I have a camera matrix $P$ which defines a projective transformation $\mathbb{P}^3 \rightarrow \mathbb{P}^2$. In the former space there is a plane $[ x|\pi^Tx=0 ]$. The image of the plane under $P$ does not preserve angles. How can I find a transformation $H : \mathbb{P}^2 \rightarrow \mathbb{P}^2$ such that a right angle in the plane remains a right angle after applying $H \circ P$?

The application for this problem is extracting texture from a photo of a planar surface where the surface and camera locations are known.