Try examples:  [2 0 0; 0 2 0; 0 0 2] does what? 

How to scale by 2?

[1 0 10; 0 1 0; 0 0 1]

Therefore, it is desirable if the global motion model we need to recover is translation, which has only two parameters. It turns out that for a pure panning motion, if we convert two images to their cylindrical maps with known focal length, the relationship between them can be represented by a translation.

Here is an example of how cylindrical maps are constructed with differently with f’s. Note how straight lines are curved.

Similarly, we can map an image to its longitude/latitude spherical coordinates as well if f is given.

A:  render as black