Image Histogram - What Is the Interpretation of PDF For digital images (assume 2D gray scale image), the normalised intensity histogram is often treated as the probability distribution function of the intensity ie., intensity is treated as a random variable (RV).


Where is the randomness in intensity coming from ? 
Should I treat this RV as the intensity value at any pixel in the overall image ie., can I infer this statement from the PDF - “choose any pixel. Probability that the intensity at that pixel has a value of 100 is 0.35” ? If so, it would seem that all pixels have the same PDF.  Shouldn’t the overall structure of the image structure have a bearing  on the PDF? eg., if the image is black at a pixel, shouldn't we would expect the PDF to be concentrated only around 0 at that pixel and zero everywhere else.
Well, If you model your image as a realization of a random variable generator then the Histogram is the best estimation (Assuming no other information like prior, etc..) you have for the PDF of the random variable.  

For instance, you can see this model is used when doing Histogram Equalization (Transforming the realization into a realization of Uniformity Generator).

Pay attention that this is a very simple model.
For instance it doesn't take care of the correlation between adjacent pixels in image.  

Indeed your interpretation is correct given the model.