Inverse uncertain homography

Question

Suppose x'= Hx, with x' and x homogeneous coordinates in an image and H a homography matrix. However, H is the result of calculations that take into account the uncertainty of x' and x, meaning H~{$\mu_H$, $\Sigma_{hh}$}, with h=vec(H). I follow the approach in the book Photogrammetric Computer Vision chapter 10, Reasoning with Uncertain Geometric Entities. My question is: if x' and H are given (both mean and covariance matrix), how do I calculate x? I know x = H$^{-1}$ x'. But how does the uncertainty of H propagate through the inverse operation on H?