Applying a blurring filter over an image is a way to reduce the noise that is produced when an image is taken by averaging out each pixel with its surrounding neighbour. This is often the first operation that is performed in an image processing task. To apply a blurring filter, you perform convolutions on every pixel over the entire image with a kernel. One example of such kernel is the Gaussian kernel. You have already seen it in the previous task. Since we are doing an average, we must take the result from the convolution and divide it by the sum of the components of our Gaussian kernel, which equals $16$ in our case. Note that $(1+2+1+2+4+2+1+2+1=16)$ It is not entirely true that we are going to perform the convolution over the entire image. Notice how our kernel is a $3$x$3$ matrix and if we apply the convolution on the edge of the image the kernel will have nothing to multiply against. Therefore, we must ignore the edge of the image and start the convolution one pixel in and stop one pixel before the end. Using the example of our $5$x$5$ image, we only perform the convolution function $9$ times. The next three diagrams show the convolution operation done on the first, the second and then the end results after it has been applied to the entire image.