10.14 The rectangle in the following binary image is of size mxn pixels (a) What would the magnitude of the gradient of this image look like based on using the approximation in Eq. (10-26)? Assume that &, and g, are obtained using the Sobel ker nels. Show all relevant different pixel values in the gradient image (b) With reference to Eq. (10-18) and Fig. 10.12. sketch the histogram of edge directions. Be precise in labeling the height of each compo- nent of the histogram. (c) What would the Laplacian of this image look like based on using Eq. (10-14)? Show all relevant different pixel values in the Lapla- cian image. Origin Gradivo Gradient vector de direction a b c FIGURE 10.12 Using the gradient to determine edge strength and direction at a point. Note that the edge direction is perpendicular to the direction of the gradient vector at the point where the gradient is computed. Each square represents one pixel. (Recall from Fig. 2.19 that the origin of our coordinate system is at the top, left.) 3rd equation M(x,y) - 18:1+18,1 (10-26) 2nd equation (x,y) =tan 8.(x,y)] (10-18) [8.(x,y) 1* equation v2f(x,y) = f(x+1, y) + f(x-1, y) + f(x,y+1) + f(x,y-1)-4f(x,y) (10-14)