How to perform an image normalization after for example adding a constant to it?
I believe that Zrep is the output range. In 8-bit it would be 255. Let's say fmin was 25, fmax was 132. You want to scale that range to 0-255. The part of the equation in brackets: [(f-fmin) / (fmax-fmin)] will give you a percentage - a value between 0 and 1. If f is 25, you'd get 0%. If f is 89, you'd get ~60%. If it's 132, you'd get 100%

So once you have the percentage, you then need to multiply that by the output range, Zrep. That converts from a percentage to whatever range you need it in, and ensures that the largest value in the input is mapped to the largest output value, and the smallest input is mapped to the smallest output value.