Let $$f$$ be an $$N \times M$$-image and suppose that $$g$$ is its equalization. Question - Why the equalization does not change the objects, why a car on $$f$$ does not convert into a bus on $$g$$?. It is not obious that after the pixel intensity $$r_k \mapsto s_k$$ recalculation for $$g$$ $$s_k =\frac{L-1}{NM}\sum_{j=0}^k n_k, k=0,1,\ldots,L-1,$$ we obtain the same scene as was for $$f$$! Here $$n_k$$ denotes the number of pixels that have intensity $$r_k.$$