Image derivatives in two dimensions

Now that we are comfortable with the theory behind image derivatives in one dimension, we will see how the concept can be scaled to two dimensions. After all, when we start our OpenCV implementation from the next section onward, we will deal with images: two-dimensional data.

From what we have gathered in this chapter until now, derivatives essentially measure how our function changes. When we are dealing with one-dimensional data, there is only one possible direction along which this change can take place. When we talk about two-dimensional functions, we have two variables that we can vary independently, typically x and y. So, changing one of them (while keeping the other constant) allows us to measure the change in our function value (the thing we call derivative) along two directions as opposed to one. Therefore, it is prudent to assume that for two-dimensional functions (such as images), two different derivatives are computed. One derivative measures...