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image to groundplane transformation

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Hello! I have a problem, and I hope that somebody can point me in the right direction on how to solve it. I have 4 pairs of points Each point consists of a image coordinate(ic) (x,y) and a ground plane coordinate (gpc) (x,y). These points are coordinates in the real world plotted on an image. What i need is a transformation T, so that ic x T = gpc I dont know anything more about the scene then these four points, and i hope to get a nice little T, that can translate any image coordinate to ground plane coordinate. The ground plane is all flat, and some error is no problem. The camera have some perspective, so no orthogonal translation is possible. My first approach was to start with a guessed camera (position, direction, up, perspective, screen ratio). Then test it on all four points by creating the transformation (with world matrix, camera matrix and perspective matrix), and then hill-climbe (by adjusting camera properties) until the error was low enough. This is a pretty complex approach, so I was hoping for something simpler. Any idea?

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