How do I reverse-project 2D points into 3D?

Question

I have 4 2D points in screen-space, and I need to reverse-project them back into 3D space. I know that each of the 4 points is a corner of a 3D-rotated rigid rectangle, and

Answer 1

This is the Classic problem for marker based Augmented Reality.

You have a square marker (2D Barcode), and you want to find its Pose (translation & rotation in relation to the camera), after finding the four edges of the marker. Overview-Picture

I'm not aware of the latest contributions to the field, but at least up to a point (2009) RPP was supposed to outperform POSIT that is mentioned above (and is indeed a classic approach for this) Please see the links, they also provide source.

• http://www.emt.tugraz.at/~vmg/schweighofer

• http://www.emt.tugraz.at/publications/EMT_TR/TR-EMT-2005-01.pdf

• http://www.emt.tugraz.at/system/files/rpp_MATLAB_ref_implementation.tar.gz

(PS - I know it's a bit old topic, but anyway, the post might be helpful to somebody)