The assumption looks wrong to me. I think [R∣t] is 3×4, but X is only 3×1, so we can't compute [R∣t]X.
In my understanding, this is the exact reason why we use homogeneous coordinates, so we can have this efficient way of computing.
So it is extra confusing for me why you then change the formula to: ~x2=K(R~X + t), since this also does not work as R is 3x3 and ~X is 4x1, and on top of that, it is the inefficient way of computing where we apply translation separately from the multiplication. So what we actually want is ~x2 = K[R∣t]~X
Am I missing something here?
