Calibration and 2D Homography

Hi there,

I am trying to implement a calbration phase to an application I have already written in C++, which uses the Wiimote and sensor bar to move a crosshair around the application window. Wherever I turn, everywhere says to use 2D Homography - a process which warps one rectangular area onto another. I would be mapping a user-defined active area of the Wiimote IR Sensor onto screen coordinates.

Potentially, as the active area is user-defined, it could be one screwed up trapezoid, making any other method of calibration that I know of close to impossible.

2D Homography involves creating a homography matrix H, which can be applied to any point (P) on the active area to transform it into the corresponding point on the screen area (P').

I have looked in several places for an explanation of how to create the homography matrix, and it is always just a bit too complicated for me to get my head around. Here I what I (think I) know:

The 4 point corrspondences which I want to use will be the 4 corners of the active area, and their respective 4 points on the screen. I know I must somehow create 2 transformations for each of these pairs (I assume one for active area -> screen, one screen-> active area) and store them in the homography matrix H, giving 8 'degrees of freedom'. This is where I am lost; how do you store an equation in a matrix? Some sites talk about the 'rank' of a matrix 'A', which seems to have come out of nowhere!

I have experience with matrices and vector transformations, but nothing really in-depth. If someone could explain it in slightly more lamen's terms, I'd greatly appreciate it! Also if you're feeling generous and could provide some psuedocode I would be overjoyed!

Thanks in advance, Simon.