Restoring 2d object from 3d world

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9KB, 593x397px

Im writing an app to read qr-like codes. Each code has a couple of identification points, so app can:
1. find em in the photo
2. check how their positions are different from original structure
3. calculate rotation, translation, scale
4. restore whole code by untransforming
5. read the data lying between id points


Its all simple as long, as the photo is taken perpendicularly. When the "projection" is tilted from the vertical by a few degrees the algorithm dramatically loses efficiency.


The question is:
tl;dr: what operation/matrix do I need to bring the 2d object back to 2d surface from 3d world?

pic related, sample perspective