If you carefully observe the example that we discussed in the previous section, you will notice that during the process of computing the output intensity at (x, y), we basically multiplied the intensity values of all the 3 x 3 neighbors by 1/9 and added them all up. Let's create a small matrix of dimensions 3 x 3 (the size of the neighborhood under consideration) and fill all the cells with the value 1/9 as shown in the following image:
We'll call this a filter or a kernel. Now, we'll make use of this filter to calculate the output intensity value corresponding to any arbitrary input pixel (x, y), say the pixel having an intensity value of 6 (see the following image). How do we go about doing that? Well, we place the filter over the image in such a manner that the central grid in the filter lies right on top of the pixel at position (x, y)-(2, 2) in our case (I have assumed 1-based indexing for both rows and columns). Once we place the filter in this manner, it will completely...