Show that the Sobel and Prewitt masks in Figs. 10.14 and 10.15 give isotropic results only...

Show that the Sobel and Prewitt masks in Figs. 10.14 and 10.15 give isotropic results only for horizontal and vertical edges and for edges oriented at ±45°, respectively.

FIGURE 10.14 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.

FIGURE 10.15 Prewitt and Sobel masks for detecting diagonal edges.