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Augmented Reality scenario: I have a piece of paper on the table and a camera pointed at it, the piece of paper appear to be slanted with two pair of edges going towards two vanishing points.

Say I draw a dot on that paper, how would I calculate its coordinate on the paper-plane, just by knowing the on-screen coords of the four vertices of the paper, as well as the on-screen coords of the dot?

Any point in the right direction will be greatly appreciated :D I don't even know what this process is called.

Thanks! ~Xrave

Xrave
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  • You may be interested in this thread: http://math.stackexchange.com/questions/96662/augmented-reality-transformation-matrix-optimization – Oneiros Jan 05 '12 at 14:51

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What you seek to accomplish is to invert the perspective transformation that produced your image. Although I am sure this is not the ideal reference (probably textbooks on image processing and computer vision are more direct), here is one: "Inverse Perspective Transformation for Video Surveillance" by Theo E. Schoutena, and Egon L. van den Broekb, PDF here.

Joseph O'Rourke
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  • Oh, thanks! This means I can use a rectangle to first obtain the "orientation" of the camera - i believe i saw that somewhere before, and then use the algorithm in there to get the dot-position translated... – Xrave Apr 11 '11 at 02:14