“Probability transforms” of digital pictures

Let g be any local property (e.g., gray level or gradient magnitude) defined on a digital picture. Let p_g(z) be the relative frequency with which g has value z. At each point (x,y) of the picture we can display p_gg(x,y)], appropriately scaled; the result is called the p_g transform of the picture. Alternatively, we can use joint or conditional frequencies of pairs of local properties to define transforms. This note gives examples of such transforms for various gs and discusses their possible uses and limitations.