Geometric transformations for augmented reality

The result 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 associated mathematical functions to make sure everything looks smooth. 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 this 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:

• Object-to-scene: This transformation refers to transforming the 3D coordinates of a virtual object and expressing them in the coordinate frame of our real-world scene. This ensures that we are placing the virtual object in the right location.
• Scene-to-camera: This transformation...