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.