The outcome of augmented reality is amazing, but there are a lot of mathematical things going on underneath. Augmented reality utilizes a lot of geometric transformations and the associated mathematical functions to make sure everything looks seamless. When talking about a live video for augmented reality, we need to precisely register the virtual objects on top of the real world. To understand it better, let's think of it as an alignment of two cameras—the real one through which we see the world, and the virtual one that projects the computer generated graphical objects.
In order to build an augmented reality system, the following geometric transformations need to be established: