Given a chessboard image x$[$n$1,$n$2].$

a$)$ Find the edges of the attached image using the Prewitt operators. Display only the convolution output images. You need to add $128$ to pixel values to observe it$.$

$$b$)$ Find the edges of the attached image using the Sobel Operators. Display only the convolution output images. You need to add $128$ to pixel values to observe it$.$

c$)$ Find the edges of the image by the high$-$pass filter

$$ h$($n$1,$n$2)=[$ h$[0,-1]=-0\mathrm{.}25$ h$[0,0]=0\mathrm{.}5,$ h$[0,1]=-0\mathrm{.}25],$

Display only the output image. Can you obtain all the edges with this filter?

d$)$ Find the edges of the image by the high$-$pass filter:$$ h$($n$1,$n$2)=[$ h$[-1,0]=-0\mathrm{.}25$ h$[0,0]=0\mathrm{.}5,$ h$[-1,0]=-0\mathrm{.}25],$

Display only the output image. Can you obtain all the edges with this filter?