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Transformations
Transformations in the images are represented by homographies of
. A homography of
is represented by a matrix . Again and
represent the same homography for all nonzero scalars .
A point is transformed as follows:

(B5) 
The corresponding transformation of a line can be obtained by transforming the points which are on the line and then finding the line defined by these points:

(B6) 
From the previous equation the transformation equation for a line is easily obtained (with
):

(B7) 
Similar reasoning in gives the following equations for transformations of points and planes in 3D space:
where is a matrix.
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Marc Pollefeys
20021122