Question about scale s in POS(xp, x) in preprocess.py

[BeauGeogeo]

Hi and first of all, thank you for the amazing work !

I have a little question about image preprocessing when you perform face alignment.

I have a hard time understanding what s really stands for. I assume it is related to some scaling. But I don't see how we get this from the least square equations. I know that R1 are the coefficients before x y z that will scale the coordinates and are related to the final x-coordinate we find, and R2 is the same for y-coordinate.

But how taking ( norm2(R1) + norm2(R2) ) / 2 is giving some sort of scaling s ? why does it make sense, what are intuitive and mathematical explanations behind this plz ?

Thanks a lot