Let's take a look at one of the applications of the Laplacian operator: detecting the amount of blur in images. Often, the pictures that we take in our day-to-day lives using digital cameras, DSLRs, and so on. turn out to be not that clear, sharp, and well-focused. This can arise due to a variety of factors ranging from the motion of the subject that is being captured to the sudden movement of the capturing device just before the picture was taken. The problem that we are going to solve is that given an image, can you detect whether it is blurry or not?
The approach that we are going to take here is to use the Laplacian operator to quantify the amount of blur that is present in the image. As we'll soon see, the higher the value of our metric, the less blurry our image would be.
Now, how do we arrive at such a metric? As it turns out, it has been proven (through peer-reviewed research that we are not going to get into) that the variance of Laplacian gives a sufficiently...