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I know that the general form of a 2D projective transformation is following rational linear mapping: $(u, v) \mapsto (x, y)$

$$ x = \frac{\mathit{a}\mathit{u}+\mathit{b}\mathit{v}+c}{\mathit{g}\mathit{u}+\mathit{h}\mathit{v}+i}\\ y = \frac{\mathit{d}\mathit{u}+\mathit{e}\mathit{v}+f}{\mathit{g}\mathit{u}+\mathit{h}\mathit{v}+i} $$

What is its 3D version?

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The transformation from 3D to 2D is same, just with two extra terms, one in the denominator and one in the numerator. This is an 11 parameter projective mapping, since one of the 12 parameters can be set to 1.

Some more info on this "camera model" can be found here.

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