Refer to Fig. in answering the following questions.FIGURE A 3 ×3 region of an image (the z...

Refer to Fig. in answering the following questions.

FIGURE A 3 ×3 region of an image (the z’s are intensity values) and various masks used to compute the gradient at the point labeled z5

(a) Assume that the Sobel masks are used to obtain gx and gy. Show that in this case the magnitude of the gradient computed using Eqs 1. and 2. give identical results.

1.

2.

(b) Show that this is true also for the Prewitt masks.