Hmm. Ok I have not ready solution, but I can try to give you idea.
You already have bunch of points, corresponds to the 2D edge, right? If so, then you should test intersection of ray, which extruded from each 2D point and the plane, which parallel with camera viewport. Your plane should positioned in the center of the needed object bounding box.
About own camera - each camera has lens and you can use this lens to extrude your ray.
myCamera.node().getLens()
Example with ray-to-plane intersection is here Super-fast mouse ray collisions with ground plane
P.S. when I said about context - I mean purposes in which you wish to get 3D points corresponds to the 2D points. For example it may be projection or selection or something else. Perhaps this purposes can be done by another way.