Convolutional Neural Networks $($CNN$)$ for image understanding applications. The image has an input layer with $5$X$5$ resolution, and the network includes a convolution layer $($C$1),$ a MAX$-$Pooling layer $($P$1),$ and a fully$-$connected layer.

Given the input binary image $,$ solve the following $3$ problems:

a$)$ Using a $2$X$2$ filter as a convolution kernel, $,$ determine the number of neurons needed in the convolutional layer.

b$)$ Compute the output feature maps of the convolutional layer with the given $2$X$2$ filter in Part $(1).$ All intermediate computation steps must be shown, explicitly.

c$)$ Use a $2$X$2$ max$-$pooling layer with a stride distance of $2$ to avoid overlapping. Compute the output feature map of the max$-$pooling layer.