## I I I I I I I I I I I I I

Old Pixel Value p

Figure 13.6 The transfer curve is the graph of a transfer function. It depicts the mathematical relationship between original pixel values, p, and new pixel values, f(p). Original pixel values lie between the pixel value in the image that displays as black and the value that displays as white.

This time, when you put p into function/, you get out p squared. Put in 1, you get out 1; but put in 2 and you get out 4. If p is 25, f(p) is 625. And so on. The term p2 tells you how the function/(p) behaves.

When mathematicians work with functions, they prefer continuous differen-tiable functions—those that have one output value for each input value and that don't make any sudden jumps. In image processing, however, the transfer function can be anything you can compute. Consider this example:

Here, the function is divided into ranges of good behavior. This notation says: "if p is less than 100, the value of the function is 0; if p is 100, then f(p) equals 1; Hp is greater than 100, the function equals 2."

In computer languages, such functions are easy to compute. Here is the same function coded as a computer algorithm:

FUNCTION F(pv) SELECT CASE pv

Linear

Sawtooth

Inverse Linear

Linear Old Pixel Value p Gamma 