Very shortly, we will be embarking on a long, but rather interesting discussion as we build our mathematical intuitions on Gaussian filtering. In order to motivate the same, we present to you some sample images that have been generated by applying the Gaussian filtering operation on Lena's image. A detailed description of each of the succeeding four output images will be presented at the end of this section. Right now, this is to motivate you and give you a glimpse of what to expect as we move ahead!
For the purpose of explaining the theoretical underpinnings and working of the Gaussian filtering method, we take a step back and consider 1D images. Just as regular 2D images are represented using a 2D grid of values, in the same manner (hypothetical) 1D images are nothing but a 1D array of pixel values.
The preceding diagram attempts to visualize the workings of a simple 1x3 box filter that replaces each pixel with the average of itself and its immediate...