Hi Cole,
the function FindGeometricTransform
seems to be perfect for this task; with ImagePerspectiveTransformation
the resulting transformation can then be applied:
imgskd = Import["skewed.png"];
imgcor = Import["corrected.png"];
gtf = Last@FindGeometricTransform[imgcor, imgskd];
ImagePerspectiveTransformation[imgskd, gtf, DataRange -> Full]
The outcome looks like this:
This is just a quick "proof of concept"; for better results you should crop you images properly.
Regards -- Henrik