Affine calibration of a plane

If the imaged line at inifinity is ${\bf l} = (l_1,l_2,l_3)^t$ , then provided $l_3 \neq 0$ a suitable projective transformation that maps ${\bf l}$ back to ${\bf l_\infty}$ is

$${\bf H} = \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ l_1&l_2&l_3 \end{array}\right] {\bf H_A}$$