Those of you who may have taken up a basic calculus course in your high school will know the definition of a derivative as it applies to functions. For the sake of others, we repeat the same here, albeit very briefly. Mathematically, a derivative is represented as follows:
Note
Note that we are not trying to be mathematically fastidious, our only intention here is to give you an intuition into the concept of a derivative and how it applies to images. So, this chapter won't go into the intricacies behind the mathematics that is involved. Rather, our focus will be on how the principles of derivatives of functions are transferred to the domain of images.
What the preceding formula essentially tells you is that the derivative of a function f(x) at any point is the ratio of the change in the output to the input, as the input is varied by an infinitesimal amount in and around that point. Imagine that you have a 2D plot of the graph of the function f(x). You sample the function...