(a) Give a continuous function for implementing the contrast stretching transformation sho...

(a) Give a continuous function for implementing the contrast stretching transformation shown in Fig. 3.2(a). In addition to m, your function must include a parameter, E, for controlling the slope of the function as it transitions from low to high intensity values. Your function should be normalized so that its minimum and maximum values are 0 and 1, respectively.

FIGURE 3.2 Intensity Transformation functions. (a) Contraststretching function. (b) Thresholding function.

---

(b) Sketch a family of transformations as a function of parameter E, for a fixed value m = L/2, where L is the number of intensity levels in the image.

---

(c) What is the smallest value of E that will make your function effectively perform as the function in Fig. 3.2(b)? In other words, your function does not have to be identical to Fig. 3.2(b). It just has to yield the same result of producing a binary image. Assume that you are working with 8-bit images, and let m = 128. Let C denote the smallest positive number representable in the computer you are using.

FIGURE 3.2 Intensity Transformation functions. (a) Contraststretching function. (b) Thresholding function.