Resizing after keystone correction

[i_am_jim]

Does anyone know a precise way to resize a picture after a keystoning correction?  When you do a correction like in the image below, the objects in the picture acquire an unnatural stretched height.  I have been squashing the images by guesswork but I'm looking for an accurate method of returning the picture to its correct proportions.

[i_am_jim]

I assume from the absence of replies others don't know how either.

[Semaphoric]

What I will often do in cases like this is use a Displacement Map to compress the top part of the image, and sometimes the left and right edges. You can only go so far, though, before the straight lines become curved.

The Dmap would look something like this: