Problem $1.$ First$-$order Edge Detection

Consider the zebra.png image. Convert it to Grayscale using library function. Detect

edges in an image using the following filters:

$3\backslash$times $3$ horizontal and vertical Prewitt kernel $($P$\_($x$)$&P$\_($y$)).$

$3\backslash$times $3$ horizontal and vertical Sobel masks $($S$\_($x$)$&S$\_($y$)).$

$3\backslash$times $3$ Kirsch kernels of $8$ equal orientations in $[0,2\backslash$pi $)$K$\_(0)$ is givenP$\_($x$)=[[-1,0,1,0,1,0,1]]$

$-1$

$-1$

$-1,$P$\_($y$)=[[1,1,1,0,0,-1,-1]]$

$-1$

$0$

S$\_($x$)=[[-1,0,1,0,2,0,1]]$

$-1$

$-2,$S$\_($y$)=[[1,2,1,0,0,-2,-1]]$

$-1$

$0$

K$\_(0)=[[5,5,5,-3,-3,-3,-3]]$

$-3$

$-3$

Display the vertical and horizontal gradients, the gradient magnitude and orientation

maps of the output of Sobel and Prewitt kernels; and each of the directional derivative

using the Kirsch kernels.