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First of all sorry if the title is somewhat opaque, the problem I am trying to solve is already hard to explain properly in my first language.

So, let's consider we have a plane, rectangle target in a three dimensional space. From two different points of views (the images of two cameras for example), we have the coordinates of each corner of that rectangle.

Knowing these coordinates, how could we translate the coordinates of any point on one of the images to the ones it would have on the other image ?

I made a (very) simple drawing that might help understanding what I'm looking for:

In this situation the first observer is right in front of the target, the other one is slightly shifted to the right. We know all coordinates but the ones of the red dot on the second point of view, which we are looking for.

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up vote 1 down vote accepted

Your problem is a common one in all field of computer vision or mapping, and the transformation between the different point of views is known as the "Essential Matrix". You can find more about it here:

Essential Matrix on Wikipedia.

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My problem is indeed linked to a computer vision software. Thanks, I did not know about that Essential Matrix. – Jukurrpa Apr 24 '12 at 12:17
Unmarking this question as I need some precision: with this method, is it possible to find the correspondence of a point which is not on the same plan as the known points ? – Jukurrpa Apr 30 '12 at 12:21
The answer is yes. – nbubis Apr 30 '12 at 13:27
Would you happen to know any kind of tutorial explaining the way to do this? (if it is using C++ and OpenCV, that'd be even greater) – Jukurrpa Apr 30 '12 at 13:31
Sorry, just meant to unmark it to get further info, and forgot to mark it approved again. – Jukurrpa May 1 '12 at 11:39

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