href="http://www.intelligence.tuc.gr/%7Epetrakis/publications/BaPeMi08.pdf" rel="nofollow noreferrer">here</a>) that characterizes images based on certain attributes. These attributes are all derived from histograms, one being the pixel intensity histogram. The images are greyscale.</p>
  <p>Now, it states that all histograms are normalized, I quote: &quot;All histograms are normalized (i.e. the sum of all histogram bins equals 1).&quot; There is also an example histogram which looks as follows:</p>
  <p><a href="https://i.stack.imgur.com/LmKuJ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/LmKuJ.png" alt="enter image description here" /></a></p>
  <p>From this, I can see the image contains a lot of white pixels (intensity 255 (256?))</p>
  <p>Now it goes on to compute the mean, standard deviation and more. This is where I get stuck, I quote: &quot;Mean Value: ... It is computed as <img src="https://latex.codecogs.com/gif.latex?%5Cmu%20%3D%20%5Cfrac%7B%5Csum_i%20h_i%7D%7B256%7D" alt="\frac{\sum_i h_i}{256}" /> where h_i is the value of the i-th histogram bin (<img src="https://latex.codecogs.com/gif.latex?i%20%5Cin%20%5B0..255%5D" alt="i \in [0..255]" />)&quot;</p>
  <p>Something got me confused here, because the way I see it, that value will now always be the same? Since the sum over all bins is 1 because it is normalized. What am I missing here? In their table a bit down they found a mean of in the 180s, which seems to suggest the mean is just the mean of all pixels (since it's greyscale that translates 1 to 1 to intensity, but then I'm still stuck for the other formulas.</p>