What are keypoints?

Now that we know that keypoints refer to the interesting regions in the image, let's dig a little deeper. What are keypoints made of? Where are these points? When we say "interesting", it means that something is happening in that region. If the region is just uniform, then it's not very interesting. For example, corners are interesting because there is sharp change in intensity in two different directions. Each corner is a unique point where two edges meet. If you look at the preceding images, you will see that the interesting regions are not completely made up of "interesting" content. If you look closely, we can still see plain regions within busy regions. For example, consider the following image:

If you look at the preceding object, the interior parts of the interesting regions are "uninteresting".

So, if we were to characterize this object, we would need to make sure that we picked the interesting points. Now, how do we define...