The intensity of a pixel in a digital image is measured by a number u between 0 and 1. Often, images can be enhanced by rescaling intensities, where pixels of intensity u are displayed with intensity g(u) for a suitable function g(u). An example is shown with a photograph of Amelia Earhart in Figure 1. One common choice is the sigmoidal correction, defined for constants a, b by

Figure 2 shows that g(u) reduces the intensity of low-intensity pixels (where g(u)

(a) Verify that ƒ'(u) > 0 and use this to show that g(u) increases from 0 to 1 for 0 ≤ u ≤ 1.

(b) Where does g have a point of inflection?

Transcribed Image Text:

g(u) = = f(u)-f(0) ƒ(1) - f(0) where f(u) = (1 + (a-u) - ¹